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Runstream - Shell Buckling

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1. The cylstif STG file can be used as is or edited and then used as input in future executions of STAGSUNIT PART 3 8 STAGSUNIT produces two files cylstif bin and cylstif inp that are valid input files for the STAGS general purpose finite element computer program The PANDA2 processor STAGSUNIT has produced two files cylstif bin cylstif inp The STAGS file cylstif bin is small as follows STAGS input file cylstif bin cylstif STAGS INPUT FOR STIFFENED CYL STAGSUNIT SHELL UNITS 1 INDIC 1 is bifur buckling INDIC 3 is nonlinear BEGIN B 1 1 IPOST 1 means save displacements every IPOSTth step 0 ILIST 0 means normal batch oriented output 0 ICOR 0 means projection in 1 means not in 1 IMPTHE index for imperfection theory 0 ICHIST index for crack archive option 0 IFLU 0 means no fluid interaction 1 ISOLVR 0 means original solver 1 new solver END B 1 rec 1 000E 00 STLD 1 starting load factor System A BEGIN C 1 rec 0 000E 00 STEP 1 load factor increment System A 1 000E 00 FACM 1 maximum load factor System A 0 000E 00 STLD 2 starting load factor System B 0 000E 00 STEP 2 load factor increment System B 0 000E 00 FACM 2 maximum load factor System B 0 ITEMP 0 means no thermal loads END C 1 rec 10000 NSEC number of CPU seconds before run termination 0 DELEV is eigenvalue error tolerance 0 00001 0 IP
2. for layer no 1 y Is this a new layer type 0 1000000 thickness for layer index no 2 0 winding angle deg for layer index no 2 1 material index 1 2 for layer index no 2 n Any more layers or groups of layers in Segment no 3 n 1 n 3 Y 0 1000000 0 1 n 0 t 50 00000 0 10 00000 10 00000 n n 1 n 4 Y 0 1000000 0 1 n n 1 n 5 Y 0 1000000 0 1 n 1 Y 100 0000 n Y 0 1000000E 08 0 3000000 3846154 0 0 n Y 60000 00 n 0 1000000 TD TD TT TTT TET DATA TAD TDA DNATA DNATA DN NAN NADNNNnNDNnNNnNnUnNnNnNnNnNnN Is the next group of layers to be a default group 12 layers number of layers in the next group in Segment no 4 Can winding layup angles ever be decision variables layer index 1 2 for layer no 1 Is this a new layer type thickness for layer index no 3 winding angle deg for layer index no 3 material index 1 2 for layer index no 3 Any more layers or groups of layers in Segment no 4 choose external 0 or internal 1 stringers Identify type of stiffener along L2 N T J Z R A stiffener spacing b width of ring base b2 zero is allowed height of stiffener type H for sketch h width of outstanding flange of stiffener w Are the rings cocured with the skin Is the next group of layers to be a default group 12 layers number of layers in the next group in Segment no 3 Can winding layup angles ever b
3. The inter ring buckling mode is found after many successive executions of STAGS in which the eigenvalue shift is changed from execution to execution cylstif out2 from STAGS run 1 eigenvalue shift 1 0 CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 8 CRITICAL LOAD FACTOR COMBINATION NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF 1 1 127122E 00 1 127122E 00 0 000000E 00 21197 lt critical buckling stringers 2 1 140843E 00 1 140843E 00 0 000000E 00 18553 3 1 151226E 00 1 151226E 00 0 000000E 00 20429 4 1 155305E 00 1 155305E 00 0 000000E 00 17785 5 1 156392E 00 1 156392E 00 0 000000E 00 21197 6 1 161864E 00 1 161864E 00 0 000000E 00 13265 7 1 161865E 00 1 161865E 00 0 000000E 00 29129 8 1 211805E 00 1 211805E 00 0 000000E 00 20381 cylstif out2 from STAGS run 2 eigenvalue shift 1 25 CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES CRITICAL LOAD FACTOR COMBINATION 10 roots skipped 1 THROUGH 8 NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF ROOT 1 1 211805E 00 1 211805E 00 0 000000E 00 20381 8 2 1 236041E 00 1 236041E 00 0 000000E 00 23025 9 3 1 249418E 00 1 249418E 00 0 000000E 00 20381 10 4 1 253260E 00 1 253260E 00 0 000000E 00 17737 11 5 1 254130E 00 1 254130E 00 0 000000E 00 20381 12 6 8 cylstif out2 from STAGS run 3 eigenvalue shift CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES NO OAIAHDUNBWNE cylstif out2 from STAGS run 4 eigenvalue shift 1 1 1 PRPRPRPRPRPRPPR 25870
4. BPW BWNHOKBWE BWNO NO FPrROOOORFFOOCOCO CURRENT VALUE 1 011E 01 3 370E 00 7 817E 00 2 534E 00 7 690E 01 2 038E 01 8 450E 02 3 185E 01 0 000E 00 9 783E 00 4 304E 00 5 673E 01 9 452E 01 CHOOSE ONE OF THE FOLLOWING DEFINITION B STR stiffener spacing b STR seg NA B2 STR width of stringer base b2 must H STR height of stiffener type H for s W STR width of outstanding flange of st T 1 SKN thickness for layer index no 1 T 2 STR thickness for layer index no 2 T 3 STR thickness for layer index no 3 B RNG stiffener spacing b RNG seg NA B2 RNG width of ring base b2 zero is a H RNG height of stiffener type H for s W RNG width of outstanding flange of st T 4 RNG thickness for layer index no 4 T 5 RNG thickness for layer index no 5 2 3 6 Want to change any other parameters in this set y y PARAMETERS WHICH CAN BE CHANGED VAR STR SEG LAYER NO RNG 1 2 STR 3 STR 4 STR NO 0 2 3 4 NO 0 0 0 0 CURRENT VALUE 1 011E 01 3 370E 00 7 817E 00 2 534E 00 CHOOSE ONE OF THE FOLLOWING DEFINITION B STR stiffener spacing b STR seg NA B2 STR width of stringer base b2 must H STR height of stiffener type H for s W STR width of outstanding flange of st 5 SKN 1 1 7 690E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 2 038E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 8 450E 02 T 3 STR thickness for layer inde
5. MAINSETUP and PANDAOPT again in order to verify that the archive file cylstif CHG is correct 1 17 Execute the PANDA2 processors called MAINSETUP and PANDAOPT again this time for the perfect shell Inspect the output from PANDAOPT the cylstif OPM file 1 19 Selected output from the cylstif OPM file obtained when the output index NPRINT 2 in the cylstif OPT file kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk PART 2 0 Processing with PANEL PANEL2 and BIGBOSOR4 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk PART 2 1 Execute the PANDA2 processor called PANEL in PART PART PART PART PART order to produce a valid input file cylstif ALL for BIGBOSOR4 for a prismatic model for local buckling Execute BIGBOSOR4 using the file cylstif ALL as input in this particular run a prismatic model for local buckling Inspect the cylstif OUT file Compare predictions from BIGBOSOR4 with those from PANDA2 that are listed in PART 1 19 CHAPTER 14 LOCAL buckling Execute the BIGBOSOR4 processor called bosorplot in order to get a plot of the critical LOCAL buckling mode Execute the PANDA2 processor called PANEL and the BIGBOSOR4 processors bigbosorall and bosorplot in order to obtain a plot of the critical GENERAL PART 2 7 buckling mode and load factor eigenvalue Execute the PANDA2 processor called PANEL2 and the BIGBOSOR4 processors bigbosorall and bosorplot in order to obtain p
6. lines skipped to save space Margin 1 1164E 01 Inter ring bucklng discrete model n 32 circ halfwaves FS 1 1 lines skipped to save space Margin 5 8244E 01 Lo n Ring sidesway discrete model n 4 circ halfwaves FS 1 1 lines skipped to save space CHAPTER 23 Compute stresses in layers and at various locations in modules for both positive and negative imperfection amplitudes from SUBROUTINE STRCON local postbuckling neglected See 1L panda2 news Items 36b d w 41b and Section E of Table 122 6 in Item 122 lines skipped to save space Margin 2 7265E 01 eff stress matl 1 SKN Iseg 2 at n 6 layer 1 z 0 3845 MID FS 1 lines skipped to save space CHAPTER 24 Present short summary of redistribution of stress resultants Nx Ny Nxy caused by prebuckling bending of an initially imperfect shell See Section 6 0 in 1K for example Additional resultants Nx Ny in panel skin from global and inter ring bending of imperfect panel Additional axial resultant dNx 2 8206E 05 Additional hoop resultant dNy 0 0000E 00 Additional in plane shear resultant dNxy 0 0000E 00 Additional axial resultants dNx along webs and flanges of stringers from global and inter ring bending of imperfect panel Additional Nx in base of stringer dNx 2 8206E 05 Additional Nx at webtip of stringer dNx 6 6356E 05 Additional Nx in flange of stringer dNx 2 7511E 05 Additional axial resultants dNx along webs and flanges of rings from globa
7. old working directory cylstif ALL bush gt bigbosor4log BIGBOSOR4 COMMANDS HAVE BEEN ACTIVATED The BIGBOSOR4 commands in the general order in which you would probably use them are help4 get information on BOSOR4 input you provide segment by seg input assemble concatenates segment data files bigbosorall batch run of pre main post proc bosorplot batch run for generating plot files resetup input for restart run same model bigrestart batch run of main amp postprocessors cleanup delete all except for DOC file getsegs generate segment files from DOC modify modify a segment file Please consult the following sources for more information about BOSOR4 1 help4 file type help4 2 bosor4 story good idea to print this file 3 bosor4 news news of BOSOR4 updates 4 Documents listed under HELP4 OVERVIEW DOC bush gt bigbosorall Enter case name cylstif B background F foreground or Q NOS network queue system f Running BIGBOSOR4 bigbosorall case cylstif Executing bigbosorall Normal termination bigbosorall Job finished Inspect the output file cylstif OUT Menu bosorplot resetup cleanup getsegs modify input help4 PART 2 3 Inspect the cylstif OUT file Inspect the cylstif OUT file Search for the string EIGENVALUE including the trailing parenthesis You will find the following list output there from the cylstif OUT file BUCKLIN
8. ITEMP 0 means no thermal loads END C 1 rec 10000 NSEC number of CPU seconds before run termination 0 DELEV is eigenvalue error tolerance 0 00001 0 IPRINT 0 means print modes iteration data END D 2 rec 8 NEIGS number of eigenvalues sought BEGIN D 3 rec 2 0 SHIFT initial eigenvalue shift 0 000E 00 EIGA lower bound of eigenvalue range 0 000E 00 EIGB upper bound of eigenvalue range END D 3 rec end of the cylstif bin file The cylstif bin file is as listed above because we need to search over several buckling modes in order to determine the lowest eigenvalue that corresponds primarily to buckling of the skin with smeared stringers between adjacent rings STAGS produces the following lines in the cylstif out2 file fragment of the cylstif out2 file CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 8 CRITICAL LOAD FACTOR COMBINATION NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF 1 1 891302E 00 1 891302E 00 0 000000E 00 38679 2 1 894643E 00 1 894643E 00 0 000000E 00 43179 3 1 908025E 00 1 908025E 00 0 000000E 00 43029 4 1 910256E 00 1 910256E 00 0 000000E 00 38781 5 2 035811E 00 2 035811E 00 0 000000E 00 16365 lt lowest inter ring 6 2 079418E 00 2 079418E 00 0 000000E 00 16965 buckling mode 7 2 140823E 00 2 140823E 00 0 000000E 00 33339 8 2 141343E 00 2 141343E 00 0 000000E 00 47883 end of fragment of the cylstif out2
9. MID FS 1 MID FS 1 MID FS M 369 MID FS 1 2 MID FS 1 1 4 buckling ring Iseg 4 as beam on foundation M 67 MID FS 1 2 buck SAND simp support general buck M 1 N 3 slope 0 FS 1 1 buck SAND rolling with smear string M 1 N 20 slope 0 FS 1 1 buck SAND rolling with smear rings M buck SAND rolling only of stringers M buck SAND hiwave roll of stringers M buck SAND rolling only of rings M buck SAND rolling only axisym rings M buck SAND STRINGERS web buckling M buck SAND RINGS web buckling M Max allowable ave axial strain ave ax lines skipped to save space MARGINS FOR MAR MARGIN NO VALUE 1 3 18E 03 2 1 03E 01 3 2 66E 01 4 1 97E 02 5 1 09E 01 6 3 02E 01 7 1 21E 02 8 5 86E 01 9 1 82E 02 10 1 23E 01 11 6 96E 00 12 1 31E 00 13 7 03E 00 14 1 71E 01 15 1 61E 01 16 8 73E 01 17 1 69E 01 18 3 89E 01 19 1 05E 00 20 6 93E 02 kkkkkkkkkkx k 9 8 5 0 0 4 2 i M Ore we we Sse W 2 2 Z Br ZIZI z IrPosp lol Hse CH Reise we we CURRENT DESIGN LOAD CASE NO 1 SUBCASE NO DEFINITION Local buckling from discrete model 1 M Bending torsion buckling M 1 FS 1 1 1 slope 0 FS 1 slope 0 FS 1 4 slope 0 FS 1 lope 0 FS 1 4 lope 0 FS 1 4 slope 0 01 FS 1 ot nns strain 1 FS 1 2 slope 0 04 FS 1 2 1 axial halfwaves FS 1 1 eff stress matl 1 STR Dseg 5 node 11 layer 1 z 0 3845 RNGS m 1 lateral torsional buckli
10. Please use ICONSV 1 as the preferred choice ICONSV 1 recommended model means a Include ARBOCZ theory when computing knockdown factors for local inter ring general buckling b Use more conservative knockdown factors for models in which the stringers are smeared c Use computed knockdown factor for smearing rings d The Donnell shell theory is used in SUBROUTINE STRIMP where imperfection sensitivity is being computed e Will use the non zero slope of buckling nodal lines in the computation of prebuckling bending and twisting Wxx Wyy Wxy of shells with general inter ring and local buckling modal imperfections panda2 news Items 620 and 645 are cancelled ICONSV 0 less conservative model means a Do NOT include ARBOCZ theory when computing knockdown factors for local inter ring general buckling b Use less conservative knockdown factors for models in which the stringers are smeared c Use computed knockdown factor for smearing rings Same as for ICONSV 1 d The user selected shell theory is used in SUBROUTINE STRIMP where imperfection sensitivity is being computed e panda2 news Items 620 and 645 are cancelled Same as for e under ICONSV 1 ICONSV 1 still less conservative model means a Do NOT include ARBOCZ theory when computing knockdown factors for local inter ring general buckling Same as for ICONSV 0 Use less conservative knockdown factors for models in
11. STR thickness for layer index no 2 T 3 STR thickness for layer index no 3 B RNG stiffener spacing b RNG seg NA B2 RNG width of ring base b2 zero is a H RNG height of stiffener type H for s W RNG width of outstanding flange of st T 4 RNG thickness for layer index no 4 T 5 RNG thickness for layer index no 5 2 3 3 Want to change any other parameters in this set y Y PARAMETERS WHICH CAN BE CHANGED VAR STR SEG LAYER NO RNG STR STR STR SKN STR DUP WNE NO WrRBRWNO NO rFPrROOOO CURRENT VALUE 1 011E 01 3 370E 00 7 817E 00 2 534E 00 7 690E 01 2 038E 01 CHOOSE ONE OF THE FOLLOWING DEFINITION B STR stiffener spacing b STR seg NA B2 STR width of stringer base b2 must H STR height of stiffener type H for s W STR width of outstanding flange of st T 1 SKN thickness for layer index no 1 T 2 STR thickness for layer index no 2 7 STR 8 9 RNG 10 RNG 11 RNG 12 RNG 13 RNG Number of parameter to change 1 4 New value of the parameter 2 5340 2 534000 BPWHRWNHOB rFPrROOOCOOF 8 450E 02 3 185E 01 0 000E 00 9 783E 00 4 304E 00 5 673E 01 9 452E 01 T 3 STR thickness for layer index no 3 B RNG stiffener spacing b RNG seg NA B2 RNG width of ring base b2 zero is a H RNG height of stiffener type H for s W RNG width of outstanding flange of st T 4 RNG thickness for layer index no 4 T 5 RNG thickness for lay
12. gt EA ie 5 i 2 2 O 4 250 300 350 400 450 500 Design Iterations 0 50 100 150 l cylstif superoptl objective png PANDA2 results from the first execution of SUPEROPT O WEIGHT OF THE ENTIRE PANEL x104 cylstif SEE FILES cylstif OPM AND cylstif OPP Spectr cht E Pico ae ileal miele eyed 3 5 4 0 45 Objective 3 0 25 2 0 fit i n tet Ih Seat et w 3 lL We cA 33 s A balssnsoanes Biko i Usil Li iial i i 250 Design Iterations 2 cylstif superopt2 objective png PANDA2 results from the 2nd execution of SUPEROPT Umetormed Deformed x10 cylstif R Z_EIGENMODE_1 N_1 1 0 0 5 0 0 0 5 Axial Station 1 5 2 0 180 440 Radius 3 cylstif localbuck panel png Local buckling mode from a BIGBOSOR4 prismatic shell model generated automatically by the PANDA2 processor called PANEL Umeformed Deformed x10 cylstif R Z_EIGENMODE_1 N_1 1 0 0 5 0 0 0 5 Axial Station 1 5 2 0 w al 180 440 Radius 4 cylstif genrlbuck panel png General buckling mode from a BIGBOSOR4 prismatic shell model generated automatically by the PANDA2 processor called PANEL Rings are smeared Umetormed Deformed cylstif R Z_ELGENMODE_1 N_4 400 350 Axial Station 150 200 250 100 50 0 50 100 150 200 Radius 5 cylstif ringsidesway panel2 png Ring sidesway buckling from a BIGBOSOR4 shell of revo
13. 0 0 000000N000000 41 1 4159E 04 FEASIBLE 0 3 0 0 0 0 0 0 0 0 000000N000000 42 1 3544E 04 FEASIBLE O 1 0 0 0 0 0 0 0 0 000000N000000 ala eae cela la el a lll leno tanto PANDAOPT many lines skipped to save space VALUES OF DESIGN VARIABLES CORRESPONDING TO BEST FEASIBLE DESIGN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 1 037E 01 B STR stiffener spacing b STR seg NA layer NA 2 STR 2 0 3 455E 00 B2 STR width of stringer base b2 must be gt 0 see Help STR seg 2 lay 3 STR 3 0 8 014E 00 H STR height of stiffener type H for sketch h STR seg 3 Layer NA 4 STR 4 0 1 829E 00 W STR width of outstanding flange of stiffener w STR seg 4 Layer NA 5 SKN 1 1 7 971E 01 T 1 SKN thickness for layer index no 1 SKN seg 1 layer 1 6 STR 3 1 2 546E 01 T 2 STR thickness for layer index no 2 STR seg 3 layer 1 7 STR 4 1 1 254E 01 T 3 STR thickness for layer index no 3 STR seg 4 layer 1 8 0 0 3 705E 01 B RNG stiffener spacing b RNG seg NA layer NA 9 RNG 2 0 0 000E 00 B2 RNG width of ring base b2 zero is allowed RNG seg 2 layer NA 10 RNG 3 0 1 109E 01 H RNG height of stiffener type H for sketch h RNG seg 3 Layer NA 11 RNG 4 0 4 287E 00 W RNG width of outstanding flange of stiffener w RNG seg 4 Layer NA 12 RNG 3 1 6 531E 01 T 4 RNG thickness for layer index no 4 RNG seg 3 layer 1 13 RNG 4 1 7 269E 01 T 5 RNG thickness for layer in
14. 0 3 0 0 0 0 0 0 0 0 000000N000000 24 1 2241E 04 MOSTLY UNFEASIB 0 9 0 0 0 0 0 0 0 0 000000N000000 eae ae a al a ea el all heaton lone PANDAOPT 25 1 2241E 04 MOSTLY UNFEASIB 0 9 0 0 0 0 0 0 0 0 000000N000000 26 1 2679E 04 FEASIBLE 0 0 0 O 0 0 0 0 0 0 000000N000000 27 1 2324E 04 FEASIBLE 0 6 0 0 0 0 0 0 0 0 000000N000000 28 1 2102E 04 NOT FEASIBLE 0 11 0 0 0 0 0 0 0 0 000000N000000 29 1 2321E 04 FEASIBLE 0 3 0 0 0 0 0 0 0 0 000000N000000 30 1 2145E 04 NOT FEASIBLE 0 10 0 0 0 0 0 0 0 0 000000N000000 rr rae AUTOCHANGE ae aaa a el a a ee el le hl helenae onto PANDAOPT 31 3 1201E 04 FEASIBLE 0 0 0 O 0 0 0 0 0 0 000000N000000 32 2 4518E 04 FEASIBLE 0 0 0 O 0 0 0 0 0 0 000000N000000 33 2 0371E 04 UNKNOWN FEASIB 0 0 0 0 0 0 0 0 0 0 000000N000000 34 1 7979E 04 UNKNOWN FEASIB 0 1 0 0 0 0 0 0 0 0 000000N000000 35 1 6643E 04 UNKNOWN FEASIB 0 2 0 0 0 0 0 0 0 0 000000N000000 36 1 5894E 04 ALMOST FEASIBLE 0 3 0 0 07 0 0 0 0 0 000000N000000 ae a etalon ala a el ella lente on tanita PANDAOPT 37 1 5894E 04 ALMOST FEASIBLE 0 3 0 0 07 0 0 0 0 0 0o00000N000000 38 1 4687E 04 MILDLY UNFEASIB 0 4 0 0 0 0 0 0 0 0 000000N000000 39 1 4141E 04 FEASIBLE 0 0 0 O 0 0 0 0 0 0 000000N000000 40 1 2907E 04 NOT FEASIBLE 0 9 0 0 0 0 0 0
15. 1 0 1000000 winding angle deg for layer index no 1 0 0 material index 1 2 for layer index no 1 h What is required here is an integer This integer is a pointer to a material the properties of which will be asked of you later The integer must be greater than or equal to 1 material index 1 2 for layer index no 1 1 I Module with T shaped stiffener Seg No 4 Segment No 3 gt Seg No 2 h Seg No l Seg No 5 z V same as Seg 1 lt b2 gt lt Module width stiffener spacing b gt Any more layers or groups of layers in Segment no 1 n n Module with T shaped stiffener Seg No 4 Segment No 3 gt Seg No 2 h Seg No l Seg No 5 3 V same as Seg 1 kas o gt lt Module width stiffener spacing b gt Next provide the properties of Segment 2 which is the base under the stiffener This base includes the skin under the stiffener plus the stiffener flange that fays with the skin except in the case of a hat with b2 w2 for which the base is simply the laminate under the hat xx x k IMPORTANT NOTE At least one of the layers in Segment 2 should ordinarily be the same as one of the layers in Segment 1 If Segment 2 represents a thickened region under the stiffener model it as being composed of the layers in Segment 1 plus additional layer s NOTE There is an exception
16. 1 Minimum load factor for local buckling Type H for HELP FSLOC 1 Minimum load factor for stiffener buckling Type H FSBSTR 1 Factor of safety for stress FSSTR 1 Do you want flat skin discretized module for local buckling Do you want to skip the KOITER local postbuckling analysis Do you want wide column buckling to constrain the design Resultant e g lb in normal to the plane of screen Nx0 1 Resultant e g lb in in the plane of the screen Ny0 1 Axial load applied along the 0 neutral plane l panel skin Uniform applied pressure positive upward See H elp p 1 Is the pressure part of Load Set A Is the pressure hydrostatic Type H for HELP Choose in plane immovable IFREE 0 or movable IFREE 1 b c 1 Are you feeling well today type H Is there a maximum allowable deflection due to pressure Out of roundness Wimpgl Max diameter Min diam 4 Wimpg1 1 Initial buckling modal general imperfection amplitude Wimpg2 1 Initial buckling modal inter ring imperfection amplitude Wpan 1 Initial local imperfection amplitude must be positive Wloc 1 Do you want PANDA2 to change imperfection amplitudes see H elp 1 Axial halfwavelength of typical general buckling mode AXLWAV 1 Do you want PANDA2 to find the general imperfection shape 1 Maximum allowable average axial strain type H for HELP 1 Is there any thermal loading in this load set Y N Do you want a complete analysis type H
17. 1 Number of eigenvalues for each circ wavenumber NVEC end of the cylstif PAN file for PANEL2 The valid input file for BIGBOSOR4 cylstif ALL now exists rw r r 1 bush bush 167939 Feb 22 11 45 cylstif ALL This is a long file and is not listed here to save space Next we must run BIGBOSOR4 We copy the file cylstif ALL to another working directory and execute BIGBOSOR4 there cd to new working directory cp old working directory cylstif ALL bush gt bigbosor4log bush gt bigbosorall Enter case name cylstif B background F foreground or Q NOS network queue system f Running BIGBOSOR4 bigbosorall case cylstif Executing bigbosorall Normal termination bigbosorall Job finished Inspect the output file cylstif OUT Menu bosorplot resetup cleanup getsegs modify input help4 Inspect the cylstif OUT file Search for the string EIGENVALUE including the trailing parenthesis You will find the following list output there begin part of the cylstif OUT file JUST LEFT SUBROUTINE OUT2 xx CRITICAL EIGENVALUE AND WAVENUMBER EIGCRT 1 6141E 00 NO OF CIRC WAVES NWVCRT 4 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk xxx k EIGENVALUES AND MODE SHAPES EIGENVALUE CIRC WAVES 1 6929E 00 2 1 6141E 00 4 lt ring sidesway critical mode 1 8127E 00 6 Compare with PANDA2 CHAPTERS 22 amp 26 2 2312E 00 8 of P
18. 1 bush bush 30 Feb 21 17 45 cylstif NAM rw r r 1 bush bush 2678 Feb 21 17 56 cylstif OPA rw r r 1 bush bush 12112 Feb 21 17 45 cylstif OPB rw r r 1 bush bush 7934 Feb 21 17 46 cylstif OPD rw r r 1 bush bush 12599 Feb 21 18 29 cylstif OPL rw r r 1 bush bush 2989030 Feb 21 17 57 cylstif OPM rw r r 1 bush bush 497082 Feb 21 17 57 cylstif OPP rw r r 1 bush bush 4547 Feb 21 12 44 cylstif OPT rw r r 1 bush bush 56760 Feb 21 17 57 cylstif P11 rw r r 1 bush bush 51084 Feb 21 17 57 cylstif P21 rw r r 1 bush bush 25752 Feb 21 17 57 cylstif PL1 rw r r 1 bush bush 0 Feb 21 18 26 cylstif PL10 rw r r 1 bush bush 34056 Feb 21 17 57 cylstif PL2 rw r r 1 bush bush 0 Feb 21 18 26 cylstif PL3 rw r r 1 bush bush 0 Feb 21 18 26 cylstif PL4 rw r r 1 bush bush 12074 Feb 21 18 29 cylstif PL5 rw r r 1 bush bush 0 Feb 21 18 26 cylstif PL6 rw r r 1 bush bush 0 Feb 21 18 26 cylstif PL7 rw r r 1 bush bush 0 Feb 21 18 26 cylstif PL8 rw r r 1 bush bush 0 Feb 21 18 26 cylstif PL9 rw r r 1 bush bush 34056 Feb 21 17 57 cylstif PLD rw r r 1 bush bush 854528 Feb 21 17 57 cylstif RN1 rw r r 1 bush bush 626688 Feb 21 17 56 cylstif RN2 rw r r 1 bush bush 574464 Feb 21 17 56 cylstif RN3 rw r r 1 bush bush 33792 Feb 21 17 46 cylstif RN4 rw r r 1 bush bush 79633 Feb 21 17 57 cylstif TIT In this particular case there is only a single Postscript file generated by DIPLOT rw r r 1 bus
19. 4 pp 469 605 1987 You should get an optimum design by several executions of PANDAOPT with 5 iterations in each execution Better yet use SUPEROPT With many executions of PANDAOPT and few design iterations with each execution you obtain the most efficient convergence to an optimum design When you execute SUPEROPT you get more Starting designs per SUPEROPT run when you use a small number like 5 for the number of iterations therefore a more complete exploration of design space in the search for the best global optimum design The developer of PANDA2 almost always uses 5 iterations How many design iterations permitted in this run 5 to 25 h Choose a number between 5 and 25 usually 5 to 8 If the design margins seem to jump around quite a bit or if the weight cycles from iteration set to iteration set use a high number of iterations 20 or 25 How many design iterations permitted in this run 5 to 25 5 5 MAXMAR Plot only those margins less than MAXMAR Type H h Choose a number between 1 and 10 1 to 5 is best Every time you give the command PANDAOPT the results from the design iterations associated with the resulting batch run are stored in a binary file called NAME PL1 in which NAME is your chosen name for the case These results are re organized in a processor called STORE and added to similarly re organized results from previous PANDAOPT runs for the same case If MAXMAR is too large you may be swamped with da
20. Buckling load factor before t s d 2 1342E 00 After t s d 2 0666E 00 lines skipped to save space BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DISCRETIZED MODEL skin stringer discretized module of local buckling AXIAL BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KNOCKDOWN ANISOTROPY M EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 1 1 21563E 00 9 83375E 01 1 00000E 00 1 19542E 00 lines skipped to save space kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxkkk LOCAL MODE HAS STRINGER SIDESWAY kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk END OF LOCAL BUCKLING EIGENVECTOR CALC IPANDA 0 Margin 8 6749E 02 Local buckling from discrete model 1 M 1 axial halfwaves FS 1 1 Margin 8 6749E 02 Bending torsion buckling M 1 FS 1 1 lines skipped to save space CHAPTER 15 Compute bending torsion low m buckling from BOSOR4 type discretized skin stringer single module model See Section 12 2 lower table on p 511 in 1A for example lines skipped to save space CHAPTER 16 Compute post local buckling from the Koiter theory given in Ref 1C See Figs 23 24 and Figs 47 49 in 1A Fig 6 in 1C and Fig 4 in Bushnell D Optimization of an axially compressed ring and stringer stiffened cylindrical shell with a general buckling modal imperfection AIAA Paper 2007 2216 48th AIAA SDM Meeting Honolulu
21. Do you want to double check PANDA type eigenvalues type H elp h This double check can take lots of computer time Generally answer N if the panel is flat Generally answer N if you plan to do optimization ITYPE 1 or test simulation ITYPE 3 Generally answer N if you are including transverse shear deformation effects LOTS of computer time is required Generally answer Y if you are analyzing a fixed design of a curved panel in which in plane shear loading is present and you are neglecting transverse shear deformation effects Answer N if you are not near an optimum design If you are near an optimum or if you are suspicious of the load factors from the PANDA type closed form analysis answer Y If you answer Y and if there is in plane shear loading or anisotropic terms in the C i j matrix constitutive law then PANDA2 will check the minimum buckling load factors obtained by an initial partial search in slope space slope of the nodal lines in the buckling mode shape by calculating eigenvalues over a range of nodal line slopes from zero to 10 0 for every wavenumber combination m n This extra search takes more computer time of course so it shouldn t be done unless you feel you are near an optimum design or you doubt the PANDA type eigenvalues There is a partial double check even if you answer N Do you want to double check PANDA type eigenvalues type H elp lt enter gt N Next you will be asked to make a choice bet
22. If ITYPE 1 print the file called cylstif OPP If ITYPE 3 or 4 print the file called cylstif OPI Run PANDAOPT several times for optimization PART 1 18 Inspect the output from PANDAOPT the cylstif OPM file Only the new margins in the new cylstif OPM file are listed here abridged cylstif OPM file for perfect shell MARGINS FOR CURRENT DESIGN LOAD CASE NO 1 SUBCASE NO 1 between rings MAR MARGIN NO VALUE DEFINITION 1 8 67E 02 Local buckling from discrete model 1 M 1 axial halfwaves FS 1 1 2 8 67E 02 Bending torsion buckling M 1 FS 1 1 3 2 73E 01 eff stress matl 1 SKN Dseg 2 node 6 layer 1 z 0 3845 MID FS 1 4 1 05E 01 m 1 lateral torsional buckling load factor FS 1 FS 1 1 5 1 12E 01 Inter ring bucklng discrete model n 32 circ halfwaves FS 1 1 6 5 82E 01 Lo n Ring sidesway discrete model n 4 circ halfwaves FS 1 1 7 2 73E 01 eff stress matl 1 SKN Iseg 2 at n 6 layer 1 z 0 3845 MID FS 1 8 6 93E 01 buckling margin stringer Iseg 3 Local halfwaves 4 MID FS 1 9 2 50E 01 buckling margin stringer Iseg 4 Local halfwaves 4 MID FS 1 10 2 02E 01 buckling stringer Isegs 3 4 together M 4 C 0 MID FS 1 4 11 8 77E 00 buckling stringer Iseg 4 as beam on foundation M 369 MID FS 1 2 12 1 44E 00 buckling margin ring Iseg 3 Local halfwaves 32 MID FS 1 13 1 06E 01 buckling ring Iseg 4 as beam on foundation M 67 MID FS 1 2 14 8 79E 01 buck SAND simp support general buck M 1 N 3
23. NPRINT output index l min O0 good 1 ok 2 more 3 too much h Usually use 0 NPRINT 0 is recommended for optimization analyses since these analyses produce another useful file NAME OPP which contains the entire design history and is much easier to read than the NAME OPM file The new plotting capability CHOOSEPLOT DIPLOT also makes it less necessary to generate lots of printed output NPRINT 3 really gets alot of output NPRINT 2 yields the C i j the force distributions in the various parts of the panel module local buckling modal displacements and resdistributed loads due to bowing and local postbuckling behavior Do not use 2 if you are doing an optimization analysis When you use 0 please make sure to consult the NAME OPP file optimization ITYPE 1 or the NAME OPI file test simulation ITYPE 3 for more information NPRINT 1 leads to minimal output margins and design only The developer of PANDA2 generally uses NPRINT 0 for optimization runs ITYPE 1 and NPRINT 2 for the analysis of a fixed design ITYPE 2 NPRINT 2 generates a large OPM file but you can find what you want by searching for the strings CHAPTER or MARGINS or WEIGHT On rare occasions you may want to use NPRINT 2 with ITYPE 1 When you do this PANDA2 prints out details pertaining to each CHAPTER both for the current design and for the perturbed designs then prints out the matrix of contraint gradients then is that
24. STLD 1 0 000000 Load factor increment for Load System A STEP 1 1 000000 Maximum load factor for Load System A FACM 1 0 Starting load factor for Load System B STLD 2 0 Load factor increment for Load System B STEP 2 0 Maximum load factor for Load System B FACM 2 1 How many eigenvalues do you want NEIGS 480 Choose element type 480 or 410 or 940 n Have you obtained buckling modes from STAGS for this case Number of stringers in STAGS model of 360 deg cylinder Number of rings in the STAGS model of the panel Are there rings at the ends of the panel Number of finite elements between adjacent stringers Number of finite elements between adjacent rings Stringer model 1 or 2 or 3 or 4 or 5 Type H elp Ring model 1 or 2 or 3 or 4 or 5 Type H elp Reference surface of cyl l outer O middle 1l inner Do you want to use fasteners they are like rigid links Are the stringers to be smeared out Are the rings to be smeared out Number of nodes over height of stiffener webs NODWEB f fon OWWWO W eN 55 Number of nodes over width of stringer flange NDFLGS Number of nodes over width of ring flange NDFLGR Do you want stringer s with a high nodal point density Do you want ring s with a high nodal point density Is there plasticity in this STAGS model Do you want to use the least squares model for torque Is stiffener sidesway permitte
25. SUBCASE NO gt 121212 121212 See Items 525 and 596 in panda2 news MM MMMM PANDAOPT 1 1 5889E 04 NOT FEASIBLE 0 7 0 0 0 0 0 0 0 0 000000N000000 2 1 6113E 04 NOT FEASIBLE 0 7 0 0 0 0 0 0 0 0 O0DO0000N000000 3 1 5595E 04 UNKNOWN FEASIB 0 6 0 0 0 0 0 0 0 0 O0DO0000N000000 4 1 5209E 04 UNKNOWN FEASIB 0 6 0 0 0 0 0 0 0 0 O0DO0000N000000 5 1 4999E 04 UNKNOWN FEASIB 0 7 0 0 0 0 0 0 0 0 O0DO0000N000000 6 1 4895E 04 ALMOST FEASIBLE 0 6 0 0 0 0 0 0 0 0 OO00000N000000 IOBJAL ITRPLT 0 6 OBJMNO OBJPLT ITRPLT 1 4895E 04 1 4895E 04 kkkxkxkkkkkkkkk NOTE KRERKRKKKKKKKKK NOTH FRRKKKKKKKKKKKK NOTH FERKKKKKKKKEK The SUPEROPT run failed after 6 iterations because the spacing between the stringers became too large for a model in which IQUICK 0 Here is part of the cylstif ERR file part of the cylstif ERR file IQUICK quick analysis indicator 0 or 1 0 xxxk k k MODEL CHANGE REQUIRED Discretized model of single panel module cannot be treated because the stringer spacing spans too large a circumferential angle of the cylindrical panel or shell 4 1494E 01 1 0000E 02 STRINGER SPACING CYLINDER RADIUS Please do one or more of the following 1 set IQUICK 1 no discrete model of module is used or 2 make stringer spacing less than cylinder radius 3 or 3 increase the cylinder radiu
26. Width b2 must be greater than zero In fact it should always be greater than a tenth of the module width b This segment of the module is considered by PANDA2 to consist of the skin plus the faying flange if any of the stiffener In the PANDA2 model b2 must be greater than about a tenth of the total module width b because the section of width b2 is considered to be a separate segment which is discretized If you make b2 too small numerical difficulties might occur If the panel skin in the width b2 has the SAME CONSTRUCTION as that outside this region set b2 to a value about b 3 IN THIS CASE IN DECIDE MAKE SURE TO LINK THE WIDTH OF b2 TO THE SPACING b b2 C b IN WHICH C IS THE LINKING CONSTANT SET C APPROXIMATELY 0 3 width of stringer base b2 must be gt 0 see Help 10 10 00000 height of stiffener type H for sketch h h The height of the stiffener is measured from the surface of the stiffener base to the middle surface of the stiffener flange as shown in the sketch below lt middle surface of stiffener flange gt flange material stiffener web gt stiffener height h stiffener base V height of stiffener type H for sketch h 10 10 00000 width of outstanding flange of stiffener w h There is no more help Do your best width of outstanding flange of stiffener w 10 10 00000 Are the stringers cocured with the skin h Stringers and skin may be cure
27. allow winding angles to be decision variables you must also allow the thickness of at least one layer also to be a decision variable Also any decision variable that is zero or that becomes zero during design iterations is dropped by PANDA2 from the list of decision variables It ceases being a decision variable from that moment on Hence if you specify that the winding angle of a layer is a decision variable and if you also specify that the winding angle of this layer is zero this layer winding angle will not be a decision variable during optimization cycles If you really want the layer winding angle to be a decision variable set it initially to 5 or 10 degrees or use CHANGE to change it from zero to 5 or 10 degrees Can winding layup angles ever be decision variables n n layer index 1 2 for layer no 1 h A layer index implies the following bundle of properties 1 thickness of the layer 2 winding layup angle of the layer degrees between the normal to the screen and the direction in which the modulus El fiber direction is measured 3 material type of the layer The three properties just listed are identical in two different layers if both of these layers have the same layer index layer index 1 2 for layer no 1 1 Is this a new layer type h There is no more help Do your best Is this a new layer type y Y thickness winding angle material for layer index thickness for layer index no 1
28. end of fragment from cylstif out2 Inner fiber effective stresses from the 5 x 3 bay STAGS model We obtain a fringe plot of the distribution of the inner fiber effective stress via the STAGS post processor STAPL The input for STAPL is as follows cylstif pin input for STAPL for the inner fiber effective stress distribution over the entire model nonlinear effective stress inner fiber same view a linear buckling mode 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 2 0 7 1 0000 1 1 PL 3 KPLOT VIEW ITEM STEP MODE IFRNG COLOR ICOMP 0 0 3 0 0 0 0 0 0 PL 5 DSCALE NROTS LWSCALE RNGMIN RGMAX 1 0 35840000E 02 SPL 6 IROT ROT 2 0 13140000E 02 SPL 6 IROT ROT 3 0 35630001E 02 SPL 6 IROT ROT end of cylstif pin file The fringe plot is contained in the following file 16 cylstif stagsunit innerfibstress 5x3 png We want to see the inner fiber effective stress in the skin only The appropriate input for the STAGS post processor STAPL is as follows cylstif pin input for STAPL for the inner fiber effective stress distribution over the panel skin only nonlinear effective stress inner fiber same view a linear buckling mode 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 2 1 7 1 0000 1 1 PL 3 KPLOT VIEW ITEM STEP MODE IFRNG COLOR ICOMP 1 0 0 3 0 0 0 0 0 0 PL 5 DSCALE NROTS LWSCALE RNGMIN RGMAX 1 0 35840
29. lines skipped to save space CHAPTER 4 Compute axisymmetric prebuckling hungry horse state of the curved panel or cylindrical shell See Ref 1E especially Fig 1 and pp 495 498 lines skipped to save space CHAPTER 5 Get static response of panel to normal pressure 1A especially Section 9 and Section 20 5 and Figs 55 60 in 1A lines skipped to save space CHAPTER 6 Do PANDA type 1B general and inter ring buckling analyses to permit later computation of amplification of panel bowing lines skipped to save space CHAPTER 7 Compute distribution of loads in panel module skin stringer segments neglecting redistribution due to initial buckling modal imperfections See Section 10 of 1A lines skipped to save space CHAPTER 8 Do PANDA type local inter ring general buckling analyses and PANDA type stringer web and ring web buckling analyses to get knockdown factors to compensate for lack of in plane shear Nxy loading and anisotropy in discretized BOSOR4 type models See Section 11 of 1A and Item No 81 in 1L lines skipped to save space CHAPTER 9 Do BOSOR4 type Skin ring buckling analyses to compute knockdown factor to compensate for inherent unconservativeness of models with smeared rings See Items 509 511 522 and 605 in 1L skin skin smeared stringers lines skipped to save space Knockdown for smeared rings on cylindrical shell Buckling load factor for n dn FNARCQ 3 0000
30. must be gt 0 see 1 DEFINITION B2 STR width 3 Y N N 0 0 00E 00 5 00E 01 7 8167E 00 2 00E 01 H STR height of stiffener type H for sketch h 4 Y N N 0 0 00E 00 5 00E 01 2 5340E 00 1 00E 01 W STR width of outstanding flange of stiffener w 5 Y Y N 0 0 00E 00 5 00E 02 7 6896E 01 1 00E 00 T 1 SKN thickness for layer index no 1 SKN seg 1 6 Y Y N 0 0 00E 00 1 00E 02 2 0380E 01 1 00E 00 T 2 STR thickness for layer index no 2 STR seg 3 7 Y y N 0 0 00E 00 1 00E 02 8 4496E 02 1 00E 00 T 3 STR thickness for layer index no 3 STR seg 4 8 Y N N 0 0 00E 00 1 00E 01 3 1850E 01 1 00E 02 B RNG stiffener spacing b RNG seg NA layer NA 9 N N N 0 0 00E 00 0 00E 00 0 0000E 00 0 00E 00 B2 RNG width of ring base b2 zero is allowed RN 10 Y N N 0 0 00E 00 5 00E 01 9 7830E 00 2 00E 01 H RNG height of stiffener type H for sketch h 11 Y N N 0 0 00E 00 5 00E 01 4 3037E 00 1 00E 01 W RNG width of outstanding flange of stiffener w 12 Y Y N 0 0 00E 00 1 00E 02 5 6729E 01 1 00E 00 T 4 RNG thickness for layer index no 4 RNG seg 3 13 Y Y N 0 0 00E 00 1 00E 02 9 4524E 01 1 00E 00 T 5 RNG thickness for layer index no 5 RNG seg 4 CURRENT VALUE OF THE OBJECTIVE FUNCTION VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 0 0 1 178E 04 WEIGHT OF THE ENTIRE PANEL TOTAL WEIGHT OF SKIN 7 2473E 03 TOTAL WEIGHT OF SUBSTIFFENERS 0 0000E 00 TOTAL WEIGHT OF STRINGERS 1 6846E 03 TOTAL
31. smeared out NOTE gt y Are the rings to be smeared out 5 Number of nodes over height of stiffener webs NODWEB 5 Number of nodes over width of stringer flange NDFLGS 5 Number of nodes over width of ring flange NDFLGR n Do you want stringer s with a high nodal point density n Do you want ring s with a high nodal point density n Is there plasticity in this STAGS model y Do you want to use the least squares model for torque n Is stiffener sidesway permitted at the panel edges 0 Edges parallel to screen 0 in plane deformable 1 rigid 0 Stringer web axial displacement index IBCXOXL 0 or 1 CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 1 CRITICAL LOAD FACTOR COMBINATION NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF 1 2 507291E 00 2 507291E 00 0 000000E 00 16797 The buckling mode corresponding to the eigenvalue 2 507291 is obtained by running the STAGS postprocessor STAPL with the following input cylstif pin file input for STAPL linear buckling of perfect shell from STAGS 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 1 0 4 0 1 PL 3 KPLOT NUNIT ITEM STEP MODE 0 0 3 PL 5 DSCALE NROTS 1 0 35840000E 02 SPL 6 IROT ROT 2 0 13140000E 02 SPL 6 IROT ROT 3 0 35630001E 02 SPL 6 IROT ROT end of cylstif pin file The critical buckling mode is shown in the plot 13 cylstif stagsunit genbuck eigl png We wish to see an end view of the sa
32. 0 0 0 0 0 0 0 000000N000000 6 1 2243E 04 MOSTLY UNFEASIB 0 9 0 0 0 0 0 0 0 0 000000N000000 oSee ter sest eee tase eS ele eee eee se sees lessee PANDAOPT 7 1 2243E 04 MOSTLY UNFEASIB 0 9 0 0 0 0 0 0 0 0 000000N000000 8 1 2679E 04 FEASIBLE 0 0 0 0 0 0 0 0 0 0 000000N000000 9 1 2325E 04 MOSTLY UNFEASIB 0 9 0 0 0 0 0 0 0 0 000000N000000 10 1 2605E 04 FEASIBLE O 2 0 0 0 0 0 0 0 0 000000N000000 11 1 2379E 04 FEASIBLE 0 3 0 0 0 0 0 0 0 0 000000N000000 12 1 2203E 04 NOT FEASIBLE 0 9 0 0 0 0 0 0 0 0 000000N000000 aetna al a ll la lll haat ton tanto PANDAOPT 13 1 2203E 04 NOT FEASIBLE 0 9 0 0 0 O 0 0 0 0 000000N000000 14 1 2638E 04 FEASIBLE 0 0 0 O 0 0 0 0 0 0 000000N000000 15 1 2285E 04 MOSTLY UNFEASIB 0 9 0 0 0 0 0 0 0 0 000000N000000 16 1 2564E 04 FEASIBLE 0 3 0 0 0 0 0 0 0 0 000000N000000 17 1 2338E 04 MOSTLY UNFEASIB 0 9 0 0 0 0 0 0 0 0 000000N000000 18 1 2517E 04 FEASIBLE 0 3 0 0 0 0 0 0 0 0 000000N000000 aaa a ea a lc a a a lll lela note PANDAOPT 19 1 2517E 04 FEASIBLE 0 3 0 0 0 0 0 0 0 0 000000N000000 20 1 2132E 04 NOT FEASIBLE 0 11 0 0 0 O 0 0 0 0 000000N000000 21 1 2477E 04 FEASIBLE 0 3 0 0 0 0 0 0 0 0 000000N000000 22 1 2198E 04 NOT FEASIBLE 0 9 0 0 0 0 0 0 0 0 000000N000000 23 1 2419E 04 FEASIBLE
33. 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 7 7 Lower bound of variable no 7 01 0 1000000E 01 Upper bound of variable no 7 1 1 000000 Any more decision variables Y or N y y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4
34. 06 0 1000000E 08 Poisson s ratio NU 1 3 0 3000000 transverse shear modulus G13 1 3 846154E 06 3846154 Thermal expansion coeff ALPHA 1 0 0 residual stress temperature positive TEMPTUR 1 0 0 Want to supply a stress strain curve for this mat l H n n Want to specify maximum effective stress h For isotropic material the answer is usually Y For orthotropic material the answer must be N In the ortho tropic case you must specify maximum tensile and compressive and shear stresses in the principle material directions along the fibers and normal to them Want to specify maximum effective stress y Y Maximum allowable effective stress in material type 1 60000 60000 00 2 allowables have now been identified 50 allowables are permitted 48 additional allowables are permitted Sometimes optimum designs are obtained for composite laminates with models in which the ENTIRE LAMINATE is treated as one layer rather than on a ply by ply basis Input data for stress allowables are generally obtained from membrane and bending tests on the ENTIRE LAMINATE Laminate tests usually reveal that the maximum bending stress before failure of the laminate is significantly larger than the maximum membrane stress In order to exploit this bending overshoot during optimization it is necessary to include stress constraints of the form max stress constraint 1 S membrane S a S bending f S a in which S means st
35. 1 THROUGH CRITICAL LOAD FACTOR COMBINATION LOAD SYSTEM A LOAD SYSTEM B 1 549722E 00 550753E 00 557151E 00 557151E 00 566488E 00 613298E 00 PRPRPRPRPPR 544794E 00 0 000000E 00 0 000000E 00 ae AK c I am BE ao B an 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 cylstif out2 from STAGS run 8 eigenvalue shift 1 MAXIMUM NUMBER OF ITERATIONS CONVERGENCE CRITERION HAS NOT BEEN SATISFIED FOR EIGENVALUES CRITICAL LOAD FACTOR COMBINATION LOAD SYSTEM A LOAD SYSTEM B NO ONHDUBWNHE PRPRPRPRPRPRPH EIGENVALUE 544794E 00 549722E 00 550752E 00 557150E 00 557151E 00 566488E 00 613298E 00 617841E 00 1 549722E 00 550752E 00 557150E 00 557151E 00 566488E 00 613298E 00 617841E 00 PRPRPRP PPR 544794E 00 0 000000E 00 0 000000E 00 OOGO 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 cylstif out2 from STAGS run 9 eigenvalue shift 1 MAXIMUM NUMBER OF ITERATIONS CONVERGENCE CRITERION HAS NOT BEEN SATISFIED FOR EIGENVALUES CRITICAL LOAD FACTOR COMBINATION LOAD SYSTEM A LOAD SYSTEM B NO OINAHADUNBWNE PRPRPRPRPRPRPPR EIGENVALUE 549721E 00 550734E 00 557141E 00 557148E 00 566487E 00 613298E 00 685983E 00 717634E 00 PRPRPRPRPRPRPPR 549721E 00 550734E 00 557141E 00 557148E 00 566487E 00 613298E 00 685983E 00 717634E 00 0 000000E 00 0 000000E 00 oo0oo0oo0oo0oo 000000
36. 1A These loads are for computing a preliminary value of wide column buckling needed for smeared stringer knockdown lines skipped to save space CHAPTER NEW2 List prebuckling stress resultants Nx Ny needed for the discretized single module skin stringer model used for a preliminary value of wide column buckling BOSOR4 type model see Figs 18 20 22 97 and 98 of 1A for examples of the discretized single skin stringer BOSOR4 type module model This distribution of Nx is used in the wide column model used to obtain the smeared stringer knockdown factor WIDKNK Ny and Nxy and the fixed non eigenvalue loads Nxo Nyo Nxyo are set to zero for this computation of wide column buckling lines skipped to save space CHAPTER NEW3 Do wide column inter ring buckling analysis See Figs 20c 22c 46d and 67 of 1A for examples The purpose of this computation is to obtain a smeared stringer knockdown factor lines skipped to save space Mode number 2 IS a wide column mode and is therefore acceptable x END OF PRELIMINARY WIDE COLUMN BUCKLING CALCULATIONS SMEARED STRINGER KNOCKDOWN FROM SKIN STRINGER DISCRETE MODEL See panda2 doc panda2 news Items 724 and 725 Buckling axial resultant Nx from simple Euler model EULER Buckling axial resultant Nx from discretized model EIGWID Knockdown factor for cross section rigidity amp t s d WIDKNK Effective axial length of the wide column model AXLEFF
37. 2 038E 01 8 450E 02 3 185E 01 0 000E 00 9 783E 00 4 304E 00 5 673E 01 9 452E 01 CHOOSE ONE OF THE FOLLOWING DEFINITION B STR stiffener spacing b STR seg NA B2 STR width of stringer base b2 must H STR height of stiffener type H for s W STR width of outstanding flange of st T 1 SKN thickness for layer index no 1 T 2 STR thickness for layer index no 2 T 3 STR thickness for layer index no 3 B RNG stiffener spacing b RNG seg NA B2 RNG width of ring base b2 zero is a H RNG height of stiffener type H for s W RNG width of outstanding flange of st T 4 RNG thickness for layer index no 4 T 5 RNG thickness for layer index no 5 2 3 2 Want to change any other parameters in this set y Y PARAMETERS WHICH CAN BE CHANGED VAR STR SEG LAYER NO RNG 1 2 STR 3 STR 4 STR 5 SKN 6 STR 7 STR 8 9 RNG 10 RNG 11 RNG 12 RNG 13 RNG Number of parameter to change 1 3 New value of the parameter 7 8167 7 816700 NO PBPWKRWNHOKWE BWNO NO rFPROOOORFrFOOCOOCO CURRENT VALUE 1 011E 01 3 370E 00 7 817E 00 2 534E 00 7 690E 01 2 038E 01 8 450E 02 3 185E 01 0 000E 00 9 783E 00 4 304E 00 5 673E 01 9 452E 01 CHOOSE ONE OF THE FOLLOWING DEFINITION B STR stiffener spacing b STR seg NA B2 STR width of stringer base b2 must H STR height of stiffener type H for s W STR width of outstanding flange of st T 1 SKN thickness for layer index no 1 T 2
38. 2 rec 1 NUNITE number of fastener strips 1 finite element units 0 NSTFS number of shell units with discrete stiffeners 21 NINTS means number of connections between shell units 273 NPATS number of records for partial nodal compatibility 248 NCONST number of Lagrange constraint conditions 0 NIMPFS number of bucklng modal imperfections 0 INERT 0 means no inertial load records 0 NINSR 0 means no crack tip element sets END B 2 rec C C Begin B 3 input data 8 NTAM number of entries in material tabl BEGIN B 3 rec 6 NTAB number of beam cross section entries 7 NTAW number of entries in shell wall table 0 NTAP 0 means user parameters not included 2 NTAMT 2 means two fastener element tables 1 NGCP 1 means the GCP system will be used END B 3 rec C C Begin B 4 B 5 input data if any C C Begin F 1 input data discretization 55 125 F 1 NROWS 1 NCOLS 1 unit 1 cyl shell 55 5 f 1 strng web NROWS 2 NCOLS 2 Unit 2 stringer no 1 55 5 f 1 outflange NROWS 3 NCOLS 3 Unit 3 stringer no 1 55 5 f 1 strng web NROWS 4 NCOLS 4 Unit 4 stringer no 2 55 5 f 1 outflange NROWS 5 NCOLS 5 Unit 5 stringer no 2 55 5 f 1 strng web NROWS 6 NCOLS 6 Unit 6 stringer no 3 many many lines skipped to save space C Output control 0000000000000 r 1 output end unit144 C C Begin unit145 ring no 10 ring segment 2 C Begin outstanding flange o
39. 3 How many eigenvalues get at least 3 do you want The valid input file for BIGBOSOR4 cylstif ALL now exists rw r r 1 bush bush 167939 Feb 22 11 45 cylstif ALL This is a long file and is not listed here to save space Next we must run BIGBOSOR4 We copy the file cylstif ALL to another working directory and execute BIGBOSOR4 there cd to new working directory cp old working directory cylstif ALL bush gt bigbosor4log bush gt bigbosorall Enter case name cylstif B background F foreground or Q NQS network queue system f Running BIGBOSOR4 bigbosorall case cylstif Executing bigbosorall Normal termination bigbosorall Job finished Inspect the output file cylstif OUT Menu bosorplot resetup cleanup getsegs modify input help4 Inspect the cylstif OUT file Search for the string EIGENVALUE including the trailing parenthesis You will find the following list output there from the cylstif OUT file BUCKLING LOADS FOLLOW AXIAL HALF WAVE NUMBER N 1 EIGENVALUES 2 88019E 00 3 62711E 00 4 75444E 00 xx CRITICAL EIGENVALUE AND WAVENUMBER EIGCRT 2 8802E 00 NO OF AXIAL HALF WAVES NWVCRT 1 ee ee ee ee ee xx x k EIGENVALUES AND MODE SHAPES EIGENVALUE AXIAL HALF WAVES Compare with the prediction from CHAPTER 26 of PART 1 19 general buckling smeared stiffeners Cl1 1 0238E 07 radius R 1 0000E 02 lines skipped to save spac
40. 300 300 0000 Do you want PANDA2 to find the general imperfection shape 1 h Almost always answer Y yes PANDA2 will then find the m n Slope for the general buckling mode in which m number of axial halfwaves n number of circumferential halfwaves slope of the buckling nodal lines The imperfection shape is assumed to be the same as the general buckling mode shape If you for some reason should answer N no then you must next supply values of m n called MUSER and NUSER In the section of PANDA2 that computes general buckling imperfection sensitivity PANDA2 will not search over m n space to find the critical general buckling modal imperfection shape but instead will use only the values MUSER NUSER that you will next supply PANDA2 will continue to search over s space s slope of buckling nodal lines for a minimum general buckling load factor with respect to s for given and fixed m n MUSER NUSER Do you want PANDA2 to find the general imperfection shape 1 y Y IF THE LOCAL IMPERFECTION IS LESS THAN OR EQUAL TO ZERO IT WILL BE SET EQUAL TO 1 10 TH OF THE THICKNESS OF THE SKIN MIDWAY BETWEEN STRINGERS THIS IS DONE TO MAKE THE VARIATION OF STIFFNESS IN THE NEIGHBORHOOD OF THE LOCAL BUCKLING LOAD SMOOTHER WHICH RESULTS IN BETTER BEHAVIOR DURING OPTIMIZATION CYCLES Maximum allowable average axial strain type H for HELP 1 h This input permits you to account for strain stress concentrations
41. 4315E 00 Knockdown factor general buckling EIGR EIGRNG 7 4384E 01 Knockdown for smeared rings RNGKNK 9 0000E 01 FNARCQ 3 0000E 00 lines skipped to save space CHAPTER 22 Compute skin ring buckling load factors for 1 medium n inter ring buckling mode See rightmost three mode shapes in top row of Fig 30 of Ref 1G 2 high n inter ring buckling mode See rightmost mode shape in middle row of Fig 30 Ref 1G 3 low n inter ring buckling mode See leftmost mode shape in top row of Fig 30 Ref 1G lines skipped to save space BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DISCRETIZED MODEL skin smeared stringer ring discretized module HOOP BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KNOCKDOWN ANISOTROPY n EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 32 2 44726E 00 1 00000E 00 1 00000E 00 2 44726E 00 35 2 48779E 00 1 00000E 00 1 00000E 00 2 48779E 00 29 2 47892E 00 1 00000E 00 1 00000E 00 2 47892E 00 Buckling load factor before t s d 2 4473E 00 After t s d 2 2273E 00 lines skipped to save space knockdown for smeared stringers from SUB EIGMOD SMRFAC 5 4900E 01 knockdown for transverse shear deformation t s d from SUB SHRRED SHRFAC 9 1013E 01 Buckling load factor BEFORE knockdown for smeared stringers 2 2273E 00 Buckling load factor AFTER knockdown for smeared stringers 1 2228E 00
42. Any more decision variables Y or N 11 Choose a decision variable 1 2 3 0 5000000 Lower bound of variable no 11 10 00000 Upper bound of variable no 11 y Any more decision variables Y or N 12 Choose a decision variable 1 2 3 0 1000000E 01 Lower bound of variable no 12 1 000000 Upper bound of variable no 12 Any more decision variables Y or N 13 Choose a decision variable 1 2 3 0 1000000E 01 Lower bound of variable no 13 1 000000 Upper bound of variable no 13 n Any more decision variables Y or N y Any linked variables Y or N 2 Choose a linked variable 1 2 3 1 To which variable is this variable linked 0 3333000 Assign a value to the linking coefficient C j n Any other decision variables in the linking expression n Any constant CO in the linking expression Y or N n Any more linked variables Y or N n Any inequality relations among variables type H y Any escape variables Y or N y Want to have escape variables chosen by default end of the cylstif DEC file In future runs of DECIDE you can use the file cylstif DEC as input or for very similar cases you can edit the cylstif DEC file and then use the edited cylstif DEC file as input for DECIDE PART 1 5 Execute the PANDA2 processor called MAINSETUP in order to establish loading and solution strategies bush gt mainsetup Please ente
43. Do you want a tutorial session and tutorial output n Want to use default for thickness decision variables type H elp 1 Choose a decision variable 1 2 3 10 Lower bound of variable no 1 50 Upper bound of variable no 1 y Any more decision variables Y or N 3 Choose a decision variable 1 2 3 0 5000000 Lower bound of variable no 3 20 00000 Upper bound of variable no 3 y Any more decision variables Y or N 4 Choose a decision variable 1 2 3 0 5000000 Lower bound of variable no 4 10 00000 Upper bound of variable no 4 y Any more decision variables Y or N 5 Choose a decision variable 1 2 3 0 5000000E 01 Lower bound of variable no 5 1 000000 Upper bound of variable no 5 y Any more decision variables Y or N 6 Choose a decision variable 1 2 3 0 1000000E 01 Lower bound of variable no 6 1 000000 Upper bound of variable no 6 y Any more decision variables Y or N 7 Choose a decision variable 1 2 3 0 1000000E 01 Lower bound of variable no 7 1 000000 Upper bound of variable no 7 y Any more decision variables Y or N 8 Choose a decision variable 1 2 3 10 00000 Lower bound of variable no 8 100 0000 Upper bound of variable no 8 y Any more decision variables Y or N 10 Choose a decision variable 1 2 3 0 5000000 Lower bound of variable no 10 20 00000 Upper bound of variable no 10
44. ISTART n is the load step number for which you want to generate data via the STAGS postprocessor POSTP n 0 means you will get the linear response Restart from ISTARTth load step 0 1st nonlinear soln ISTART 0 0 Local buckling load factor from PANDA2 EIGLOC h Use EIGLOC 0 unless INDIC 1 bifurcation buckling You can find EIGLOC in the NAME OPM file Look for the margin or margins corresponding to local buckling The load factor for local buckling is given by EIGLOC FSLOC MARGIN 1 in which FSLOC is the factor of safety for local buckling Local buckling load factor from PANDA2 EIGLOC 1 155 1 155000 Are the dimensions in this case in inches y Y Nonlinear 0 or linear 1 kinematic relations ILIN h Ordinarily you should set ILIN 0 However occasionally general buckling mode shapes are dirty That is smooth relatively long wavelength general buckling modes are polluted by very short wavelength noise Example see Fig 39 p 1612 of Optimization of perfect and imperfect ring and stringer stiffened cylindrical shells with PANDA2 and evaluation of the optimum designs with STAGS AIAA Paper 2002 1408 Proceedings of the AIAA 43rd SDM Conference Denver CO 2002 pp 1562 1613 With ILIN 1 much perhaps all of the short wavelength noise will be filtered out Try ILIN 0 first If you get polluted general buckling mode shapes which are usually unsuitable to use as initial imperfection sh
45. NO VALUE DEFINITION ICONSV 1 14 8 24E 01 buck SAND simp support general buck M 1 N 3 slope 0 FS 1 1 ICONSV 0 13 9 73E 01 buck SAND simp support general buck M 1 N 3 slope 0 FS 1 1 ICONSV 1 13 1 19E 00 buck SAND simp support general buck M 1 N 3 slope 0 FS 1 1 ICONSV 1 which is the recommended value corresponds to the most conservative PANDA2 model and ICONSV 1 corresponds to the least conservative PANDA2 model The general buckling load factor is obtained from the general buckling margin from the following buckling load factor factor of safety x margin 1 0 For the least conservative PANDA2 model ICONSV 1 the general buckling load factor is given by buckling load factor 1 1 x 1 19 1 0 2 409 This general buckling load factor from PANDA2 is fairly close to that predicted by STAGS 2 507 PART 3 17 Produce and run a different STAGS model one which covers only a small sub domain of the entire shell with all stiffener segments modeled as flexible shell units Run a STAGS model yet again this time with the use of different input data in cylstif STG Now only a sub domain of the cylindrical shell is to be included in the STAGS model a piece of the cylindrical shell that contains 5 stringer bays and 3 ring bays There are rings along the two curved edges of the sub domain and there are stringers along the two straight edges of the sub domain These edge stiffeners have half the
46. PANDA2 case name cylstif We use the same input file for CHOOSEPLOT that we used after the first execution of SUPREOPT The interactive CHOOSEPLOT execution rolls by on the screen very fast bush gt diplot Enter the PANDA2 case name cylstif Print the plot file on the printer called lt lp gt y or n n The PostScript files cylstif 3 ps through cylstif 10 ps contain the graphics for your plot They can be printed on any PostScript printer or viewed on the console with a PostScript previewing software program The Postscript file for plotting is rw r r 1 bush bush 30646 Feb 22 07 50 cylstif 5 ps This plot contains the objective versus design iterations during the SUPEROPT execution In order to see the plot on your screen type the following command gv cylstif 5 ps gv means ghost view a utility for reading Postscript files and producing the plot image on your screen A screen snapshot of the plot is taken and stored in the 2 cylstif superopt2 objective png All the png files are appended at the end of this file PART 1 12 Execute the PANDA2 processor called MAINSETUP again in order to set up a run for a fixed design ITYPE 2 the optimum design with the weight 1 178E 04 1b Next we wish to obtain results for the optimized design We edit the cylstif OPT file input for MAINSETUP by changing ITYPE from 1 optimization to 2 analysis of a fixed design 2 Choose type of analysis ITYP
47. PANDA2 computes the constraint gradient matrix and then aborts You may want to set NPRINT 2 with ITYPE 1 in a case for which you suspect that there is a bug in the program or perhaps in your input data You can inspect the constraint gradient matrix to see if there are any very large gradients that might have been generated because of a bug Then you will want to inspect the results for the current and for the perturbed designs in an attempt to determine the cause or causes of the overly large constraint gradients NPRINT output index l min O0 good 1 ok 2 more 3 too much 0 0 Next you will be asked to provide an index ISAND for the type of shell theory to be used in the PANDA type closed form buckling analysis You can choose either ISAND 0 or ISAND 1 or ISAND 2 ISAND 0 means that Donnell theory will be used corrected for live pressure that effects primarily n 2 and n 3 buckling load factors of cylindrical shells ISAND 1 means that Sanders theory will be used ITEMs 128 410 ISAND 2 means that Marlowe s theory will be used ITEM 411 The Donnell theory kinematic and work done terms are appear in Eqs 53 and 49b on p 552 of Vol 27 of Computers and Structures 1987 Theoretical basis of the PANDA with modifications described in ITEM 68 of the file PANDA2 NEWS The Sanders theory is described in ITEMs 128 410 of PANDA2 NEWS The Marlowe theory is described in ITEM 411 of PANDA2 NEWS
48. Prebuckling choose 0 bending included 2 use membrane theory Buckling choose 0 simple support or 1 clamping end of the cylstif BEG file input for BEGIN This cylstif BEG file can be edited and used for future executions of BEGIN for the same or very similar cases PART 1 3 Execute the PANDA2 processor called SETUP SETUP sets up templates for BOSOR4 type of models bush gt setup Enter case name cylstif Running PANDA2 setup case cylstif Executing setup KKEKKKKKKKKKKKE SETUP kkkkkkkkkkkkk kk The purpose of SETUP is to set up an input data file called NAME ALL in which NAME is your name for this case This file NAME ALL is a BOSOR4 type of input data file It is used as input for B4READ kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk GENERATING BOSOR4 TYPE DISCRETIZED MODELS FOR A SINGLE PANEL MODULE AND FOR THE ENTIRE PANEL WIDTH WITH SMEARED STRINGERS The command SETUP causes templates of the stiffness and load geometric matrices to be set up for the buckling problems involving 1 a single panel module which is used for a local buckling and postbuckling analysis b wide column buckling analysis and c the nonlinear local static response of an axially stiffened panel to uniform normal pressure 2 the entire panel with smeared stiffeners which is used for a general instability for a panel with an axial load that varies across the span of the panel and b the nonl
49. SAY PLEASE SAY SOMETHING KKK KKK KKK KKK KKK KKK KKK KKK RK KKK KKK KKK KR KEK RK KKK KKK KKK Are you correcting adding to or using an existing file y The interactive MAINSETUP session rolls by on the screen very fast We next give the command PANDAOPT and thereby obtain results for the fixed optimized design PART 1 13 Execute the PANDA2 processor called PANDAOPT for the analysis of the fixed optimized design bush gt pandaopt The purpose of PANDAOPT is to launch the batch run which performs optimization or buckling according to the strategy parameters established the last time you did a MAINSETUP Output from PANDAOPT is stored in a file called casename OPM in which casename is the name of the case You will want to examine casename OPM as soon as PANDAOPT is finished Enter case name cylstif B background F foreground or Q NOS network queue system f Running PANDA2 pandaopt case cylstif Executing main Normal termination main still processing Please wait Executing store Normal termination store still processing Please wait cylstif mainprocessor run completed successfully Menu PANDAOPT CHOOSEPLOT MAINSETUP CHANGE Please examine the files cylstif OPM cylstif OPP and cylstif OPI If ITYPE 1 print the file called cylstif OPP If ITYPE 3 or 4 print the file called cylstif OPI Run PANDAOPT several times for optimization PART 1 14 Inspect the output from PANDAOPT the cylsti
50. SKIN RING MODULE The command SETUP2 causes templates of the stiffness and load geometric matrices to be set up for the buckling problems involving 1 a single panel skin ring module which is used for a local buckling analysis and b the nonlinear local static response of a ring stiffened panel to uniform normal pressure and axial compression DESCRIPTION OF FILES GENERATED BY THIS CASE cylstif AL2 Input data for BOSOR4 type of preprocessor correponding to discretized single skin ring panel module cylstif CBL Contains part of cylstif data base For further information about files generated during operation of PANDA2 give the command HELPAN FILES This command will cause to be generated matrix templates for solution of the local skin ring buckling eigenvalue problem in which the panel module cross section is discretized according to the conventions used in BOSOR4 Next give either the command DECIDE or MAINSETUP Normal termination setup2 still processing Please wait Executing setup3 KKKEKKKKKKKKKKE SETUP3 kkkkkkkkkkkkk kk The purpose of SETUP3 is to set up an input data file called NAME AL3 in which NAME is your name for this case This file NAME AL3 is a BOSOR4 type of input data file It is used as input for B4READ skin substringer module 2004 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk GENERATING BOSOR4 TYPE DISCRETIZED MODEL FOR A SINGLE PANEL MODULE skin substringer The command S
51. STR 4 1 8 450E 02 T 3 STR thickness for layer index no 3 STR seg 4 layer 1 8 0 0 3 185E 01 B RNG stiffener spacing b RNG seg NA layer NA 9 RNG 2 0 0 000E 00 B2 RNG width of ring base b2 zero is allowed RNG seg 2 layer NA 10 RNG 3 0 9 783E 00 H RNG height of stiffener type H for sketch h RNG seg 3 layer NA 11 RNG 4 0 4 304E 00 W RNG width of outstanding flange of stiffener w RNG seg 4 layer NA 12 RNG 3 1 5 673E 01 T 4 RNG thickness for layer index no 4 RNG seg 3 layer 1 13 RNG 4 1 9 452E 01 T 5 RNG thickness for layer index no 5 RNG seg 4 layer 1 Kk k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k kkk k kkk k kkk k k kkkk kkkk kkkkkkkkkkkk DESIGN OBJECTIVE kkk kkk kkk kkk kkk kkk kkk kkk kkk k KKKKKKKKKKK CORRESPONDING VALUE OF THE OBJECTIVE FUNCTION VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 0 0 1 178E 04 WEIGHT OF THE ENTIRE PANEL kkk kkk kkk kkk k kkkk kkkkkkkkkkkkkkkk DESIGN OBJECTIVE kkk kkk kkk kkk kkk Kk k k k k k k k k k k k k k k k k k k k k k k k k k k k kk k k kk k k kk k k kkk k kkk k k kkk end of abridged cylstif OPP file KKKKKKKKKKKE It turns out there IS a slightly smaller optimized weight 1 178E 04 lb versus the 1 221E 04 lb determined in PART 1 8 Next we want to obtain a plot of the objective versus the design iterations during the second execution of SUPEROPT bush gt chooseplot Please enter
52. System A FACM 1 Starting load factor for Load System B STLD 2 Load factor increment for Load System B STEP 2 Maximum load factor for Load System B FACM 2 How many eigenvalues do you want NEIGS Choose element type 480 or 410 or 940 Have you obtained buckling modes from STAGS for this case Number of stringers in STAGS model of 360 deg cylinder Number of rings in the STAGS model of the panel Are there rings at the ends of the panel Number of finite elements between adjacent stringers Number of finite elements between adjacent rings Stringer model 1 or 2 or 3 or 4 or 5 Type H elp Ring model 1 or 2 or 3 or 4 or 5 Type H elp Reference surface of cyl l outer 0 middle 1l inner Do you want to use fasteners they are like rigid links Are the stringers to be smeared out Are the rings to be smeared out Number of nodes over height of stiffener webs NODWEB Number of nodes over width of stringer flange NDFLGS Number of nodes over width of ring flange NDFLGR Do you want stringer s with a high nodal point density Do you want ring s with a high nodal point density Is there plasticity in this STAGS model Do you want to use the least squares model for torque Is stiffener sidesway permitted at the panel edges 0 Edges parallel to screen 0 in plane deformable 1 rigid 0 Stringer web axial displacement index IBCXOXL 0 or 1 end of the cylstif STG file input for STAGSUNIT
53. a plot of the objective v iterations Y N Do you want to get more plots before your next SUPEROPT px BBB NNNUNN This short file contains valid input for the next execution of CHOOSEPLOT PART 1 10 Execute the PANDA2 processor called DIPLOT in order to generate Postscript files for plotting bush gt diplot Enter the PANDA2 case name cylstif Print the plot file on the printer called lt lp gt y or n n The PostScript files cylstif 3 ps through cylstif 10 ps contain the graphics for your plot They can be printed on any PostScript printer or viewed on the console with a PostScript previewing software program The files now existing in the working directory are as follows rw r r 1 bush bush 76 Feb 21 18 29 cylstif 010 rw r r 1 bush bush 30290 Feb 21 18 30 cylstif 5 ps rw r r 1 bush bush 2046 Feb 21 17 56 cylstif AL2 rw r r 1 bush bush 2058 Feb 21 17 46 cylstif AL3 rw r r 1 bush bush 2058 Feb 21 17 56 cylstif ALL rw r r 1 bush bush 5604 Feb 21 11 18 cylstif BEG rw r r 1 bush bush 110324 Feb 21 17 57 cylstif BL1 rw r r 1 bush bush 110324 Feb 21 17 57 cylstif BL2 rw r r 1 bush bush 110324 Feb 21 17 56 cylstif BL3 rw r r 1 bush bush 110324 Feb 21 17 46 cylstif BL4 rw r r 1 bush bush 481 Feb 21 17 56 cylstif BOS rw r r 1 bush bush 182500 Feb 21 18 29 cylstif CBL rw r r 1 bush bush 360 Feb 21 18 29 cylstif CPL rw r r 1 bush bush 3126 Feb 21 17 45 cylstif DEC rw r r
54. ae Sy te ee GS y eae r 0 6447E 01 solution scale 0 11271E 01 eigenvector deformed geometry mode 1 per x 35 84 y 13 14 Oz 35 63 step verfect shell from STAGS linear buckling of p 22 cylstif stagsunit 6x3 eigl png critical local buckling load factor from sub domain 6 x 3 bay model in which all stiffener segments are modeled as flexible shell units xo eo a ai sage E ee g is a Ta gA O e ae amp S ee eS p N LE a a A a N ae See O ee ASO IO RE OC OR ae Es E oe oe tT et om by ote L5 J solution scale 0 7208E 01 mode 8 per 0 19100E 01 Ox 35 84 y Zz 2 ae O y 13 14 x step 0 eigenvector deformed geometry Oz 3563 linear buckling of perfect shell from STAGS a 23 cylstif stagsunit 6x3 eig43 png The 43rd eigenvalue corresponds to the critical inter ring buckling mode from a model in which all of the stiffener segments are modeled as flexible shell units solution scale 0 6672E 01 mode 8 per 0 19100E 01 Ox 35 84 vz l y 13 14 y x step 0 eigenvector deformed geometry Oz 2563 linear buckling of perfect shell from STAGS NA 24 cylstif stagsunit 6x3 eig43 skin png same inter ring buckling mode as shown in the previous figure only the shell unit that represents the skin is plotted here
55. based on the assumption that the skin is flat that is the stringers are close enough together so that it may not be too conservative to ignore the curvature of the cylindrical panel The local postbuckling state is entered sooner for a skin stringer panel module with a flat skin than for one with a curved skin Therefore the stresses computed from the approximate post local buckling analysis in PANDA2 will be higher than those of the actual curved panel provided that the local buckling load factor for the curved panel is greater than unity at the design load no postbuckling occurs for the curved panel If you think that the flat skin postbuckling model is too conservative then answer Y to the current prompt Then PANDA2 will skip the KOITER local postbuckling analysis and compute the stresses as if the amplitude of the local post buckling deformation is zero The default answer is N A N answer generates IIKOIT 1 and a Y answer generates IIKOIT 0 in which IIKOIT is the control index used in PANDA2 IIKOIT 0 means don t perform postbuckling computations 1 means yes perform postbuckling computations It would be a good idea to optimize panels with this choice taken first one way then the other way KKKKKKK NOTH RKKKK If you are planning to do a ITYPE 3 analysis you MUST choose a N answer here ITYPE 3 fixed design under increasing load test simulation kkK KKK END NOTE Do you want to s
56. be asked if you want stringer s and or ring s to have a denser finite element mesh than all the others in the STAGS model Ordinarily you should answer N no First you will be asked with regard to stringers then with regard to rings For each category stringers rings if you answer Y you will next be asked to give the stringer number s or ring number s which are to have the higher nodal point density The stringers are numbered from the bottom to the top or right to left The rings are numbered from the bottom to the top or left to right See Fig 2 of the paper Difficulties in optimization AIAA Paper No 2006 1943 AIAA SDM Meeting Newport RI May 2006 for an example of a STAGS model produced by STAGSUNIT Stringer numbers increase with coordinate y ring numbers increase with coordinate x Do you want stringer s with a high nodal point density h The nodal point density referred to is with respect to the stringer cross section not the density along the axis of the stringer The density along the axis of the stringer is the same as the density along the x coordinate in the panel skin You may wamt one or more stringers with a higher nodal point density over the cross section than exists in the others especially if there occurs local stress and or buckling behavior not well represented by your previously specified nodal point distribution over the cross section used for all the stringers in your previous mod
57. bifurcation analysis or an INDIC 4 bifurcation from nonlinear prebuckled state analysis If your answer is N the amplitude of the imperfection WIMPL that you provided above will be set to zero and your STAGS run will therefore NOT include the effect of initial imperfections If you want to include the effect of initial imperfections run STAGS with either the INDIC 1 or INDIC 4 options first Have you obtained buckling modes from STAGS for this case n n Number of stringers in STAGS model of 360 deg cylinder h The first stringer is at circ angle theta 0 degrees and the last stringer is at theta 360 dtheta in which dtheta is the circ angle between the lines of attachment of adjacent stringers NOTE Make sure that the stringer spacing is equal to the PANDA2 variable called B 1 or B STR You may have to run PANDA2 again with B 1 set so that there are exactly the right number of uniformly spaced stringers in the complete 360 deg cylindrical shell Number of 62 Number of The first or it may depending stringers in STAGS model of 360 deg cylinder 62 rings in the STAGS model of the panel h ring may be at the beginning of the panel be one half ring spacing in from this edge on how you answer the next question NOTE Make sure that the ring spacing is equal to the PANDA2 variable called B 2 or B RNG You may have to run PANDA2 again with B 2 set so that there are exactly the right number of
58. buckling load factor for inter ring buckling when we go from a model in which the stringers are smeared eigenvalue 2 035 to a model in which the stringers in which the stringers are smeared are modeled as flexible shell segments eigenvalue 1 91 a buckling mode 1 91 From STAGS we find that there is only a Therefore in this particular case PANDA2 s prediction of inter ring buckling is conservative when the conservativeness index ICONSV 1 which is the recommended value of ICONSV The inter ring buckling mode found from BIGBOSOR4 is represented by the file 6 cylstif interring panel2 png and the corresponding buckling load factor from BIGBOSOR4 is 2 338 PANDA2 obtains an inter ring buckling load factor of 2 03 before knockdown for smeared stringers and a bit more than half that after knockdown for smeared stringers when ICONSV 1 SMRFAC 1 0 when ICONSV 0 SMRFAC or l 5 7026E 01 when ICONSV knockdown factor The series of 16 STAGS runs that were required to find the inter ring buckling load factor and mode shape from STAGS are listed next The input datum eigenvalue shift occurs near the end of the cylstif bin file This input datum is changed before each of the STAGS runs is executed The fragments listed below are from the STAGS output files cylstif out2 A column headed ROOT has been added in most cases That column is not included in the regular STAGS output
59. causes tensile membrane loads then you should probably put the pressure in Load Set B If the pressure is external causes destabilizing membrane loads then you should probably put the pressure in Load Set A If the structure is a TRUSS CORE sandwich construction make the pressure part of Load Set A Is the pressure part of Load Set A y Y Is the pressure hydrostatic Type H for HELP h Answer Y if you want PANDA2 to print warning about including the contribution of the pressure to the axial load Nx p r 2 or Nxo p r 2 Is the pressure hydrostatic Type H for HELP y Y Choose in plane immovable IFREE 0 or movable IFREE 1 b c 1 h The static response to normal pressure may be strongly dependent on whether the edges of the panel are allowed to move in the horizontal direction in plane for flat panel normal to each edge IFREE 0 means that this horizontal motion is not allowed immovable IFREE 1 means that this horizontal motion is allowed movable Generally you will get larger normal deflections more bowing due to pressure if the edges are movable IFREE 1 The membrane strains will be lower and the bending strains will be higher with movable edges than with immovable edges Note that the analysis with IFREE 0 is more rigorous than with IFREE 1 With IFREE 0 Newton iterations converge to a nonlinear solution The assumed displacements u v w appear as Eqs 9 5 in the long PANDA2 paper Compu
60. factor that accounts for the softening effect of the in plane loads WPG means normal deflection W due to pressure P from a Global smeared stiffener model Is there a maximum allowable deflection due to pressure n n HYDROSTATIC PRESSURE WARNING x INPUT DATA FOR LOAD SET NO 1 THE PANEL IS CURVED Radius of curvature R 1 0000E 02 NORMAL PRESSURE positive acting upward p 5 0000E 02 AXIAL RESULTANT GENERATED BY PRESSURE Nx p r 2 2 5000E 04 Pressure is in Load Set A CURRENTLY APPLIED AXIAL RESULTANTS Nx load set A 2 5000E 04 Nxo load set B 0 0000E 00 MAKE SURE THAT ONE OF THE AXIAL LOADS Nx or Nxo THAT YOU HAVE ALREADY SUPPLIED FOR THIS LOAD CASE INCLUDES THE COMPONENT p r 2 GENERATED BY THE HYDROSTATIC PRESSURE p xkkKKKKKKX END OF HYDROSTATIC PRESSURE WARNING x xxxx You will next be asked to provide amplitudes for the following modes of initial geometric imperfections Wimpgl Wimpg2 Wpan Wloc a overall out of roundness amplitude Wimpgl where Wimpgl Max diameter Min diameter 4 NOTE Use zero if the panel is flat Wimpgl will be reset to zero if PANDA2 detects that the panel is flat NOTE If the panel is curved Whatever circumferential angle the panel spans pretend for the purpose of this input datum that it represents part of a complete 360 deg cylindrical shell that has an out of roundness with amplitude Wimpgl If Wimpg2 see next paragraph is zero t
61. file It turns out that the lowest eigenvalue that corresponds primarily to buckling of the skin with smeared stringers between adjacent rings is Eigenvalue no 5 The buckling load factor is 2 035811 The STAGS post processor STAPL is used to obtain the inter ring buckling mode The input for STAPL is as follows cylstif pin file input for STAPL linear buckling of perfect shell from STAGS 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 1 0 4 0 5 PL 3 KPLOT NUNIT ITEM STEP MODE 0 0 3 PL 5 DSCALE NROTS 1 0 35840000E 02 PL 6 IROT ROT 2 0 13140000E 02 SPL 6 IROT ROT 3 0 35630001E 02 SPL 6 IROT ROT end of cylstif pin file A plot of the appropriate buckling mode obtained from STAGS is contained in the file 21 cylstif stagsunit 6x3 smrstr eig5 png PART 3 22 Compare STAGS prediction with those from BIGBOSOR4 and PANDA2 From PANEL2 and BIGBOSOR4 we obtain the following buckling load factors for an analogous type of buckling xx x k EIGENVALUES AND MODE SHAPES EIGENVALUE CIRC WAVES 1 6929E 00 2 1 6141E 00 4 lt ring sidesway critical mode 1 8127E 00 6 Compare with PANDA2 CHAPTERS 22 amp 26 2 2312E 00 8 2 7896E 00 10 3 3854E 00 3 8828E 00 14 3 8381E 00 16 3 3807E 00 18 3 0163E 00 20 2 7499E 00 22 2 5632E 00 24 2 4399E 00 26 2 3680E 00 28 2 3381E 00 30 lt inter ring critical mode 2 3432E 00 32 Compare with PANDA2 CHAPTER 22 2 3782E 0
62. for Help Want to provide another load set Do you want to impose minimum TOTAL thickness of any segment Do you want to impose maximum TOTAL thickness of any segment Do you want to impose minimum TOTAL thickness of any segment Do you want to impose maximum TOTAL thickness of any segment Use reduced effective stiffness in panel skin H elp Y or N NPRINT output index 1l1 min 0 good 1 ok 2 more 3 too much Index for type of shell theory 0 or 1 or 2 ISAND Does the postbuckling axial wavelength of local buckles change Want to suppress general buckling mode with many axial waves Do you want to double check PANDA type eigenvalues type H elp Choose 0 transverse inextensional l transverse extensional Choose ICONSV 1 or 0 or 1 or H elp ICONSV 1 Choose type of analysis ITYPE 1 or 2 or 3 or 4 or 5 Y Do you want to prevent secondary buckling mode jumping N Do you want to use the alternative buckling solution 5 How many design iterations permitted in this run 5 to 25 1 000000 MAXMAR Plot only those margins less than MAXMAR Type H N Do you want to reset total iterations to zero Type H 1 Index for objective l min weight 2 min distortion 1 000000 FMARG Skip load case with min margin greater than FMARG end of cylstif OPT file input for MAINSETUP This file or an edited version of it can be used for future executions of the PANDA2 processor cal
63. for a single load set for monotonically increasing load levels test simulation analysis type 3 Results of the interactive session in MAINSETUP are saved on a file called cylstif OPT which will appear at the beginning of the cylstif OPM file when the mainprocessor batch run launched by your command PANDAOPT has been completed NOTE JUST HIT RETURN FOR DEFAULT VALUE OF INPUT DATUM IF PANDA2 REQUIRES AN INPUT IT WILL SAY PLEASE SAY SOMETHING KKK KKK KKK KKK KKK KKK KKK KKK KERR KR KR KKK KEKE KKK RK RKKK KRKK K Are you correcting adding to or using an existing file y The input for MAINSETUP rolls by fast bush gt pandaopt The purpose of PANDAOPT is to launch the batch run which performs optimization or buckling according to the strategy parameters established the last time you did a MAINSETUP Output from PANDAOPT is stored in a file called casename OPM in which casename is the name of the case You will want to examine casename OPM as soon as PANDAOPT is finished Enter case name cylstif B background F foreground or Q NOS network queue system f Running PANDA2 pandaopt case cylstif Executing main Normal termination main still processing Please wait Executing store Normal termination store still processing Please wait cylstif mainprocessor run completed successfully Menu PANDAOPT CHOOSEPLOT MAINSETUP CHANGE Please examine the files cylstif OPM cylstif OPP and cylstif OPI
64. friction at the axially loaded ends of the test specimen In actual panels sidesway can occur if the stiffener tips or outstanding flanges are not attached to other structure To simulate the PANDA2 model with use of IQUICK 0 answer Y If IQUICK 1 in your PANDA2 model then you should probably answer N Is stiffener sidesway permitted at the panel edges n n Edges parallel to screen 0 in plane deformable 1 rigid h This input is for the STAGS model of the panel generated via the command STAGSUNIT Choose 0 if you think the two edges of the panel that run parallel to the rings panel width wise coordinate direction or circumferential direction ARE relatively free to deform in the x direction that is in the axial direction in the plane of the panel skin Choose 1 if you think these two edges of the panel ARE NOT free to deform in the x direction NOTE The projection of these two edges onto the surface of the undeformed panel are ALWAYS free to move in the x direction as straight lines Edges parallel to screen 0 in plane deformable 1 rigid 0 0 Next you will be asked to provide an index IBCX0XL which controls the distribution of axial displacement u over the heights of the webs of the stringers at axial stations x 0 and x XSTAGS which are the axial coordinates at the two axially loaded ends of the STAGS model of the panel The index IBCXOXL is defined as follows IBCXOXL 0 no constraint of u is imposed o
65. height h of the stiffener 4 width w of the outstanding flange of the stiffener if any 5 number of unique segments in the module 4 in above figure 6 For each unique segment of the module 6 1 number of layers thru thickness 6 2 layer type indicator for each layer 6 3 For each new layer type 6 3 1 thickness 6 3 2 winding angle which means layup angle 6 3 3 material type indicator Identify type of stiffener along L1 N T J 2Z R A C G h L1 is the length of the panel normal to the plane of the screen For choice G isoGrid L1 is irrelevant no stiffeners along L1 at all T shaped cross section J shaped cross section or angle with flange away from skin Z shaped cross section with riveted faying flange rectangular cross section blade stiffener hat shaped or trapezoidal cross section enclosing area PANGUHSA tou woueou Truss core sandwich construction added July 1989 isoGrid added September 1992 With isoGrid the stiffeners can be T shaped J shaped or rectangular blade Identify type of stiffener along L1 N T J 2Z R A C G t t Module with T shaped stiffener Seg No 4 Segment No 3 gt Seg No 2 h Seg No l Seg No 5 j 3 V same as Seg 1 lt b2 gt lt Module width stiffener spacing b gt stiffener spacing b h There is no more help Do your best stiffener spacing b 30 30 width of stringer base b2 must be gt 0 see Help h
66. if it leads to an out of plane wall rotation that is greater than 0 1 radian If this happens a warning such as the following which happens to apply only to the local buckling modal imperfection will be printed in the OPM file KKKKKKKEK WARNING WARNING WARNING THE CIRCUMFERENTIAL HALFWAVELENGTH OF THE LOCAL IMPERFECTION Wimp local WHICH HAS THE SAME FORM AS THE LOCAL BUCKLING MODE IS SHORT WHILE ITS AMPLITUDE IS RATHER HIGH Circumferential halfwavelength of Wimp local Wlength 2 97E 01 Present amplitude of the local imperfection Wimp local 1 67E 00 PLEASE CONSIDER REDUCING Wimp local YOUR DESIGN MAY BE TOO CONSERVATIVE RKKKKKKKKKKKK END WARNING END WARNING R The following material printed in the OPM file informs the user by what factor the user supplied imperfection amplitude was reduced in this case in order to keep the maximum out of plane wall rotation less than 0 1 rad LOCAL AND GLOBAL IMPERFECTION AMPLITUDES AMPLITUDE MODIFIERS THAT KEEP MAX WALL ROTATION GENERATED BY THE MODAL IMPERFECTION COMPONENT LESS THAT 0 1 RADIAN AND AMPLIFICATION FACTORS TO ACCOUNT FOR GROWTH OF THE INITIAL IMPERFECTIONS DURING LOADING USER PROVIDED AMPLITUDE AMPLIFICATION IMPERFECTION MODIFIER FACTOR WYYAMP AMPLITUDE AMPMDi FROM LOADING local imperfection 1 6750E 00 5 4998E 01 1 0182E 00 In the above case the local buckling modal imperfection amplitude actu
67. in the prebuckling phase there may be significant bending between these large rings due to the pressure then set up models in which there are stringers only The entire axial length of each model must be equal to the spacing of the large rings The boundary conditions along the edges where the large rings are supposed to be should be clamped for the prebuckling phase and simply supported for the buckling phase of the analysis if the stringers are not tapered in the neighborhoods of the large rings If the stringers are tapered near the large rings then use simple support for both the prebuckling and the buckling phases of the analysis Prebuckling choose 0 bending included 2 use membrane theory h This prompt is used for boundary conditions for curved cylindrical panels only Please reply either 0 or 2 What is meant here is the b c for the two CURVED boundaries only The straight boundaries that is the two edges that are normal to the plane of the screen are always assumed to be symmetry conditions for the prebuckling phase of the analysis but uniform in plane shearing is permitted 0 Prebuckling axisymmetric axial bending is included Please see pp 495 498 in the paper Approximate method for the Computers amp Structures Vol 59 pp 489 527 1996 for an explanation of the axisymmetric prebuckling theory used in PANDA2 2 The prebuckled state is derived from membrane theory That is both the stringers and rings are
68. linked to that of the first mentioned layer The linking constant C1 1 0 in this example Any linked variables Y or N y y PARAMETERS FROM WHICH A LINKED VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must Choose a linked variable 1 2 3 2 2 LINKED VARIABLE MUST BE LINKED TO ONE OF THE DECISION VARIABLES VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 To which variable is this variable linked 1 1 Assign a value to the linking coefficient C j 0 3333 0 3333000 B2 STR width of stringer base b2 must be gt 0 see Help STR seg 2 lay 0 3333 V 1 Any other decision variables in the linking expression n n Any constant CO in t
69. module HOOP BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KNOCKDOWN ANISOTROPY n EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 30 2 21541E 00 1 00000E 00 1 00000E 00 2 21541E 00 33 2 24156E 00 1 00000E 00 1 00000E 00 2 24156E 00 27 2 26516E 00 1 00000E 00 1 00000E 00 2 26516E 00 Buckling load factor before t s d 2 2154E 00 After t s d 2 1201E 00 knockdown for smeared stringers from SUB EIGMOD SMRFAC 1 0000E 00 ICONSV 0 Buckling load factor BEFORE knockdown for smeared stringers 2 1201E 00 Buckling load factor AFTER knockdown for smeared stringers 2 1201E 00 ICONSV 0 From CHAPTER 22 of the PANDA2 file cylstif OPM we have for ICONSV 0 BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DISCRETIZED STAGS worthy MODEL skin smeared stringer ring discretized module HOOP BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KNOCKDOWN ANISOTROPY n EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 30 2 21541E 00 1 00000E 00 1 00000E 00 2 21541E 00 33 2 24156E 00 1 00000E 00 1 00000E 00 2 24156E 00 27 2 26516E 00 1 00000E 00 1 00000E 00 2 26516E 00 Buckling load factor before t s d 2 2154E 00 After t s d 2 1201E 00 knockdown for smeared stringers from SUB EIGMOD SMRFAC 1 0000E 00 ICONSV 0 Buckling load fa
70. near bolt holes Use a value such that if this value were reached along axial lines of fasteners there would be no failure because of the fasteners This allowable is placed in the load loop because you may want to provide different values for tension and compression A factor of safety of unity is used in PANDA2 for this allowable Also the margin is calculated using only the axial strain component EXAVE The concept of effective strain resulting from the three in plane strain components EXAVE EYAVE and EXYAVE is not used Therefore you must set the maximum allowable average axial strain small enough to yield a reliable design If you are not concerned with this just type zero or a large number Use a positive number Units are strain not percent Maximum allowable average axial strain type H for HELP 1 1 1 000000 Is there any thermal loading in this load set Y N h What is meant is thermal loading other than curing Usually you answer N If there is aerodynamic heating or other source of heating which may be significant in your case answer Y If you answer Y you will be asked to provide two temperatures for the panel skin corresponding to the uppermost and lowermost surfaces of the panel skin and stringer ring bases and one temperature each for the outstanding stringer flange and outstanding ring flange With blade stiffening you will be asked to provide the temperature at the blade tip The temperatures you
71. no 5 Number of parameter to change 1 2 3 8 8 New value of the parameter 31 850 31 85000 Want to change any other parameters in this set y Y PARAMETERS WHICH CAN BE CHANGED CHOOSE ONE OF THE FOLLOWING VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 1 011E 01 B STR stiffener spacing b STR seg NA 2 STR 2 0 3 370E 00 B2 STR width of stringer base b2 must 3 STR 3 0 7 817E 00 H STR height of stiffener type H for s 4 STR 4 0 2 534E 00 W STR width of outstanding flange of st 5 SKN 1 1 7 690E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 2 038E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 8 450E 02 T 3 STR thickness for layer index no 3 8 0 0 3 185E 01 B RNG stiffener spacing b RNG seg NA 9 RNG 2 0 0 000E 00 B2 RNG width of ring base b2 zero is a 10 RNG 3 0 9 783E 00 H RNG height of stiffener type H for s 11 RNG 4 0 4 304E 00 W RNG width of outstanding flange of st 12 RNG 3 1 5 673E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 9 452E 01 T 5 RNG thickness for layer index no 5 Number of parameter to change 1 2 3 10 10 New value of the parameter 9 7830 9 783000 Want to change any other parameters in this set y Y PARAMETERS WHICH CAN BE CHANGED CHOOSE ONE OF THE FOLLOWING VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 1 011E 01 B STR stiffener spacing b STR seg NA 2 STR 2 0 3 370E 00 B2 STR width of str
72. nodes over width of ring flange NDFLGR Do you want stringer s with a high nodal point density Do you want ring s with a high nodal point density Is there plasticity in this STAGS model Do you want to use the least squares model for torque Is stiffener sidesway permitted at the panel edges Do you want symmetry conditions along the straight edges Edges parallel to screen 0 in plane deformable 1 rigid Stringer web axial displacement index IBCXOXL 0 or 1 NOTE gt pK DSB Ooo K BKBBDB The STAGS input file cylstif bin is as follows cylstif bin file one of the 2 input files for STAGS cylstif STAGS INPUT FOR STIFFENED CYL STAGSUNIT SHELL UNITS 1 INDIC 1 is bifur buckling INDIC 3 is nonlinear BEGIN B 1 1 IPOST 1 means save displacements every IPOSTth step 0 ILIST 0 means normal batch oriented output 0 ICOR 0 means projection in 1 means not in 1 IMPTHE index for imperfection theory 0 ICHIST index for crack archive option 0 IFLU 0 means no fluid interaction 1 ISOLVR 0 means original solver 1 new solver END B 1 rec 1 000E 00 STLD 1 starting load factor System A BEGIN C 1 rec 0 000E 00 STEP 1 load factor increment System A 1 000E 00 FACM 1 maximum load factor System A 0 000E 00 STLD 2 starting load factor System B 0 000E 00 STEP 2 load factor increment System B 0 000E 00 FACM 2 maximum load factor System B 0
73. of the cylstif OPM file when the mainprocessor batch run launched by your command PANDAOPT has been completed NOTE JUST HIT RETURN FOR DEFAULT VALUE OF INPUT DATUM IF PANDA2 REQUIRES AN INPUT IT WILL SAY PLEASE SAY SOMETHING KKK KKK KKK KKK KEK KEK KKK KKK KK RRR KKK RK KR KKK KEKE RK RKKK KKK Are you correcting adding to or using an existing file y The MAINSETUP interactive session rolls by fast Not reproduced here in order to save space Next execute SUPEROPT again This time it should not bomb because the stringer spacing cannot exceed 30 inches which is less than a third of the radius of the cylindrical shell PART 1 8 Execute the PANDA2 processor called SUPEROPT in order to search for a global optimum design bush gt superopt The purpose of SUPEROPT is to launch the batch run which performs multiple executions of the panda2 processors in the order autochange setup pandaopt pandaopt pandaopt The processor autochange automatically changes the decision variables as follows y i x i 1 dx i i 1 2 3 no of dec var in which x i is the old value of the ith decision variable y i is the new value and dx i is a random number between 0 5 and 1 5 The purpose of the successive cycles of autochange setup pandaopt pandaopt pandaopt is to try to find a global optimum design by redesigning in each cycle from a different starting point The user should use a small maximum number of de
74. of the cylindrical shell and the roots of the stringers and rings when these stiffeners are modelled as shell branches rather than as beams The fasteners act like tiny springs between fastened nodes The fastener spring constant is chosen automatically by STAGSUNIT It is set rather high in order that fasteners act in a manner similar to rigid links Do you want to use fasteners they are like rigid links n n Are the stringers to be smeared out h Generally you should answer N Are the stringers to be smeared out n n Are the rings to be smeared out h Generally you should answer N Are the rings to be smeared out n n Number of nodes over height of stiffener webs NODWEB h You must provide an odd integer First try a small number such as 3 In a convergence study or with models in which the cylindrical shell does not have a huge number of nodes huge 500000 or more or with models in which there are not many stiffeners you can try more especially if you suspect that significant web bending occurs during buckling and or nonlinear collapse In STAGSUNIT the webs of both stringers and rings will have the same number of nodal points over their heights Number of nodes over height of stiffener webs NODWEB 5 5 Number of nodes over width of stringer flange NDFLGS 5 5 Number of nodes over width of ring flange NDFLGR 5 5 This section pertains to STAGS models generated via STAGSUNIT You will next
75. of the panel XSTAGS 628 3185 Panel length in the plane of the screen L2 y Is the nodal point spacing uniform along the stringer axis 51 Number of nodes in the X direction NODEX 101 Number of nodes in the Y direction NODEY 25000 00 Resultant e g lb in normal to the plane of screen Nx 50000 00 Resultant e g lb in in the plane of the screen Ny 0 000000 In plane shear in load set A Nxy 500 0000 Normal pressure in STAGS model in Load Set A p 0 Resultant e g lb in normal to the plane of screen Nx0 0 Resultant e g lb in in the plane of the screen Ny0 0 Normal pressure in STAGS model in Load Set B p0 1 000000 Starting load factor for Load System A STLD 1 0 000000 Load factor increment for Load System A STEP 1 1 000000 Maximum load factor for Load System A FACM 1 0 Starting load factor for Load System B STLD 2 0 Load factor increment for Load System B STEP 2 0 Maximum load factor for Load System B FACM 2 1 How many eigenvalues do you want NEIGS 480 Choose element type 480 or 410 or 940 n Have you obtained buckling modes from STAGS for this case 62 Number of stringers in STAGS model of 360 deg cylinder 10 Number of rings in the STAGS model of the panel y Are there rings at the ends of the panel 1 Number of finite elements between adjacent stringers 3 Number of finite elements between adjacent rings 3 Stringer model 1 or 2 or 3 or 4 or 5 Type H elp 3 Ring mode
76. parts FSBSTR also You probably will usually set FSBSTR equal to unity IF YOU PLAN TO USE A VALUE OF FSBSTR THAT IS LESS THAN UNITY MAKE SURE THAT YOU READ CAREFULLY ITEMS 37 60 c AND 67 IN PANDA2 NEWS There is no capability to handle local postbuckling of ring parts PANDA2 assigns factors of safety to buckling of ring parts You have no control over them Now please provide the first Load Set A Nx Ny Nxy Resultant e g lb in normal to the plane of screen Nx 1 h What is wanted is the applied line load in the L1 axial direction in units of force length Negative for compression If this axial load varies in the L2 circumferential direction use the largest compressive value applied to that edge of the panel What is wanted now is the axial load in Load Set A that is the eigenvalue load the load to be multiplied by the critical load factor the eigenvalue in computations of the critical applied load Resultant e g lb in normal to the plane of screen Nx 1 25000 25000 00 Resultant e g lb in in the plane of the screen Ny 1 50000 50000 00 In plane shear in load set A Nxy 1 0 0 000000 Does the axial load vary in the L2 direction h The L2 direction is in the plane of the screen circum ferential If you answer Y you will next be asked to provide values of Nx at the beginning and end of the panel edge which lies in the plane of the screen PANDA2 assumes that Nx varies linearly acros
77. rather local stress concentrations in the panel skin and local buckling of the panel skin only in the neighborhoods of rings in a curved panel or at the ends of a clamped curved or flat panel with applied pressure The use of a complete analysis might then cause the panel skin to be overly thick over most of the panel length in order that it not buckle due to local compressive resultants present only near rings or at ends The best design might well be a panel the skin of which is thinner midway between rings than near rings The skin near rings would be thickened locally to reduce stress and prevent local buckling there Since PANDA2 does not handle axially varying thickness or stringer cross section directly you might want to perform two sequential optimizations the first in which you do the complete analysis in order to ensure that the worst conditions generated by both Subcases 1 and 2 are included and the second in which only the conditions for Subcase 1 constrain the design Before doing the second optimization you might have to rerun DECIDE in order to eliminate the stringer and ring spacings and perhaps the stringer cross section dimensions as decision variables and to reset lower bounds on stringer and ring thicknesses and perhaps web heights and flange widths to the values obtained from the first optimization This you might need to do to ensure that the final design can be fabricated and that it will survive the conditions at Su
78. shell multiplied by the axial length modifier LENMOD Rings are smeared in this model ILOCAL 2 general buckling The original stiffnesses are used for the shell skin with all stiffeners smeared CS i j The axial length of the shell model is the total length of the shell multiplied by the axial length modifier LENMOD Enter ILOCAL 0 or 1 or 1 or 2 Type H elp ILOCAL 1 1 Number of halfwaves in the axial direction see H elp NWAVE h For general instability NWAVE is usually equal to 1 For a value you might use inspect the NAME OPM file In the list of buckling margins you will find the number of axial halfwaves predicted via PANDA2 for various kinds of buckling You can use PANEL BOSORALL to check the PANDA2 results via BOSOR4 for general and or local buckling and for buckling of the stiffener parts and for stiffener rolling Please note that 1 BOSOR4 does not account for shear loading in its predictions of buckling so that PANDA2 and BOSOR4 results will agree only if there is no applied in plane shear loading 2 BOSOR4 does not account for the transverse shear deformation effect Number of halfwaves in the axial direction see H elp NWAVE 1 1 How many eigenvalues get at least 3 do you want 3 3 DESCRIPTION OF FILES GENERATED BY THIS CASE cylstif ALL Input data for BIGBOSOR4 type of preprocessor correponding to discretized entire panel cylstif CBL Contains part of cylstif data base For fur
79. slope 0 FS 1 1 15 1 76E 01 buck SAND rolling with smear rings M 93 N 1 slope 0 FS 1 1 16 4 18E 01 buck SAND rolling only of stringers M 8 N 0 slope 0 FS 1 4 8 N 0 17 1 28E 00 buck SAND hiwave roll of stringers M 54 N 0 slope 0 FS 1 2 18 6 12E 01 buck SAND rolling only axisym rings M 0 N 0 slope 0 FS 1 4 19 6 93E 01 buck SAND STRINGERS web buckling M 4 N 1 slope 0 FS 1 20 1 42E 00 buck SAND RINGS web buckling M 26 N 1 slope 0 FS 1 21 6 93E 02 Max allowable ave axial strain ave axial strain 1 FS 1 MARGINS FOR CURRENT DESIGN LOAD CASE NO 1 SUBCASE NO 2 at rings MAR MARGIN NO VALUE DEFINITION 1 8 67E 02 Local buckling from discrete model 1 M 1 axial halfwaves FS 1 1 2 1 95E 01 Bending torsion buckling M 1 FS 1 3 4 01E 01 eff stress matl 1 STR Dseg 5 node 11 layer 1 z 0 3845 RNGS FS 1 4 1 05E 01 m 1 lateral torsional buckling load factor FS 1 FS 1 1 5 1 12E 01 Inter ring bucklng discrete model n 32 circ halfwaves FS 1 1 6 5 82E 01 Lo n Ring sidesway discrete model n 4 circ halfwaves FS 1 1 7 4 01E 01 eff stress matl 1 SKN Iseg 2 at n 6 layer 1 z 0 3845 RNGS FS 1 8 6 93E 01 buckling margin stringer Iseg 3 Local halfwaves 4 RNGS FS 1 9 2 50E 01 buckling margin stringer Iseg 4 Local halfwaves 4 RNGS FS 1 10 2 02E 01 buckling stringer Isegs 3 4 together M 4 C 0 RNGS FS 1 4 11 8 77E 00 buckling stringer Iseg 4 as beam on foundation M 369 RNGS FS 1 2 12 1 44E 00 buckling margin r
80. smeared out and the presence of constraint along the two curved edges and where rings occur is ignored The prebuckled membrane deformation is uniform Cases in which membrane prebuckling theory is used will run quicker because there is only one Subcase per load set However the fact is that conditions are actually different midway between rings from those that exist at the rings because of prebuckling axisymmetric bending You may want to optimize first with use of membrane theory then permit bending for further optimization If the panel is curved and there are no rings use membrane theory Prebuckling choose 0 bending included 2 use membrane theory 2 2 Buckling choose 0 simple support or 1 clamping h What is meant here is the boundary conditions for the two edges that lie in the plane of the screen and parallel to this plane the two curved edges if the panel is cylindrical Use simple support if the ends of the panel represent the locations of rings as discussed above Use simple support if the stringers are tapered at the ends of the panel NOTE If you are using PANDA2 to analyze a ring stiffened cylindrical shell use simple support 0 here If you have chosen the arc length of the panel in the plane of the screen to be equal to pi radius of the cylinder then the number of half waves over this arc length will be equal to the number of full waves in the buckling pattern around the entire circumference of a complete 360 d
81. y y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 5 5 Lower bound of variable no 5 05 0 5000000E 01 Upper bound of variable no 5 1 0 1 000000 Any more decision variables Y or N y Y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T
82. 0 34 2 4388E 00 36 2 5220E 00 38 2 6253E 00 40 The inter ring buckling mode analogous to that displayed in the file 2l cylstif stagsunit 6x3 smrstr eig5 png is the BIGBOSOR4 mode with 30 circumferential waves the mode associated with the eigenvalue 2 3381 ICONSV 1 From CHAPTER 22 of the PANDA2 file cylstif OPM we have for ICONSV 1 BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DISCRETIZED STAGS worthy MODEL skin smeared stringer ring discretized module HOOP BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KNOCKDOWN ANISOTROPY n EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 30 2 21541E 00 1 00000E 00 1 00000E 00 2 21541E 00 33 2 24156E 00 1 00000E 00 1 00000E 00 2 24156E 00 27 2 26516E 00 1 00000E 00 1 00000E 00 2 26516E 00 Buckling load factor before t s d 2 2154E 00 After t s d 2 0332E 00 The buckling load factor 2 0332 is further knocked down by PANDA2 as follows knockdown for smeared stringers from SUB EIGMOD SMRFAC 5 7026E 01 ICONSV 1 Buckling load factor BEFORE knockdown for smeared stringers 2 0332E 00 Buckling load factor AFTER knockdown for smeared stringers 1 1595E 00 ICONSV 1 From CHAPTER 22 of the PANDA2 file cylstif OPM we have for ICONSV 1 BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DISCRETIZED STAGS worthy MODEL skin smeared stringer ring discretized
83. 0 Panel length normal to the plane of the screen L1 314 1600 Panel length in the plane of the screen L2 t Identify type of stiffener along L1 N T J Z R A C G 30 stiffener spacing b 10 00000 width of stringer base b2 must be gt 0 see Help 10 00000 height of stiffener type H for sketch h 10 00000 width of outstanding flange of stiffener w n Are the stringers cocured with the skin 1000000 What force axial length will cause web peel off n Is the next group of layers to be a default group 12 layers 1 number of layers in the next group in Segment no 1 n Can winding layup angles ever be decision variables 1 layer index 1 2 for layer no 1 y Is this a new layer type 0 1000000 thickness for layer index no 1 0 winding angle deg for layer index no 1 1 material index 1 2 for layer index no 1 n Any more layers or groups of layers in Segment no 1 n Is the next group of layers to be a default group 12 layers 1 number of layers in the next group in Segment no 2 n Can winding layup angles ever be decision variables 1 layer index 1 2 for layer no 1 n Is this a new layer type n Any more layers or groups of layers in Segment no 2 n Is the next group of layers to be a default group 12 layers 1 number of layers in the next group in Segment no 3 n Can winding layup angles ever be decision variables 2 layer index 1 2
84. 0 If IHIAXL and ILAMHI are both unity IHIAXL is a user supplied index and ILAMHI initially zero is possibly reset later a constraint condition is set up by means of which the buckling load factor associated with the general buckling mode with the high number of axial halfwaves is forced to be at least 5 per cent higher than that associated with the general buckling mode with thelow number of axial halfwaves In order for IMLOC to be set to zero the norm of the applied axial and hoop stress resultants sqrt Nx 2 Ny 2 must be greater than ten times the applied in plane shear resultant Nxy the hoop resultant Ny must by greater than 1 9 times the axial resultant Nx and both Nx and Ny must be negative compressive loading Want to suppress general buckling mode with many axial waves lt enter gt Y Next you will be asked Do you want to double check PANDA type eigenvalues Please answer H for HELP if you are not familiar with this prompt This double check can take lots of computer time Generally answer N if the panel is flat Generally answer N if you plan to do optimization ITYPE 1 or test simulation ITYPE 3 Generally answer N if you are including transverse shear deformation effects LOTS of computer time is required The double check very rarely has any effect on the results However if you are running an ITYPE 2 fixed design analysis for a final design configuration of a curved panel you might answer Y
85. 0000E 00 18571 49 3 1 988909E 00 1 988909E 00 0 000000E 00 15927 50 4 1 988975E 00 1 988975E 00 0 000000E 00 25687 51 5 1 989196E 00 1 989196E 00 0 000000E 00 20399 52 6 1 995014E 00 1 995014E 00 0 000000E 00 13283 53 7 1 995014E 00 1 995014E 00 0 000000E 00 28331 54 8 2 002111E 00 2 002111E 00 0 000000E 00 21233 55 Plots of the inter ring buckling mode with associated eigenvalue are contained in the two files 23 cylstif stagsunit 6x3 eig43 png 24 cylstif stagsunit 6x3 eig43 skin png What is called here the inter ring buckling mode is a mode in which the stringers bend in the axial direction between rings along with the skin and there are nodal lines in the skin deformation at the axial stations where the web roots of the rings intersect the skin This 43rd buckling mode is analogous to that from STAGS depicted in the file buckling load factor eigenvalue 2 035 BIGBOSOR4 depicted in the file and that from 21 cylstif stagsunit 6x3 smrstr eig5 png 6 cylstif interring panel2 png buckling load factor eigenvalue 2 338 The inter ring buckling load factor from BIGBOSOR4 2 338 is higher than that from STAGS 2 035 mainly because BIGBOSOR4 does not handle the effects of transverse shear deformation t s d and the STAGS 480 finite element does O WEIGHT OF THE ENTIRE PANEL cylstif SEE FILES cylsti OPM AND cylstif OPP 4 10 i i i n f ag i i H n i an ne 4 m g i it 05 i i i
86. 000E 02 SPL 6 IROT ROT 2 0 13140000E 02 SPL 6 IROT ROT 3 0 35630001E 02 SPL 6 IROT ROT end of cylstif pin file The inner fiber effective stress fringe plots are contained in the following two files 17 cylstif stagsunit innerfibstress 5x3 skin png 18 cylstif stagsunit innerfibstress skin zoom png PART 3 19 Compare with the PANDA2 prediction PANDA2 predicts the maximum effective stress as follows from the list of margins for the perfect shell MARGINS FOR CURRENT DESIGN LOAD CASE NO 1 SUBCASE NO 1 MAR MARGIN NO VALUE DEFINITION 3 2 64E 01 eff stress matl 1 SKN Dseg 2 node 6 layer 1 z 0 3845 MID FS 1 7 2 64E 01 eff stress matl 1 SKN Iseg 2 at n 6 layer 1 z 0 3845 MID FS 1 In the above Dseg means module segment number in the discretized model The stress is computed in SUBROUTINE STRTHK Iseg means module segment number in the closed form model The stress is computed in SUBROUTINE STRCON Dseg Iseg 2 is in this case the base under the stringer node 6 and n 6 mean the sixth nodal point in Dseg and Iseg respectively The sixth nodal point is the nodal point that lies in the panel skin where the skin intersects the root of the stringer web The effective stress is found from the margin by the following effective stress allowable stress margin 1 0 x factor of safety effective stress 60000 0 264 1 0 x 1 0 47468 psi STAGS predicts a
87. 1 SKN thickness for layer index no 1 PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 6 6 Lower bound of variable no 6 01 0 1000000E 01 Upper bound of variable no 6 1 1 000000 Any more decision variables Y or N y Y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 7 STR 4 1 1
88. 1 PL 3 KPLOT NUNIT ITEM STEP MODE 0 0 3 PL 5 DSCALE NROTS 1 0 35840000E 02 PL 6 IROT ROT 2 0 13140000E 02 PL 6 IROT ROT 3 0 35630001E 02 SPL 6 IROT ROT end of cylstif pin Next execute the STAGS post processor STAPL stapl cylstif generates a file called cylstif pdf which shows the buckling mode For plots of the STAGS model see the two files 7 cylstif stagsunit model png 8 cylstif stagsunit model zoom png For a plot of the buckling mode see the file 9 cylstif stagsunit eigl png PART 3 11 Compare with BIGBOSOR4 and PANDA2 predictions of local buckling It is seen that buckling occurs only near the two ends of the cylindrical shell and that the buckling load factor is somewhat lower than those predicted by BIGBOSOR4 and by PANDA2 as follows from BIGBOSOR4 BUCKLING LOADS FOLLOW AXIAL HALF WAVE NUMBER N 1 EIGENVALUES 1 21180E 00 1 21651E 00 1 22461E 00 x CRITICAL EIGENVALUE AND WAVENUMBER EIGCRT 1 2118E 00 NO OF AXIAL HALF WAVES NWVCRT 1 ee ee ee ee xxx k EIGENVALUES AND MODE SHAPES EIGENVALUE AXIAL HALF WAVES From CHAPTER 14 in the PANDA2 file cylstif OPM BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DISCRETIZED MODEL skin stringer discretized module of local buckling AXIAL BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KN
89. 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 8 8 Lower bound of variable no 8 10 10 00000 Upper bound of variable no 8 100 100 0000 Any more decision variables Y or N y Y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 10 10 Lower bound of variable no 10 5 0 5000000 Upper bound of variable no 10 20 20 00000 Any more decision variables Y or N y y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO R
90. 2 bit architecture amp code 4 byte integers ia32 same as linux but linux is preferred sgi Silicon Graphics 32 bit IRIS workstation sgin SGI 64 bit architecture 32 bit object code sgi4 SGI 64 bit architecture amp code 4 byte integers sgi8 SGI 64 bit architecture amp code 8 byte integers sol SUN SPARC Solaris workstation star Stardent Multi Processor workstation sun4 SUN 4 SPARC Sun OS workstation Machine type is hp8 x You are initializing STAGS Version 5 0 Your current machine type is gt gt gt gt gt gt gt gt gt gt gt gt hp8 lt lt lt lt lt lt lt lt lt lt lt lt lt Next execute stags stags b cylstif The linear bifurcation buckling INDIC 1 run requires about 12 minutes on feynman From the STAGS output file cylstif out2 we have the following CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 1 CRITICAL LOAD FACTOR COMBINATION NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF 1 1 030548E 00 1 030548E 00 0 000000E 00 46315 end of fragment from the STAGS file cylstif out2 PART 3 10 Execute the STAGS post processor STAPL to get a plot of a bifurcation buckling mode cp temp pin cylstif pin input for STAPL is in the cylstif pin file The cylstif pin file is as follows cylstif pin input for STAPL linear buckling mode linear buckling of perfect shell from STAGS 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 1 0 4 0
91. 258E 01 5 8065E 01 6 3871E 01 6 9677E 01 7 5484E 01 8 1290E 01 8 7097E 01 9 2903E 01 9 8710E 01 1 0452E 02 1 1032E 02 1 1613E 02 1 2194E 02 1 2774E 02 1 3355E 02 1 3935E 02 1 45116E 02 1 5097E 02 1 5677E 02 1 6258E 02 1 6839E 02 1 7419E 02 1 8000E 02 1 8581E 02 1 9161E 02 1 9742E 02 2 0323E 02 2 0903E 02 2 1484E 02 2 2065E 02 2 2645E 02 2 3226E 02 2 3806E 02 2 4387E 02 2 4968E 02 2 5548E 02 2 6129E 02 2 6710E 02 2 7290E 02 2 7871E 02 2 8452E 02 2 9032E 02 2 9613E 02 3 0194E 02 3 0774E 02 3 1355E 02 3 1935E 02 3 2516E 02 3 3097E 02 3 3677E 02 3 4258E 02 3 4839E 02 3 5419E 02 VALUES USED TO GENERATE STAGS INPUT FILE INP Panel dimensions axial circ XSTAGS 3 0000E 02 YSTAGS 6 2832E 02 IREF ISWAY IBC12 IEDGE ICLOSE NODWEB 0 0 2 0 1 5 MAJOR STRINGER QUANTITIES NSTRNG ISMRST IBMSTR NELSTR ILINK1 IZSTIF 1 R 62 0 3 1 0 0 1 0000E 02 MAJOR RING QUANTITIES NRINGS ISMRRG IBMRNG NELRNG ILINK2 IZSTIF 2 IPOSNR TY 2 TX 1 10 0 3 3 0 0 1 7 6896E 01 7 6896E 01 Membrane constitutive coefficients used to get EPS1 and EPS2 CS0 1 1 CS0 1 2 CS0 2 2 1 0233E 07 2 5350E 06 1 1335E 07 stringer web iwalll fnxstr 2 eltab iwalll epsl tx 3 1 2 9133E 03 1 0000E 07 1 4295E 03 2 0380E 01 strng outflange iwalll fnxstr 3 eltab iwalll epsl tx 4 2 1 2079E 03 1 0000E 07 1 4295E 03 8 4496E 02 ring web iwalll fnxrng 2 eltab iwalll eps2 ty 3 3 2 3209E 04 1 0000E 07 4 0912E 03 5 6729E 01 ring outflange iwalll fnxrng 3 elt
92. 3 1 1 Can winding layup angles ever be decision variables n n layer index 1 2 for layer no 1 4 4 Is this a new layer type y y thickness winding angle material for layer index thickness for layer index no 4 1 0 1000000 winding angle deg for layer index no 4 0 0 material index 1 2 for layer index no 4 1 1 Any more layers or groups of layers in Segment no 3 n n Module with T shaped stiffener Seg No 4 Segment No 3 gt Seg No 2 h Seg No l Seg No 5 z V same as Seg 1 lt b2 gt lt Module width stiffener spacing b gt Next provide the properties of Segment 4 4 4 4 Ais Is the next group of layers to be a default group 12 layers n n number of layers in the next group in Segment no 4 1 1 Can winding layup angles ever be decision variables n n layer index 1 2 for layer no 1 5 5 Is this a new layer type y Y thickness winding angle material for layer index thickness for layer index no 5 1 0 1000000 winding angle deg for layer index no 5 0 0 material index 1 2 for layer index no 5 1 1 Any more layers or groups of layers in Segment no 4 n n choose external 0 or internal 1 rings h The HELP comment given for the stringers or isogrid does not apply here a If there are stringers the ring cross section will lie above the panel skin if the ring
93. 458930E 00 0 000000E 00 16846 18 1 484976E 00 0 000000E 00 18409 19 1 501850E 00 0 000000E 00 23457 20 1 509602E 00 0 000000E 00 21005 1 513893E 00 0 000000E 00 26293 1 515067E 00 0 000000E 00 18361 1 515148E 00 0 000000E 00 15717 1 515550E 00 0 000000E 00 21005 1 51 1 THROUGH 8 CRITICAL LOAD FACTOR COMBINATION LOAD SYSTEM A LOAD SYSTEM B DOF ROOT 1 501850E 00 0 000000E 00 18169 20 1 509599E 00 0 000000E 00 21005 21 1 513885E 00 0 000000E 00 15717 22 1 515059E 00 0 000000E 00 18361 23 1 515067E 00 0 000000E 00 25909 24 1 515507E 00 0 000000E 00 21005 25 1 519851E 00 0 000000E 00 12689 26 1 519851E 00 0 000000E 00 28937 27 1 53 1 THROUGH 8 CRITICAL LOAD FACTOR COMBINATION LOAD SYSTEM A LOAD SYSTEM B DOF ROOT 1 513885E 00 0 000000E 00 15333 22 1 515059E 00 0 000000E 00 18361 23 1 515067E 00 0 000000E 00 25909 24 1 515507E 00 0 000000E 00 21005 25 1 519851E 00 0 000000E 00 13073 26 1 519851E 00 0 000000E 00 28937 27 1 544794E 00 0 000000E 00 15525 28 yA BUNE PRRPRPRPPPR 544794E 00 15 roots skipped 17 roots skipped 4 THROUGH 21 roots skipped 27 roots skipped 8 8 1 549722E 00 1 549722E 00 0 000000E 00 cylstif out2 from STAGS run 7 eigenvalue shift 1 MAXIMUM NUMBER OF ITERATIONS CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES NO NNDUBWNE PRPRPRPRPRPPR EIGENVALUE 544794E 00 549722E 00 550753E 00 557151E 00 557151E 00 566488E 00 613298E 00 23457 57
94. 53 3 1 762175E 00 1 762175E 00 0 000000E 00 12905 4 1 871755E 00 1 871755E 00 0 000000E 00 15525 5 1 887114E 00 1 887114E 00 0 000000E 00 20813 6 1 890529E 00 1 890529E 00 0 000000E 00 18169 7 1 891057E 00 1 891057E 00 0 000000E 00 20813 8 1 891468E 00 1 891468E 00 0 000000E 00 15525 cylstif out2 from STAGS run 12 eigenvalue shift 1 73 34 roots skipped 4 eigenvalues sought MAXIMUM NUMBER OF ITERATIONS CONVERGENCE CRITERION HAS NOT BEEN SATISFIED FOR EIGENVALUES CRITICAL LOAD FACTOR COMBINATION 1 THROUGH 3 NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF ROOT 1 1 613298E 00 1 613298E 00 0 000000E 00 27416 34 2 1 642475E 00 1 642475E 00 0 000000E 00 26053 3 1 871754E 00 1 871754E 00 0 000000E 00 26101 35 cylstif out2 from STAGS run 13 eigenvalue shift 1 80 34 roots skipped 1 eigenvalue sought CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 1 CRITICAL LOAD FACTOR COMBINATION NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF ROOT 1 1 871755E 00 1 871755E 00 0 000000E 00 20813 35 xxkkkk NOTE There is a big eigenvalue hole betwee 1 613298 root 34 and 1 871754 root 35 Why Don t know why KKKKKKK cylstif out2 from STAGS run 14 eigenvalue shift 1 95 34 roots skipped 8 eigenvalues sought MAXIMUM NUMBER OF ITERATIONS CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 4 CONVERGENCE CRITERION HAS NOT BEEN SATISFIED FOR EIGENVALUES CRITICAL LOAD FACTOR COMBINATION 5 THROUGH 8 NO EIGENVALUE LO
95. 561E 04 Maximum value 5 10101E 04 9 p76 49 17 cylstif stagsunit innerfibstress 5x3 skin png stress in skin only 5 101E 04 5 001E 04 4 902E 04 4 802E 04 4 702E 04 4 603E 04 4 503E 04 4 403E 04 4 303E 04 4 204E 04 4 104E 04 4 004E 04 3 905E 04 3 805E 04 3 705E 04 3 606E 04 y 2 x NY 18 cylstif stagsunit innerfibstress skin zoom png zoomed view from previous plot 19 cylstif stagsunit outerfibstress skin zoom png outer fiber stress in the skin a Se f an N Ta i i TA Oe i z A 20 cylstif stagsunit innerfibstress webzoom png local stress concentrations at the web roots PANDA2 cannot capture this type of local concentration of stress at the edges y 2 smeared Ox 35 84 O y 13 14 Oz 35 63 aa NRS a Ww _ r a 9 Ect O aang o D fer o o SE 4 aw al Nana E F 5 0 Otte UA HE iep WwW oO _ wD O Q ADO ooon gt W 1 2 i D v l De oO d g o oO a4 Ow 2 zZ O O oa na Gg Ss oO pas y Z Eo 2 Of fe CC Ww v The critical inter ring buckling mode corresponds to the 5th eigenvalue The previous 4 eigenvalues correspond to various ring sidesway buckling modes without 21 cylstif stagsunit 6x3 smrstr eig5 png critical inter ring buckling mode participation of the panel skin with smeared stringers stringers kn y ie A LD ef SS Ty Ot ie kiN 4 k i SS rae ge k R
96. 672E 04 Subring axial Nx height 0 0000E 00 0 0000E 00 Axial equilibrium Nx added over x cross section off by 4 4211E 01 per cent Hoop equilibrium Ny added over y cross section off by 5 3541E 01 per cent EQUILIBRIUM FOR LOAD SET B Check for axial equilibrium with eff stringer web height HSTEFF 8 2012E 00 FNX Applied axial resultant Nx FNXTOT Computed value FNXSTR 1 I FNXSTR 2 I FNXSTR 3 I Nx in stringer fayflange web outflange FNXSKN I Nx in skin smeared stringers FNX FNXTOT FNXSKN I FNXSTR 1 I FNXSTR 2 I FNXSTR 3 1I 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 Substringer axial Nx height 0 0000E 00 0 0000E 00 Check for hoop equilibrium with effective ring web height HRGEFF 1 0167E 01 FNY Applied hoop resultant Ny FNYTOT Computed value FNXRNG 1 I FNXRNG 2 I FNXRNG 3 I Ny in ring fayflange web outflange FNYSKN I Ny in skin smeared rings FNY FNYTOT FNYSKN I FNXRNG 1 I FNXRNG 2 I FNXRNG 3 T 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 Subring axial Nx height 0 0000E 00 0 0000E 00 Axial equilibrium Nx added over x cross section off by 0 0000E 00 per cent Hoop equilibrium Ny added over y cross section off by 0 0000E 00 per cent PART 3 7 STAGSUNIT produces the file cylstif STG which is valid input for the PANDA2 processor STAGSUNIT The user provided input data during the STAGSUNIT interactive session has been saved in the file cylstif
97. 7 SLOPEX 0 00E 00 0 00E 00 0 00E 00 0 00E 00 0 00E 00 0 00E 00 0 00E 00 MWAVEX 1 1 2 4 0 1 1 NWAVEX 3 3 3 5 0 3 0 lines skipped to save space Buckling load factor before t s d 2 7174E 00 After t s d 2 4489E 00 lines skipped to save space Number of circumferential halfwaves in buckling pattern 3 0000E 00 Buckling load factor BEFORE knockdown for smeared stringers 2 4489E 00 Buckling load factor AFTER knockdown for smeared stringers 2 2966E 00 General buckling load factor before and after knockdown EIGGEN before modification by 5 factors below 2 2966E 00 Knockdown factor from modal imperfection s 1 0000E 00 Knockdown factor for smearing rings on cyl shell 9 0000E 01 Knockup factor to avoid twice accounting for t s d 1 0000E 00 lst modifying factor FKNMOD 1 or 1 EIG9X FMDKD9 1 0000E 00 2nd modifying factor EIGMR9 1 or EIGGNX EIGGEN 1 0000E 00 After knockdn EIGGEN FKNOCK 9 RNGKNK SHRFCT FKNMOD EIGMR9 2 0669E 00 The final general buckling load factor from PANDA2 2 0669 is conservative because the knockdown factors used in this case to compensate for the inherent un conservatveness of smearing rings and stringers are conservative in PANDA2 models in which ICONSV 1 Here is how the PANDA2 margins for general buckling vary with the conservativeness index ICONSV set equal to its three possible values in the cylstif OPT file MARGINS FOR CURRENT DESIGN LOAD CASE NO 1 SUBCASE NO 1 MAR MARGIN
98. 7 3416E 01 6 7542E 01 6 3220E 01 5 9983E 01 5 7526E 01 8 B RNG stiffener spacing b RNG seg NA layer NA 5 0000E 01 4 5000E 01 4 1400E 01 4 2049E 01 3 9896E 01 3 8262E 01 9 B2 RNG width of ring base b2 zero is allowed RNG seg 2 layer NA 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 10 H RNG height of stiffener type H for sketch h RNG seg 3 layer NA 1 0000E 01 1 1000E 01 1 1880E 01 1 1120E 01 1 0550E 01 1 0982E 01 11 W RNG width of outstanding flange of stiffener w RNG seg 4 layer NA 1 0000E 01 9 0000E 00 8 2800E 00 7 7501E 00 7 3533E 00 7 0877E 00 12 T 4 RNG thickness for layer index no 4 RNG seg 3 layer 1 8 1573E 01 7 3416E 01 6 7542E 01 6 3220E 01 5 9983E 01 6 1926E 01 13 T 5 RNG thickness for layer index no 5 RNG seg 4 layer 1 8 1573E 01 8 2849E 01 7 6221E 01 7 1343E 01 6 7690E 01 7 0463E 01 kkeAKKEe OBJECTIVE FOR 6 ITERATIONS x 1 WEIGHT OF THE ENTIRE PANEL 1 5889E 04 1 6113E 04 1 5595E 04 1 5209E 04 1 4999E 04 1 4895E 04 1 Absolute values of maximum constraint gradients GRDPLT 3 6548E 00 6 8547E 00 4 8373E 00 4 9903E 00 4 6780E 00 0 0000E 00 lines skipped to save space SUMMARY OF STATE OF THE DESIGN WITH EACH ITERATION ITERA WEIGHT FOR EACH LOAD SET ANY ABRUPT CHANGES IN MODE TION OF IQUICK NO OF CRITICAL MARGINS SLOPE CHANGE m n CHANGE NO PANEL LOAD SET NO gt 1 2 3 4 5 EIG RATIOS EIG RATIOS LOAD SET NO gt 1 2 3 1 2 3
99. 8E 00 258708E 00 324552E 00 EIGENVALUE 249418E 00 253260E 00 254130E 00 258708E 00 258708E 00 324550E 00 363465E 00 378948E 00 MAXIMUM NUMBER OF ITERATIONS CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES NO ONHDUBWNEH cylstif out2 from STAGS run 5 eigenvalue shift CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES NO OINHDUBWNEHE cylstif out2 from STAGS run 6 eigenvalue shift CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES NO PRPRPRPRPRPRPH PRPRPRPRPRPRPPH EIGENVALUE 458930E 00 484976E 00 501850E 00 509602E 00 513893E 00 515067E 00 515148E 00 515550E 00 EIGENVALUE 501850E 00 509599E 00 513885E 00 515059E 00 515067E 00 515507E 00 519851E 00 519851E 00 EIGENVALUE 513885E 00 515059E 00 515067E 00 515507E 00 519851E 00 519851E 00 1 258708E 00 0 000000E 00 12449 13 1 258708E 00 0 000000E 00 28313 14 1 324552E 00 0 000000E 00 20813 15 1 35 1 THROUGH 8 CRITICAL LOAD FACTOR COMBINATION LOAD SYSTEM A LOAD SYSTEM B DOF ROOT 1 249418E 00 0 000000E 00 26533 10 1 253260E 00 0 000000E 00 23025 11 1 254130E 00 0 000000E 00 21245 12 1 258708E 00 0 000000E 00 29177 13 1 258708E 00 0 000000E 00 12449 14 1 324550E 00 0 000000E 00 20813 15 1 363465E 00 0 000000E 00 20453 16 1 378948E 00 0 000000E 00 21269 17 1 45 1 THROUGH 3 CONVERGENCE CRITERION HAS NOT BEEN SATISFIED FOR EIGENVALUES CRITICAL LOAD FACTOR COMBINATION LOAD SYSTEM A LOAD SYSTEM B DOF ROOT 1
100. 97 99 101 103 105 107 109 111 113 115 117 119 121 123 Column numbers of sub stringer skin junctions ICSTSB i Major ring logic ILOGRG T Row numbers of major ring web skin junctions IROWRG i 1 7 13 19 25 31 37 43 49 55 Row numbers of sub ring skin junctions IRRGSB i All column numbers of stringer web skin junctions ICOLAL i 1 3 5 7 9 11 13 15 17 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 103 105 107 109 111 113 115 117 119 121 123 All row numbers of ring web skin junctions IROWAL i 1 7 13 19 25 31 37 43 49 55 EQUILIBRIUM FOR LOAD SET A Check for axial equilibrium with eff stringer web height HSTEFF 8 2012E 00 FNX Applied axial resultant Nx FNXTOT Computed value FNXSTR 1 1 FNXSTR 2 1 FNXSTR 3 I1 Nx in stringer fayflange web outflange FNXSKN I Nx in skin smeared stringers FNX FNXTOT FNXSKN TI FNXSTR 1 I FNXSTR 2 I FNXSTR 3 T 2 5000E 04 2 5111E 04 2 2451E 04 0 0000E 00 2 9133E 03 1 2079E 03 Substringer axial Nx height 0 0000E 00 0 0000E 00 Check for hoop equilibrium with effective ring web height HRGEFF 1 0167E 01 FNY Applied hoop resultant Ny FNYTOT Computed value FNXRNG 1 1I FNXRNG 2 1 FNXRNG 3 I Ny in ring fayflange web outflange FNYSKN I Ny in skin smeared rings FNY FNYTOT FNYSKN I FNXRNG 1 I FNXRNG 2 I FNXRNG 3 I 5 0000E 04 5 0268E 04 3 8195E 04 0 0000E 00 2 3209E 04 3 8
101. A Nxy 500 0000 Normal pressure in STAGS model in Load Set A p 0 Resultant e g lb in normal to the plane of screen Nx0 0 Resultant e g lb in in the plane of the screen Ny0 0 Normal pressure in STAGS model in Load Set B p0 1 000000 Starting load factor for Load System A STLD 1 0 000000 1 000000 Load factor increment for Load System A STEP 1 Maximum load factor for Load System A FACM 1 Starting load factor for Load System B STLD 2 Load factor increment for Load System B STEP 2 Maximum load factor for Load System B FACM 2 How many eigenvalues do you want NEIGS Choose element type 480 or 410 or 940 Have you obtained buckling modes from STAGS for this case Number of stringers in STAGS model of 360 deg cylinder Number of rings in the STAGS model of the panel Are there rings at the ends of the panel Number of finite elements between adjacent stringers Number of finite elements between adjacent rings Stringer model 1 or 2 or 3 or 4 or 5 Type H elp Ring model 1 or 2 or 3 or 4 or 5 Type H elp Reference surface of cyl l outer 0O middle 1l inner n OWW WO W Do you want to use fasteners they are like rigid links Are the stringers to be smeared out Are the rings to be smeared out Number of nodes over height of stiffener webs NODWEB Number of nodes over width of stringer flange NDFLGS Number of
102. AD SYSTEM A LOAD SYSTEM B DOF ROOT 1 1 925127E 00 1 925127E 00 0 000000E 00 32713 44 2 1 928869E 00 1 928869E 00 0 000000E 00 34489 45 3 1 971939E 00 1 971939E 00 0 000000E 00 20399 46 4 1 982155E 00 1 982155E 00 0 000000E 00 34285 47 5 1 987382E 00 1 987382E 00 0 000000E 00 34285 6 1 987598E 00 1 987598E 00 0 000000E 00 15111 7 1 988930E 00 1 988930E 00 0 000000E 00 26503 8 1 989121E 00 1 989121E 00 0 000000E 00 21215 cylstif out2 from STAGS run 15 eigenvalue shift 1 90 41 roots skipped 8 eigenvalues sought CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES CRITICAL LOAD FACTOR COMBINATION 1 T HROUGH NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF ROOT 1 1 886993E 00 1 886993E 00 0 000000E 00 20813 36 2 1 890303E 00 1 890303E 00 0 000000E 00 15525 37 3 1 890900E 00 1 890900E 00 0 000000E 00 20813 38 4 1 891182E 00 1 891182E 00 0 000000E 00 15525 39 5 1 896987E 00 1 896987E 00 0 000000E 00 12881 40 6 1 896987E 00 1 896987E 00 0 000000E 00 28745 41 7 1 904430E 00 1 904430E 00 0 000000E 00 26101 42 8 1 910033E 00 1 910033E 00 0 000000E 00 10053 43 lt inter ring buckling mixed with stringer sidesway cylstif out2 from STAGS run 16 eigenvalue shift 2 0 54 roots skipped 8 eigenvalues sought CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 8 CRITICAL LOAD FACTOR COMBINATION NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF ROOT 1 1 987379E 00 1 987379E 00 0 000000E 00 34285 48 2 1 987534E 00 1 987534E 00 0 00
103. D cleanpan BEG from begin DEC from decide OPT from mainsetup CHG from change CPL from chooseplot PAN from panel or panel2 STG from stagsunit or from stagsmodel These preserved files are valid input for the interactive processors begin decide mainsetup change chooseplot panel or panel2 stagsunit or stagsmodel respectively PART 1 2 Execute the PANDA2 processor called BEGIN in order to establish a starting design material properties boundary conditions bush gt begin Please enter PANDA2 case name cylstif KKKEKKKKKKKKKKKKE BEGIN KKKKKKKKKKKKKKKKKE Purpose of BEGIN is to permit you to provide a starting design in an interactive mode You give starting dimensions material properties allowables The interactive session is stored on a file called cylstif BEG in which cylstif is a name that you have chosen for the case cylstif must remain the same as you use all the PANDA2 processors In future runs of the same or a slightly modified case you will find it convenient to use the file cylstif BEG as input Rather than answer all the questions interactively you can use cylstif BEG or an edited version of cylstif BEG as input to BEGIN BEGIN also generates an output file called cylstif OPB cylstif OPB lists a summary of the case and if you choose the tutorial option the questions helps and your answers for each input datum kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
104. E 1 or 2 or 3 or 4 or 5 We also change the output index NPRINT from 0 to 1 as follows 1 NPRINT output index l min 0 good l ok 2 more 3 too much This is done only for the purpose of this presentation Ordinarily you would use NPRINT 0 or NPRINT 2 Next we execute MAINSETUP with the new values for ITYPE ITYPE 2 and NPRINT NPRINT 1 bush gt mainsetup Please enter PANDA2 case name cylstif Kk kk kk kk k k k k k k k k k MAINSETUP kkk k kk k k k k k k k k k k The purpose of this processor is to permit you to choose loads and initial imperfections Nx Ny Nxy Mx My Nxo Nyo p T iseg Wimp global Wimp local up to 5 sets of them safety factors for general instability panel instability local instability panel skin local instability stiffener parts and stress and strategy parameters for subsequent batch execution of an optimization analysis analysis type 1 or an analysis of a fixed design at fixed load levels analysis type 2 or an analysis of a fixed design for a single load set for monotonically increasing load levels test simulation analysis type 3 Results of the interactive session in MAINSETUP are saved on a file called cylstif OPT which will appear at the beginning of the cylstif OPM file when the mainprocessor batch run launched by your command PANDAOPT has been completed NOTE JUST HIT RETURN FOR DEFAULT VALUE OF INPUT DATUM IF PANDA2 REQUIRES AN INPUT IT WILL
105. E 00 from discrete model 1 8086E 00 Buckling load factor for ring with bending stiffness EI perit ntdn 2 1 EI r 3 p 2 4315E 00 Knockdown factor general buckling EIGR EIGRNG 7 4385E 01 END OF SECTION ON GENERATION OF KNOCKDOWN FACTOR FOR COMPENSATING FOR THE UNCONSERVATIVENESS OF SMEARING RINGS 4 7211E 05 2 3590E 05 4 9966E 01 3 1850E 01 Knockdown for smeared rings RNGKNZ 9 0000E 01 FNARCQ 3 0000E 00 lines skipped to save space CHAPTER 10 Compute knockdown factors and prebuckling bending associated with initial general inter ring local buckling modal imperfections See Ref 1E Also see Sections 13 and 14 and Tables 9 and 10 of Ref 1K lines skipped to save space CHAPTER 10 1 Compute knockdown factor and prebuckling bending associated with GENERAL buckling modal initial imperfection See Sectons 13 and 14 and Tables 9 and 10 of 1K for a detailed example lines skipped to save space CHAPTER 10 2 Compute knockdown factor and prebuckling bending associated with INTER RING buckling modal initial imperfection lines skipped to save space CHAPTER 10 3 Compute knockdown factor and prebuckling bending associated with LOCAL buckling modal initial imperfection lines skipped to save space CHAPTER 10 4 Present a summary of imperfection sensitivity results See Section 13 and Table 9 of 1K lines skipped to save space LOCAL INTER RING GENERAL BUCKLING BUCKLING BUCKLING RATIO
106. E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 cylstif out2 from STAGS run 10 eigenvalue shift MAXIMUM NUMBER OF ITERATIONS CONVERGENCE CRITERION HAS NOT BEEN SATISFIED FOR EIGENVALUES CRITICAL LOAD FACTOR COMBINATION LOAD SYSTEM A LOAD SYSTEM B NO o NAU BUNE PRPRPPRPRPRPH EIGENVALUE 549760E 00 550656E 00 557145E 00 557303E 00 566482E 00 613298E 00 715446E 00 744187E 00 1 PRPRPRPRPRPPR 549760E 00 550656E 00 557145E 00 557303E 00 566482E 00 613298E 00 715446E 00 744187E 00 0 000000E 00 0 000000E 00 ooo0oo0oo0oo 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 DOF 15525 18169 20813 12881 28745 20813 24766 63 DOF 26101 26101 20813 12881 28745 20813 27416 12449 65 DOF 18169 20813 28745 12881 20813 27416 23265 20375 1 71 DOF 23481 20813 28745 12881 20813 24766 25861 13001 29 ROOT 28 ROOT 33 roots skipped 34 roots skipped 1 THROUGH 34 roots skipped 1 THROUGH 34 roots skipped 1 THROUGH 8 8 8 cylstif out2 from STAGS run 11 eigenvalue shift 1 76 34 roots skipped MAXIMUM NUMBER OF ITERATIONS CONVERGENCE CRITERION HAS NOT BEEN SATISFIED FOR EIGENVALUES CRITICAL LOAD FACTOR COMBINATION 1 THROUGH 8 NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF 1 1 676389E 00 1 676389E 00 0 000000E 00 20789 2 1 700713E 00 1 700713E 00 0 000000E 00 129
107. E SEGMENTS OF A RING CROSS SECTION Do you want to impose minimum TOTAL thickness of any segment n n Do you want to impose maximum TOTAL thickness of any segment n n Use reduced effective stiffness in panel skin H elp Y or N h Generally answer Y in order to avoid unconservative designs However occasionally you may want to answer N in order to avoid too much conservativeness for cases for which you believe the panel skin is fully effective for overall bending of the panel You should answer Y if you panel has any local initial imperfection If the panel skin is permitted to buckle locally that is if the factor of safety for local buckling FSLOC is significantly less than unity e g FSLOC lt 0 9 then you should always answer Y A N answer may be suitable for panels in which the stringer spacing b is about the same as the stringer height h or width w such as may be the case for hat stiffened panels with closely pitched corrugated skin or for truss core panels provided that local buckling of the panel skin is not permitted to occur If you answer Y to this question reduced membrane stiffnesses C11 C12 C22 and C33 are used for the panel skin segments for calculation of overall bending of the panel under uniform pressure and for predictions of general instability load factors that are used for determination of amplification of axial bowing Use reduced effective stiffness in panel skin H elp Y or N y y
108. ENMODE 1 N 1 2 cylstif R Z EIGENMODE 2 N 1 3 cylstif R Z EIGENMODE 3 N_ 1 4 cylstif R Z RingLocation CR to QUIT Please choose the number of the file you wish to plot 1 Plotting Undeformed amp Deformed Axial Station as a function of Radius The PostScript file metafile ps has been created Please choose one of the three options below 1 Rename the PostScript file This is useful if you don t have access to a PostScript printer on your machine but you wish to save to a file so you can later transfer it to a different machine for printing Example mv metafile ps plotl ps 2 Enter an lpr command This is useful if your default printer is not PostScript but there is a PostScript printer available on your system Example lpr PApplelaser metafile ps 3 Press the return key This executes the command lpr metafile ps This assumes that your default printer is a PostScript printer Enter your command gt lt enter gt Printing PostScript plot on the default printer Text file s have been created containing plot data The names of the files explain to a greater or lesser extent what the data represent Some plot files contain data for more than one plot 1 cylstif R Z EIGENMODE 1 N 1 2 cylstif R Z EIGENMODE 2 N 1 3 cylstif R Z EIGENMODE 3 N_ 1 4 cylstif R Z RingLocation CR to QUIT Please choose the number of the file you wish to plot lt enter gt end of obtaining the plot fil
109. ETUP3 causes templates of the stiffness and load geometric matrices to be set up for the buckling problem involving a single panel module with skin and substringer which is used for local buckling analysis DESCRIPTION OF FILES GENERATED BY THIS CASE cylstif AL3 Input data for BOSOR4 type of preprocessor correponding to discretized single panel module consisting of skin and substringer cylstif CBL Contains part of cylstif data base For further information about files generated during operation of PANDA2 give the command HELPAN FILES The next module will cause to be generated matrix templates for solution of the local buckling eigenvalue problem in which the cross section of the panel module is discretized skin substringer according to the conventions used in BOSOR4 Normal termination setup3 still processing Please wait Executing pandaread lst pass Normal termination pandaread 1 Skin stringer panel module templates finished still processing Please wait Executing pandaread 2nd pass Normal termination pandaread 2 Entire smeared panel templates finished still processing Please wait Executing globst Normal termination globst Global model common blocks stored Executing pandaread 3rd pass Normal termination pandaread 3 skin ring panel module templates finished still processing Please wait Executing glbst2 Normal termination glbst2 skin ring panel module common blocks stored E
110. FACIM2 for local buckling in which EILOC9 EILOC8 EILOC7 are buckling load factors for the imperfect shell and EILOC91 EILOC81 EILOC71 are buckling load factors for the perfect shell The factors FACIM1 and FACIM2 are given by FACIM1 1 EILOC9 1 and FACIM2 1 EILOC91 1 for general buckling FACIM1 1 EILOC8 1 and FACIM2 1 EILOC81 1 for inter ring buckling and FACIM1 1 EILOC7 1 and FACIM2 1 EILOC71 1 for local buckling Choose ICONSV 1 or 0 or 1 or H elp ICONSV lt enter gt 1 Choose type of analysis ITYPE 1 or 2 or 3 or 4 or 5 h 1 means an optimization analysis will be performed Make sure that you have chosen decision variables linked variables geometrical inequality constraints and escape variables via DECIDE 2 means PANDA2 will perform a buckling stress analysis of a fixed design for up to 5 load sets 3 means PANDA2 will simulate a test of a panel with fixed design For one of the load sets the behavior of the panel under monotonically increasing loads will be investigated Note that this option requires that IQUICK 0 for that load set which is selected by the user Also the KOITER branch MUST be entered IIKOIT 1 4 means that margins will be calculated for all design variables fixed except one user selected variable Margins will be calculated for a sequence of designs in which the user selected variable is incremented from a user selected starting value to a use
111. February 28 2011 PANDA2 RUN STREAM STARTING FROM SCRATCH Commands from the user are in 16 pt bold face note the string bush gt is not part of the command typed by the user Optimization of an aluminum hydrostatically compressed cylindrical shell with T shaped stringers and T shaped rings The user provided name of the case is cylstif INTRODUCTION This file is long because in it are described not only executions of PANDA2 but also executions of BIGBOSOR4 and STAGS BIGBOSOR4 a shell of revolution analyzer and STAGS a general purpose code are used to verify PANDA2 predictions for the T stringer and T ring stiffened cylindrical shell optimized by PANDA2 PANDA2 has processors PANEL and PANEL2 which produce valid input files for BIGBOSOR4 and STAGSUNIT which produces valid input files for STAGS The example a hydrostatically compressed cylindrical shell with T shaped stringers and with T shaped rings is complex The optimized design exhibits many different kinds of buckling general buckling inter ring buckling local buckling as well as various types of buckling of the T shaped stringers and T shaped rings SUMMARY This report consists of three parts PART 1 0 First we find from PANDA2 an optimum design of an imperfect T stringer and T ring stiffened cylindrical shell made of aluminum The T stiffened cylindrical shell is 300 inches long and has a radius of 100 inches The T stringers are external and the
112. G LOADS FOLLOW AXIAL HALF WAVE NUMBER N 1 EIGENVALUES 1 21180E 00 1 21651E 00 1 22461E 00 xx x CRITICAL EIGENVALUE AND WAVENUMBER EIGCRT 1 2118E 00 NO OF AXIAL HALF WAVES NWVCRT 1 ee ee ee ee ee ee xxx k EIGENVALUES AND MODE SHAPES EIGENVALUE AXIAL HALF WAVES PART 2 4 Compare predictions from BIGBOSOR4 with those from PANDA2 that are listed in PART 1 19 CHAPTER 14 LOCAL buckling Compare with the eigenvalue from CHAPTER 14 of the PANDA2 file cylstif OPM for the perfect shell BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DISCRETIZED MODEL skin stringer discretized module of local buckling AXIAL BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KNOCKDOWN ANISOTROPY M EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 1 1 21563E 00 9 83375E 01 1 00000E 00 1 19542E 00 PART 2 5 Execute the BIGBOSOR4 processor called bosorplot in order to get a plot of the critical LOCAL buckling mode Get a plot of the buckling mode bush gt bosorplot Please enter the BIGBOSOR4 case name cylstif Do you want to use Xgraph or create a PostScript file Choose X or P p One maybe Two moments please Text file s have been created containing plot data The names of the files explain to a greater or lesser extent what the data represent Some plot files contain data for more than one plot 1 cylstif R Z EIG
113. Hawaii April 2007 lines skipped to save space Skipping the NONLINEAR PART of the KOITER posbuckling analysis because the user indicates in the OPT file that he she wants to skip it and because IICURV 1 panel skin is curved in the single discretized skin stringer module model lines skipped to save space LOCAL BIFURCATION BUCKLING LOAD FACTOR ESTIMATES AND AMPLITUDE Wo OF LOCAL IMPERFECTION Wo buckling mode Critical number of axial half waves 1 Slope of buckling nodal lines from Koiter Theory m 1 71E 03 Knockdown factor for C44 C45 C55 for transv shear 9 83E 01 Local buckling load Factor from Koiter type Theory 1 21E 00 Load Factor from BOSOR4 type panel module model 1 20E 00 BOSOR4 type load factor without knockdowns for effects of anisotropy e g C 4 6 of the skin transverse shear def or in plane shear loading 1 22E 00 Amplitude Wo of local imperfection 3 8448E 02 lines skipped to save space CHAPTER 17 Compute stresses in layers and at various locations in skin stringer module model including local post buckling if any Compute stringer popoff constraints Figs 5 7 in 1A Local post buckling such as that shown in Figs 48 amp 49 of 1A is included Therefore SUBROUTINE STRTHK is used lines skipped to save space Margin 2 7265E 01 eff stress matl 1 SKN Dseg 2 node 6 layer 1 z 0 3845 MID FS 1 lines skipped to save space CHAPTER 18 Present summary of state of loaded imperfe
114. LUE DEFINITION 1 0 0 1 011E 01 B STR stiffener spacing b 2 STR 2 0 3 370E 00 B2 STR width of stringer base b2 must 3 STR 3 0 7 817E 00 H STR height of stiffener type H for s 4 STR 4 0 2 534E 00 W STR width of outstanding flange of st 5 SKN 1 1 7 690E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 2 038E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 8 450E 02 T 3 STR thickness for layer index no 3 8 0 0 3 185E 01 B RNG stiffener spacing b RNG seg NA 9 RNG 2 0 0 000E 00 B2 RNG width of ring base b2 zero is a 10 RNG 3 0 9 783E 00 H RNG height of stiffener type H for s 11 RNG 4 0 4 304E 00 W RNG width of outstanding flange of st 12 RNG 3 1 5 673E 01 T 4 RNG thickness for layer index no 4 13 RNG Number of parameter to change 1 4 1 9 452E 01 T 5 RNG thickness for layer index no 5 2 3 4 h Choose an index from the left most column in the above table Number of parameter to change 1 1 New value of the parameter 10 110 10 11000 2 3 1 Want to change any other parameters in this set y Y PARAMETERS WHICH CAN BE CHANGED VAR STR SEG LAYER NO RNG 1 2 STR 3 STR 4 STR 5 SKN 6 STR 7 STR 8 9 RNG 10 RNG 11 RNG 12 RNG 13 RNG Number of parameter to change 1 2 New value of the parameter 3 3698 3 369800 NO BPW BRWNHOKBWE BWNO NO rFPRrROOOORRFFOCOCOO CURRENT VALUE 1 011E 01 3 370E 00 7 817E 00 2 534E 00 7 690E 01
115. My in which Nx0 p and Ny0 p are stress resultants induced by the normal pressure considered in this example to be part of Load Set B it is permitted to put the pressure in Load Set A however You are allowed to provide up to 5 sets of loads imperfections and factors of safety that is up to 5 sets of Nx Ny Nxy Mx My Nx0 Ny0 p Wimp global Wimp local FSGEN FSPAN FSLOC FSBSTR FSSTR and temperature distributions PANDA2 will generate buckling and stress or strain constraints corresponding to each of the load and imperfection sets that you provide The resulting design will be the best that PANDA2 can find that is subjected during its mission to all of the load sets If the panel is clamped in the prebuckling phase and if there is applied pressure p then those load sets with non zero p will each have two subcases the first corresponding to conditions at the midlength of the panel and the second to conditions at the panel ends Two subcases are also run for cylindrical panels with rings Subcase 1 corres ponds to conditions midway between adjacent rings and Subcase 2 corresponds to conditions at the rings For each load set Nx Ny Nxy you will have to provide five factors of safety FSGEN FSPAN FSLOC FSBSTR and FSSTR FSGEN pertains to general instability buckling modes which include both rings and stringers FSPAN pertains to panel instability buckling modes for which the rings rotate only and f
116. NDAOPT has been completed NOTE JUST HIT RETURN FOR DEFAULT VALUE OF INPUT DATUM IF PANDA2 REQUIRES AN INPUT IT WILL SAY PLEASE SAY SOMETHING KKK KKK KKK KKK KKK KKK KKK KKK RK kkk kkk kkk KKK KKK RKKK RKKK KK Are you correcting adding to or using an existing file y Output from MAINSETUP rolls by fast on the screen bush gt pandaopt The purpose of PANDAOPT is to launch the batch run which performs optimization or buckling according to the strategy parameters established the last time you did a MAINSETUP Output from PANDAOPT is stored in a file called casename OPM in which casename is the name of the case You will want to examine casename OPM as soon as PANDAOPT is finished Enter case name cylstif B background F foreground or Q NOS network queue system f Running PANDA2 pandaopt case cylstif Executing main Normal termination main still processing Please wait Executing store Normal termination store still processing Please wait cylstif mainprocessor run completed successfully Menu PANDAOPT CHOOSEPLOT MAINSETUP CHANGE Please examine the files cylstif OPM cylstif OPP and cylstif OPI If ITYPE 1 print the file called cylstif OPP If ITYPE 3 or 4 print the file called cylstif OPI Run PANDAOPT several times for optimization Inspect the cylstif OPM file to make sure that your input data for CHANGE are correct compare the cylstif OPM file with the cylstif OPM file listed ab
117. NG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 11 11 Lower bound of variable no 11 0 5 0 5000000 Upper bound of variable no 11 10 10 00000 Any more decision variables Y or N y Y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for lay
118. NOTE END NOTE Next provide applied resultants Nx Ny Nxy Mx My and Nx0 Ny0 which are considered to be applied to the panel edges These are stress resultants in units for example of lb in for the in plane loads Nx Ny Nxy and in lb in for the moment resultants Mx My Nx Ny Nxy Mx My constitute part of Load Set A eigenvalue loads Nx0 Ny0O are part of Load Set B fixed and uniform loads In the absence of normal pressure the loads corresponding to general instability bifurcation buckling are given by Nx crit Nx0 T Nx0 eigenvalue Factor of safety Nx Ny crit Ny0 T Ny0 eigenvalue Factor of safety Ny Nxy crit eigenvalue Factor of safety Nxy Mx crit eigenvalue Factor of safety Mx My crit eigenvalue Factor of safety My in which Nx0 T and Ny0 T are the stress resultants from curing and temperature loading considered in this example to be part of Load Set B it is permitted to have them in Load Set A however Also provide uniform normal pressure p The pressure p can be considered either as part of Load Set A or as part of Load Set B If the pressure is part of Load set B the loads corresponding to bifurcation buckling are given by Nx crit Nx0 T Nx0 Nx0 p eigenvalue Factor of safety Nx Ny crit Ny0 T Ny0 Ny0 p eigenvalue Factor of safety Ny Nxy crit eigenvalue Factor of safety Nxy Mx crit eigenvalue Factor of safety Mx My crit eigenvalue Factor of safety
119. OCKDOWN ANISOTROPY M EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 1 1 21563E 00 9 83375E 01 1 00000E 00 1 19542E 00 PART 3 12 Produce and run a slightly different STAGS model Run a STAGS model again this time with the use of different input data as the last two entries of the cylstif STG file The new cylstif STG file follows cylstif STG file input for STAGSUNIT n Do you want a tutorial session and tutorial output 1 Choose type of STAGS analysis 1 3 4 5 6 INDIC 0 Restart from ISTARTth load step 0 lst nonlinear soln ISTART 1 155000 Local buckling load factor from PANDA2 EIGLOC y Are the dimensions in this case in inches 0 Nonlinear 0 or linear 1 kinematic relations ILIN 1 Type 1 for closed 360 deg cyl shell 0 otherwise ITOTAL 300 X direction length of the STAGS model of the panel XSTAGS 628 3185 Panel length in the plane of the screen L2 Is the nodal point spacing uniform along the stringer axis 51 Number of nodes in the X direction NODEX 101 Number of nodes in the Y direction NODEY 25000 00 Resultant e g lb in normal to the plane of screen Nx 50000 00 Resultant e g lb in in the plane of the screen Ny 0 000000 In plane shear in load set A Nxy 500 0000 Normal pressure in STAGS model in Load Set A p 0 Resultant e g lb in normal to the plane of screen Nx0 0 Resultant e g lb in in the plane of the screen Ny0 0 Normal pressure in STAGS mod
120. OS network queue system b H high or L low priority 1 Diagnostics will be mailed to you upon program termination 1 9539 9541 bush gt ps PID TTY TIME CMD 8496 ptsl 00 00 00 tcsh 9539 ptsl 00 00 00 tcsh 9540 ptsl 00 00 00 csh 9541 ptsl 00 00 00 mail 9607 ptsl 00 00 06 main linux 9608 ptsl 00 00 00 ps bush gt usr sbin sendmail No such file or directory In this case the SUPEROPT run bombed At the time of the bomb the cylstif OPP file abridged was as follows abridged cylstif OPP file 1 B STR stiffener spacing b STR seg NA layer NA 3 0000E 01 3 3000E 01 3 5640E 01 3 7920E 01 3 9861E 01 4 1494E 01 2 B2 STR width of stringer base b2 must be gt 0 see Help STR seg 2 lay 9 9990E 00 1 0999E 01 1 1879E 01 1 2639E 01 1 3286E 01 1 3830E 01 3 H STR height of stiffener type H for sketch h STR seg 3 layer NA 1 0000E 01 9 0000E 00 8 2800E 00 7 7501E 00 7 3533E 00 7 0521E 00 4 W STR width of outstanding flange of stiffener w STR seg 4 layer NA 1 0000E 01 1 0000E 01 9 2000E 00 8 6112E 00 8 2114E 00 7 8751E 00 5 T 1 SKN thickness for layer index no 1 SKN seg 1 layer 1 8 1573E 01 8 9730E 01 9 0890E 01 9 6707E 01 1 0000E 00 1 0000E 00 6 T 2 STR thickness for layer index no 2 STR seg 3 layer 1 8 1573E 01 8 9730E 01 9 6909E 01 1 0000E 00 1 0000E 00 9 5904E 01 7 T 3 STR thickness for layer index no 3 STR seg 4 layer 1 8 1573E 01
121. RINT 0 means print modes iteration data END D 2 rec 1 NEIGS number of eigenvalues sought BEGIN D 3 rec 8 085E 01 SHIFT initial eigenvalue shift 0 000E 00 EIGA lower bound of eigenvalue range 0 000E 00 EIGB upper bound of eigenvalue range END D 3 rec end of STAGS input file cylstif bin The cylstif inp file is very large and so is not completely listed here The beginning and end of cylstif inp are as follows beginning of the long STAGS input file cylstif inp cylstif STAGS INPUT FOR STIFFENED CYL STAGSUNIT SHELL UNITS C C Begin B 1 input data IGRAV 0 means g 386 4 inches per sec 2 else B 4 ICHECK 0 means normal execution ILIST 0 means normal batch oriented output INCBC 0 buck bcs same as prebuc 1 different NRUNIT 0 means plot entire model NROTS 3 means plot model with 3 rotations as on B 1b KDEV 1 means use PostScript file format for plot END B 1 IROT 1 means rotation about global X axis BEGIN B 1b se os SSS FPOWNDrFRFDWOOO 3 584E 01 ROT 0 means rotate 0 deg about global X axis END B 1b 2 IROT 2 means rotation about global Y axis BEGIN B 1b 1 314E 01 ROT 80 means rotate 80 deg about global Y axis END B 1b 3 IROT 3 means rotation about global Z axis BEGIN B 1b 3 563E 01 ROT 0 means rotate 0 deg about global Z axis END B 1b C C Begin B 2 input data 145 NUNITS number of shell units BEGIN B
122. RNG height of stiffener type H for s W RNG width of outstanding flange of st T 4 RNG thickness for layer index no 4 T 5 RNG thickness for layer index no 5 2 3 13 Want to change any other parameters in this set n n Do you want to change values of fixed parameters n n Do you want to change values of allowables n n DESCRIPTION OF FILES GENERATED BY THIS CASE cylstif CHG Summary of interactive session you have just completed This file can be edited and used for future runs of CHANGE cylstif CBL Contains part of cylstif data base cylstif OPC Output from CHANGE Please list this file and inspect it and the cylstif CHG file carefully before proceeding For further information about files generated during operation of PANDA2 give the command HELPAN FILES Next give the commands SETUP etc a end of the CHANGE interactive session The input for the CHANGE interactive session are saved in the file cylstif CHG A list of this file follows list of the file cylstif CHG input for CHANGE n Do you want a tutorial session and tutorial output y Do you want to change any values in Parameter Set No 1 1 Number of parameter to change 1 2 3 10 11000 New value of the parameter y Want to change any other parameters in this set 2 Number of parameter to change 1 2 3 3 369800 New value of the parameter y Want to change any o
123. S OF BUCKLING LOADS FROM ARBOCZ THEORY TO THOSE FROM PANDA2 THEORY FOR THE PERFECT STRUCTURE ARBOCZ PANDAZ2 1 0000E 00 1 0000E 00 1 0000E 00 KNOCKDOWN FACTORS FOR IMPERFECTIONS DERIVED FROM PANDA2 THEORY VS THOSE FROM ARBOCZ 1992 UPDATE OF KOITERs 1963 SPECIAL THEORY FROM PANDA2 THEORY 1 0000E 00 1 0000E 00 1 0000E 00 FROM ARBOCZ THEORY 1 0000E 00 1 0000E 00 1 0000E 00 THE GOVERNING KNOCKDOWN FACTOR FOR EACH TYPE OF BUCKLING LOCAL INTER RING GENERAL IS SET EQUAL TO THE MINIMUM KNOCKDOWN FACTOR FOR THAT TYPE OF BUCKLING REDUCED FURTHER BY THE RATIO ARBOCZ PANDA2 FOR THE PERFECT PANEL IF THE RATIO ARBOCZ PANDA2 IS LESS THAN UNITY The ARBOCZ theory is used only if ICONSV 1 ICONSV 1 USED NOW IN PANDA2 1 0000E 00 1 0000E 00 1 0000E 00 FACTOR APPLIED TO 1 0000E 00 FOR ALTERNATIVE SOLUTION FOR GENERAL BUCKLING WITH DISCRETE STIFFENERS FKNMLT 1 0000E 00 FACTOR APPLIED TO 1 0000E 00 FOR ALTERNATIVE SOLUTION FOR INTER RING BUCKLING WITH DISCRETE STIFFENERS FKNMLS 1 0000E 00 x NOTE IF THERE IS INTERNAL PRESSURE THESE KNOCKDOWN FACTORS MAY BE CHANGED AS NOTED BELOW lines skipped to save space CHAPTER 11 Get change in stress resultants Nx Ny Nxy in various segments of the skin stringer module during prebuckling bending of the imperfect shell Also do PANDA type 1B local inter ring gen eral buckling analyses and PANDA type stringer web and ring web buckling analyses to get knockdown factors to compensate for t
124. SCALE RNGMIN RGMAX 1 0 35840000E 02 SPL 6 IROT ROT 2 0 13140000E 02 SPL 6 IROT ROT 3 0 35630001E 02 SPL 6 IROT ROT end of cylstif pin file The stress fringe plot is contained in the following file 19 cylstif stagsunit outerfibstress skin zoom png STAGS predicts outer fiber effective stresses that are about the same as the inner fiber effective stresses because there is not much bending of the optimized stiffened shell The maximum outer fiber effective stress in the skin predicted by STAGS is 50250 psi compared to 51010 psi for the maximum inner fiber effective stress in the skin The STAGS model exhibits stress concentrations in the stringer webs near the roots of the stringer webs These stress concentrations cannot be predicted by PANDA2 of course In actual stiffened cylindrical shells the wall thicknesses would be increased in the immediate neighborhoods of the curved edges of the shell in order to reduce possible local stress concentrations there The very local stress concentrations at the roots of three of the stringer webs are displayed in the file 20 cylstif stagsunit innerfibstress webzoom png The maximum effective stress 57860 occurs at the roots of the stringer webs at the ends of the shell PART 3 21 Produce and run a different STAGS model one which again covers only a small 6 x 3 bay sub domain of the entire shell with all ring segments modeled as flexible shell uni
125. SCRETIZED MODEL skin stringer discretized module of local buckling AXIAL BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KNOCKDOWN ANISOTROPY M EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 1 1 21563E 00 9 83375E 01 1 00000E 00 1 19542E 00 The latest buckling mode from STAGS is shown in the plot 10 cylstif stagsunit eigl rigidends png It is seen that this mode is no longer confined to the ring bays nearest the two ends of the cylindrical shell and that there is much better agreement with the predictions from BIGBOSOR4 and PANDA2 PART 3 13 Produce and run a different STAGS model one with smeared stringers Run a STAGS model again this time with the use of different input data in cylstif STG Now the stringers are smeared out and the last two entries are changed back from 1 to 0 The new cylstif STG file follows cylstif STG file input for STAGSUNIT n Do you want a tutorial session and tutorial output 1 Choose type of STAGS analysis 1 3 4 5 6 INDIC 0 Restart from ISTARTth load step 0 lst nonlinear soln ISTART 1 155000 Local buckling load factor from PANDA2 EIGLOC y Are the dimensions in this case in inches 0 Nonlinear 0 or linear 1 kinematic relations ILIN 1 Type 1 for closed 360 deg cyl shell 0 otherwise ITOTAL 300 X direction length of the STAGS model
126. STG A list of the file cylstif STG follows 1 155000 y 3 628 3185 1 25000 00 50000 00 0 000000 500 0000 1 000000 0 000000 1 000000 55 p lt BBS 0 1 00 51 01 0 0 0 oon TU TT TT TD TTD TTD TA TAD TATA DNDN DAN DNDANDNDAAnDNNnAnNnNUnNnNnUnNUnNnN the cylstif STG file input for STAGSUNIT Do you want a tutorial session and tutorial output Choose type of STAGS analysis 1 3 4 5 6 INDIC Restart from ISTARTth load step 0 1st nonlinear soln ISTART Local buckling load factor from PANDA2 EIGLOC Are the dimensions in this case in inches Nonlinear 0 or linear 1 kinematic relations ILIN Type 1 for closed 360 deg cyl shell 0 otherwise ITOTAL X direction length of the STAGS model of the panel XSTAGS Panel length in the plane of the screen L2 Is the nodal point spacing uniform along the stringer axis Number of nodes in the X direction NODEX Number of nodes in the Y direction NODEY Resultant e g lb in normal to the plane of screen Nx Resultant e g lb in in the plane of the screen Ny In plane shear in load set A Nxy Normal pressure in STAGS model in Load Set A p Resultant e g lb in normal to the plane of screen Nx0 Resultant e g lb in in the plane of the screen Ny0 Normal pressure in STAGS model in Load Set B p0 Starting load factor for Load System A STLD 1 Load factor increment for Load System A STEP 1 Maximum load factor for Load
127. SUNIT bush gt stagsunit Please enter PANDA2 case name cylstif kkkkkkkkkkkkkxkkk STAGSUNIT k kkkkkkkkkkkk The purpose of STAGSUNIT is to produce input files NAME inp NAME bin and NAME ppn for a multi module model of a panel NAME is your name for the case The files NAME inp NAME bin can be used as input for the STAGS computer program STAGS is a general finite element code for the nonlinear static and dynamic analysis of stiffened shell structures You should use STAGS to check the load carrying capacity of the panels you designed with PANDA2 The file NAME ppn can be used directly as input for the STAGS postprocessor POSTP STAGSUNIT also creates a file called NAME STG which can be used as input for future runs of STAGSUNIT kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Are you correcting adding to or using an existing file n n Do you want a tutorial session and tutorial output n n Choose type of STAGS analysis 1 3 4 5 6 INDIC h INDIC 1 means linear bifurcation buckling analysis The purposes are a to compare with PANDA2 predictions for local and or general buckling load factors and mode shapes b to obtain one or more buckling mode shapes to be used later with an INDIC 3 nonlinear analysis of an imperfect shell The imperfections are in the shapes of user selected buckling modes predicted with the INDIC 1 analysis INDIC 3 means nonlinear static analysis over a user pro
128. T PANDA2 will explore all of the load cases and subcases The test for possible elimination of a load subcase is applied only after completion of all calculations for the first design iteration If the test on minimum margin for a load subcase indicates that that subcase should be skipped it will be skipped for all remaining design iterations in the current PANDAOPT except the last during which calculations for that load subcase are reintroduced If that last iteration shows any negative margins you must raise the value of FMARG before executing PANDAOPT again Otherwise the design that evolves will have negative margins FMARG Skip load case with min margin greater than FMARG lt enter gt 1 000000 DESCRIPTION OF FILES GENERATED BY THIS CASE cylstif OPT Summary of interactive session you have just completed This file can be edited and used for future runs of MAINSETUP cylstif CBL Contains part of cylstif data base cylstif OPM Output from MAINSETUP Please list this file and inspect it and the cylstif OPT file carefully before proceeding NOTE The cylstif OPM file will be empty unless the session just finished was a tutorial For further information about files generated during operation of PANDA2 give the command HELPAN FILES Next give the command CHOOSETEMP or PANDAOPT or SUPEROPT IN ORDER TO AVOID FALSE CONVERGENCE OF THE DESIGN BE SURE TO RUN PANDAOPT MANY TIMES DURING AN OPTIMIZATION INSPECT THE cylsti
129. T rings are internal The loading is uniform axial compression Nx p x r 2 and uniform circumferential compression Ny p x r in which p is the uniform external pressure The imperfection is in the form of the general buckling mode After we find an optimum design via two executions of the PANDA2 processor called SUPEROPT we obtain predictions for that same optimum design from an analysis in which the amplitude of the general buckling modal imperfection is set equal to zero PART 2 0 Second we use the PANDA2 processors PANEL and PANEL2 to set up BIGBOSOR4 models then run BIGBOSOR4 and compare results with the predictions from PANDA2 for the optimized design The shell is perfect PART 3 0 Third we use the PANDA2 processor STAGSUNIT to set up STAGS models then compare the results from STAGS with predictions from BIGBOSOR4 and PANDA2 for the optimized design The shell is perfect TABLE OF CONTENTS kkkkxkkkkkkkkkkkkkkkkkkkkkkkkkkkk PART 1 0 Processing with PANDA2 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk PART 1 1 PART 1 2 PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART Activate the PANDA2 commands Execute the PANDA2 processor called BEGIN in order to establish a starting design material properties boundary conditions Execute the PANDA2 processor called SETUP SETUP sets up templates for BOSOR4 type of models Execute the PANDA2 proc
130. The developer of PANDA2 now almost always uses ISAND 1 Don t worry about computer time Computers run much faster now than they did when the following paragraph was written You should always first do optimization first with ISAND 0 On the last iteration for each PANDAOPT PANDA2 automatically checks buckling load factors with ISAND 1 when the user provides ISAND 0 in MAINSETUP If results from these last iterations are significantly different from those corresponding to ISAND 0 then the optimization must be run with ISAND 1 or 2 ISAND 1 or 2 requires much more computer time than does ISAND 0 Results from ISAND 2 are rarely different from those from ISAND 1 Index for type of shell theory 0 or 1 or 2 ISAND h ISAND 0 means Donnell theory is used with appropriate correction for live pressure effect ISAND 1 means Sanders theory is used See PANDA2 NEWS ITEM 128 410 for details ISAND 2 means Marlowe theory is used see PANDA2 NEWS ITEM 411 for details The developer of PANDA2 now almost always uses ISAND 1 Don t worry about computer time Computers run much faster now than they did when the following paragraph was written Generally use ISAND 0 as it runs much faster on the computer In optimization runs ITYPE 1 in which ISAND 0 PANDA2 automatically checks margins with use of ISAND 1 after the last design iteration in the current set of design iterations If you use ISAND 0 che
131. WEIGHT OF RINGS 2 8460E 03 SPECIFIC WEIGHT WEIGHT AREA OF STIFFENED PANEL 1 2497E 01 IN ORDER TO AVOID FALSE CONVERGENCE OF THE DESIGN BE SURE TO RUN PANDAOPT MANY TIMES DURING AN OPTIMIZATION INSPECT THE cylstif OPP FILE AFTER EACH OPTIMIZATION RUN OR BETTER YET RUN SUPEROPT xx NOTE It is almost always best to set the number of xxxx iterations per execution of PANDAOPT equal to 5 RRKK x in response to the following prompt in MAINSETUP How many design iterations permitted in this run 5 to 25 xx Hence the OPT file should almost always have the x following line in it RRKK 5 How many design iterations in this run 5 to 25 kkxkxkxkkkkkkkkkkkkkkkxkk k END OF cylstif OPM FILE RR RRKKKKKKKKEKE end of the cylstif OPM file fixed optimum design In the list above MARGINS FOR CURRENT DESIGN LOAD CASE NO 1 SUBCASE NO 1 means conditions at midbay in this case midway between adjacent rings SUBCASE 1 MARGINS FOR CURRENT DESIGN LOAD CASE NO 1 SUBCASE NO 2 means conditions at a ring station SUBCASE 2 PART 1 15 Execute the PANDA2 processor called CHANGE in order to archive the optimized design Next we wish to save the optimized design by executing the interactive session bush gt change CHANGE as follows Please enter PANDA2 case name cylstif kkkkkkkkkkkkkkkk kk kkkkxkkkkkkkkkkkkkkk CHANGE You use CHANGE to change parameters wi
132. ab iwalll eps2 ty 4 4 3 8672E 04 1 0000E 07 4 0912E 03 9 4524E 01 EQUILIBRIUM FOR LOAD SET A Check for axial equilibrium with nominal stringer web height H 1 7 8167E 00 FNX Applied axial resultant Nx FNXTOT Computed value FNXSTR 1 1 FNXSTR 2 1 FNXSTR 3 I1 Nx in stringer fayflange web outflange FNXSKN I Nx in skin smeared stringers FNX FNXTOT FNXSKN I FNXSTR 1 I FNXSTR 2 I FNXSTR 3 I 2 5000E 04 2 5000E 04 2 2451E 04 0 0000E 00 2 9133E 03 1 2079E 03 Substringer axial Nx height 0 0000E 00 0 0000E 00 Check for hoop equilibrium with nominal ring web height H 2 9 7830E 00 FNY Applied hoop resultant Ny FNYTOT Computed value FNXRNG 1 1I FNXRNG 2 1I FNXRNG 3 I Ny in ring fayflange web outflange FNYSKN I Ny in skin smeared rings FNY FNYTOT FNYSKN I FNXRNG 1 I FNXRNG 2 I FNXRNG 3 I 5 0000E 04 5 0000E 04 3 8195E 04 0 0000E 00 2 3209E 04 3 8672E 04 Subring axial Nx height 0 0000E 00 0 0000E 00 Axial equilibrium Nx added over x cross section off by 0 0000E 00 per cent Hoop equilibrium Ny added over y cross section off by 0 0000E 00 per cent Membrane constitutive coefficients used to get EPS1 and EPS2 CS0 1 1 CS0 1 2 CS0 2 2 1 0233E 07 2 5350E 06 1 1335E 07 stringer web iwalll fnxstr 2 eltab iwalll epsl tx 3 1 0 0000E 00 1 0000E 07 0 0000E 00 2 0380E 01 strng outflange iwalll fnxstr 3 eltab iwalll epsl tx 4 2 0 0000E 00 1 0000E 07 0 0000E 00 8 4496E 02 ring web iwa
133. ad factor There are many panels and loadings for which the local buckling load factor versus the number of axial halfwaves has more than one minimum If you answer Y PANDA2 will search for critical local buckling load factors over two ranges of axial halfwaves a high range and a low range The developer of PANDA2 always answers Y Don t worry about computer time The next paragraph was written when computers were much slower Generally in order to ensure reliability you should answer this question Y However as you gain more experience with PANDA2 you may occasionally want to answer N since quite a bit of computer time can be saved by doing so especially if you are doing optimization You can always do preliminary optimization in which you answer N no low wavenumber search followed by more refined and more costly optimization runs in which you answer Y Do you want to perform a low axial wavenumber search y y Factor of safety for general instability FSGEN 1 h You can use FSGEN 1 0 if your applied load set corresponds to the ULTIMATE load condition in constrast to LIMIT load or OPERATING load and if you specify reasonable ampltiudes for initial imperfections Wimpg Wimpgl Wimpg2 Wpan Wloc If you do NOT specify amplitudes for Wimpg etc and or if the applied load is less than that corresponding to the ULTIMATE condition then the factor of safety FSGEN should account for unknown initial imperfections an
134. ally used by PANDA2 is 1 675 x 0 54998 0 92122 You may however want to answer the question N For example if you wish to use PANDA2 to evaluate a damaged panel with a known probably rather large initial imperfection you will not want PANDA2 to take charge and automatically modify the imperfection amplitude as it did in the above example Do you want PANDA2 to change imperfection amplitudes see H elp 1 y Y PANDA2 will next ask you to provide an axial halfwavelength of the general buckling modal imperfection For axially stiffened panels or panels under external pressure or flat panels please use the axial length of the panel PANDA2 uses the axial half wavelength you give here to change your given amplitude of the general buckling modal imperfection if the axial halfwavelength of the general buckling mode of the perfect shell turns out to be different from that you will next provide here imperfection amplitude becomes smaller if the axial halfwavelength of the critical buckling mode of the perfect shell is shorter than that you provide here and larger if it is longer than that you will provide here The purpose of this strategy is to prevent wild swings in margins corresponding to small changes in design caused by abruptly different critical general buckling mode shapes Please see 17 and ITEM NO 525 of panda2 doc panda2 news for more details Axial halfwavelength of typical general buckling mode AXLWAV 1
135. alue INDIC 1 and transient INDIC 6 analysis types Maximum load factor for Load System A FACM 1 1 0 1 000000 Starting load factor for Load System B STLD 2 0 0 Load factor increment for Load System B STEP 2 0 0 Maximum load factor for Load System B FACM 2 0 0 How many eigenvalues do you want NEIGS h This input datum is for the STAGS input file If the STAGS analysis type INDIC 1 buckling of unloaded structure you will probably want NEIGS 1 to 8 If the STAGS analysis type INDIC 5 vibration of loaded structure you will probably want NEIGS 1 The purpose of the eigenvalue analysis in this case is to establish a reasonable estimate for the time step in a subsequent dynamic response analysis If the STAGS analysis type INDIC 4 buckling of loaded structure you may well want to use NEIGS gt 1 NEIGS must be less than twenty Probably should be from 4 to 8 How many eigenvalues do you want NEIGS 1 1 Choose element type 480 or 410 or 940 h Descriptions of the 480 410 and 940 elements appear in the STAGS user s manual The 480 finite element is the one favored by the developer of PANDA2 The 940 element usually converges from above Choose element type 480 or 410 or 940 480 480 Have you obtained buckling modes from STAGS for this case h In order to include the effect of initial imperfections in the STAGS model you must have previously generated buckling modes from either an INDIC 1 linear
136. apes use ILIN 1 for the linear bifurcation buckling analysis NOTE For the nonlinear INDIC 3 STAGS runs always use ILIN 0 Nonlinear 0 or linear 1 kinematic relations ILIN 0 0 Type 1 for closed 360 deg cyl shell 0 otherwise ITOTAL h If you are modeling a cylindrical shell that spans 360 degrees answer ITOTAL 1 If you are modeling a flat or cylindrical panel that spans less than 360 degrees then answer ITOTAL 0 except in the following circumstance If you are setting up a compound cylindrical model and the compound model spans 360 degrees answer ITOTAL 1 See Fig 56 in the paper Difficulties in optimization of imperfect stiffened cylindrical shells AIAA Paper 2006 1943 47th AIAA SDM Meeting Newport RI May 1 4 2006 for an example of a compound model If the compound model is a complete 360 degree cylindrical shell it is closed ITOTAL 1 The logic will proceed as if the shell is closed even though you set YSTAGS to a value considerably less than that which corresponds to 360 degrees Type 1 for closed 360 deg cyl shell 0 otherwise ITOTAL 1 1 X direction length of the STAGS model of the panel XSTAGS h This is the axial length of the part of the panel to be included in the STAGS model The X direction is along the stringer axis If PANDA2 indicates that there are many axial waves in the local buckling pattern then it may be best to use STAGS to explore only the local bifurcation and
137. art 1 19 2 7896E 00 10 3 3854E 00 12 3 8828E 00 14 3 8381E 00 16 3 3807E 00 18 3 0163E 00 20 2 7499E 00 22 2 5632E 00 24 2 4399E 00 26 2 3680E 00 28 2 3381E 00 30 lt inter ring critical mode 2 3432E 00 32 Compare with PANDA2 CHAPTER 22 2 3782E 00 34 of Part 1 19 2 4388E 00 36 2 5220E 00 38 2 6253E 00 40 Compare with the prediction from PANDA2 listed in CHAPTER 22 of PART 1 19 From CHAPTER 22 of PART 1 19 inter ring buckling mode BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DISCRETIZED MODEL skin smeared stringer ring discretized module HOOP BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KNOCKDOWN ANISOTROPY n EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 32 2 44726E 00 1 00000E 00 1 00000E 00 2 44726E 00 35 2 48779E 00 1 00000E 00 1 00000E 00 2 48779E 00 29 2 47892E 00 1 00000E 00 1 00000E 00 2 47892E 00 Buckling load factor before t s d 2 4473E 00 After t s d 2 2273E 00 lines skipped to save space knockdown for smeared stringers from SUB EIGMOD SMRFAC 5 4900E 01 knockdown for transverse shear deformation t s d from SUB SHRRED SHRFAC 9 1013E 01 Buckling load factor BEFORE knockdown for smeared stringers 2 2273E 00 Buckling load factor AFTER knockdown for smeared stringers 1 2228E 00 lines skipped to save space Margin 1 1164E 01 Inter ri
138. bcase 2 which is not checked during the second optimization Both the first optimum design from the complete analysis and the second optimum design from the Subcase 1 only analysis you would incorporate into the actual panel during manufacture the panel skin and stringer dimensions from the first optimum design would be used for a certain axial length of panel near the rings and the panel skin and stringer dimensions and ring dimensions from the second optimum design would be used for the panel midlength or midbay region and for the rings You would have to specify the axial extent of each of the two regions Unfortunately PANDA2 cannot do this for you You will have to rely on engineering judgment If you use PANDA2 this way to generate designs that are really beyond the straightforward scope of PANDA2 it is especially important for you to apply some general purpose finite element code such as STAGS to verify the feasiblility of your fancy hybrid optimum design before you actually fabricate the panel SEE ITEM 175 IN PANDA2 NEWS FOR MORE INFORMATION AND AN EXAMPLE Do you want a complete analysis type H for Help y y Want to provide another load set n n IMPOSE TOTAL THICKNESS LIMITS FOR THE SEGMENTS OF AN X ORIENTED CROSS SECTION OF THE PANEL MODULE Do you want to impose minimum TOTAL thickness of any segment n n Do you want to impose maximum TOTAL thickness of any segment n n IMPOSE TOTAL THICKNESS LIMITS FOR TH
139. ck the end of the OPM file to see if there are any significantly negative margins generated from the buckling analyses in which ISAND 1 If so then do optimization with ISAND 1 or 2 You will rarely if ever need to use ISAND 2 since for practical panels the Sanders and Marlowe theories give essentially the same results Index for type of shell theory 0 or 1 or 2 ISAND 1 1 Next you will be asked Does the postbuckling axial wavelength of local buckles change What is meant is Does the postbuckling axial wavelength of local buckles change continuously as the applied load is increased above the load which causes initial local buckling of the panel skin between rings and stringers Just hit Enter if you don t know The question is relevant only for analyses with IQUICK 0 as it applies only to the postbuckling analysis which is based on the discretized single panel module model The default is Y and in practically all cases you should answer Y or hit Enter which has the same effect You should always answer Y if this run is to be an optimization run You might want to answer N if your purpose in using PANDA2 is to generate post local buckling 3x3 tangent stiffness matrices to be compared with results from STAGS or some other general purpose finite element computer code In panels with the ratio of ring spacing to stringer spacing less than about 5 or 6 the axial wavelength of local buckling of the skin of
140. ckling mode 3 Inter ring buckling modal imperfection imperfection has the shape of the critical bay buckling mode from a model in which the stringers are smeared out and the panel is simply supported at adjacent rings 4 Local buckling modal imperfection imperfection has the shape of the critical local skin buckling mode from a model in which the local piece of skin is simply supported at adjacent stringers and rings If the user supplies reasonable amplitudes for these types of imperfections then he she may use factors of safety FSGEN and FSPAN of unity provided that the load corresponds to ULTIMATE load not operating load FSLOC plays a special role If you do not want local buckling of the panel skin to occur you don t want any postbuckling capability of the panel skin then set FSLOC greater than unity as with FSGEN and FSPAN With IQUICK 0 if you set FSLOC 1 0 PANDA2 will automatically increase it to 1 1 IF YOU WANT SKIN POSTBUCKLING CAPABILITY BUT YOU DO NOT WANT LOCAL BUCKLING TO OCCUR AT LESS THAN A CERTAIN FRACTION OF THE APPLIED LOAD THEN SET FSLOC EQUAL TO THAT FRACTION OF THE LOAD IF YOU DON T CARE AT WHAT LOAD LOCAL BUCKLING OCCURS SET FSLOC EQUAL TO ZERO PANDA2 WILL THEN ALLOW THE PANEL TO BUCKLE LOCALLY AND IF IQUICK 0 WILL INCLUDE POST LOCAL BUCKLING PHENOMENA IN CALCULATIONS OF GENERAL AND PANEL INSTABILITY AND STRESS The comments for FSLOC apply to the buckling factors of safety for stringer
141. ct panel and give effective stiffnesses of possibly locally postbuckled skin stringer module These effective stiffnesses are used later for overall buckling and inter ring buckling See Table 12 in the paper Bushnell D Optimization of an axially compressed ring and stringer stiffened cylindrical shell with a general buckling modal imperfection AIAA Paper 2007 2216 48th AIAA SDM Meeting Honolulu Hawaii April 2007 lines skipped to save space CHAPTER 19 Do wide column inter ring buckling analysis with possibly locally postbuckled skin stringer module model See Figs 20c 22c 46d and 67 of 1A for examples lines skipped to save space CHAPTER 20 Compute width wise wide column buckling and lateral torsional buckling load factors from the possibly locally postbuckled skin stringer module model inter ring buckling modes See panda2 news Item Numbers 379 and 381 in 1L lines skipped to save space CHAPTER 21 Compute skin ring buckling load factor for computing knockdown to compensate for inherent unconservativeness of smeared ring models See bottom row in Fig 30 of Ref 1G Also see panda2 news Items 509 511 522 532 605 617 619 632 633 676 lines skipped to save space Knockdown for smeared rings on cylindrical shell Buckling load factor for n dn FNARCQ 3 0000E 00 from discrete model 1 8086E 00 Buckling load factor for ring with bending stiffness EI perit ntdn 2 1 EI r 3 p 2
142. ctor BEFORE knockdown for smeared stringers 2 1201E 00 Buckling load factor AFTER knockdown for smeared stringers 2 1201E 00 The eigenvalue 2 035811 from STAGS that corresponds to inter ring buckling of skin plus smeared stringers agrees very well with those from PANDA2 obtained before knockdown for compensating for the inherent unconservativeness of smearing the stringers As we shall see from the next STAGS model treating the stringers as flexible shell segments shell units in STAGS jargon leads to an inter ring buckling load factor eigenvalue only about 6 per cent less than that from the STAGS model in which the stringers are smeared Therefore in this particular case PANDA2 yields a conservative result when the conservativeness index ICONSV is set equal to unity PART 3 23 Produce and run a different STAGS model one which covers the same 6 x 3 bay sub domain of the entire shell with all stiffener segments modeled as flexible shell units Note that now the STAGS index ILIN 1 not 0 STAGS runs with same model as in PART 3 21 except that instead of being smeared the stringers are now modeled as flexible shell segments and the STAGS index ILIN is set equal to unity The input file for STAGSUNIT cylstif STG follows cylstif STG input for STAGSUNIT n Do you want a tutorial session and tutorial output 1 Choose type of STAGS analysis 1 3 4 5 6 INDIC 0 Restart from ISTARTth load s
143. d at the panel edges Do you want symmetry conditions along the straight edges Edges parallel to screen 0 in plane deformable 1 rigid Stringer web axial displacement index IBCX0XL 0 or 1 the new cylstif STG file u a K B KBDBDB The following fragment appears in the STAGS output file cylstif out2 CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 1 CRITICAL LOAD FACTOR COMBINATION NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF 1 1 181702E 00 1 181702E 00 0 000000E 00 15935 The buckling mode corresponding to the eigenvalue 1 181702 is obtained by running the STAGS postprocessor STAPL with the following input cylstif pin file input for STAPL linear buckling of perfect shell from STAGS 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 1 0 4 0 1 PL 3 KPLOT NUNIT ITEM STEP MODE 0 0 3 PL 5 DSCALE NROTS 1 0 35840000E 02 SPL 6 IROT ROT 2 0 13140000E 02 SPL 6 IROT ROT 3 0 35630001E 02 SPL 6 IROT ROT end of cylstif pin file The critical buckling mode is shown in the plot 15 cylstif stagsunit locbuck 5x3bay eigl png The eigenvalue 1 181702 is close to the eignvalue 1 186805 obtained from the STAGS model that includes the entire cylindrical shell with both rings and stringers modeled as flexible shell segments shell units in STAGS jargon Compare the two plots 10 cylstif stagsunit eigl rigidends png 360 degree model 15 cylstif s
144. d or insufficient applied load as well as for the approximate manner in which the general buckling load factor is calculated in PANDA2 Panels that buckle locally at loads far below the design load are not particularly sensitive to initial imperfections For such panels use Tet x FSGEN lt 2 0 Panels designed so that local and general instability loads are nearly equal are somewhat sensitive to initial imperfections and FSGEN should be about 1 4 even if the panel is flat Axially stiffened cylinders under axial compression should usually have FSGEN 2 Axially compressed monocoque cylinders under axial compression should have FSGEN 4 if r t gt 300 FSGEN 2 if r t lt 100 Cylinders under uniform external pressure should have FSGEN 1 4 Cylinders under uniform torsion in plane shear should have FSGEN 1 3 NOTE The above are general guidelines only For more details consult the extensive NASA literature ASME Code Case N 284 and run PANDA with the option to get interaction curves for imperfect shells Also see COMPUTERIZED BUCKLING ANALYSIS OF SHELLS by David Bushnell Nijhoff and Co The Netherlands 1985 The best way to design panels with PANDA2 is to use ULTIMATE loads and to specify reasonable conservative amplitudes for the various components Wimpg Wimpgl Wimpg2 Wpan Wloc of imperfections then use FSGEN 1 0 When you have an optimum design check its performance by using STAGS Occasionally you may want to
145. d separately then glued together at room temperature or they may be cocured Which method is used very much affects the residual stresses and residual deformations of the panel The residual stresses and deformations in cocured panels are caused by the different thermal expansion properties of the stringers and skin as the panel cools down from the curing temperature to room tempera ture If this is not a composite panel the answer here should probably be N Are the stringers cocured with the skin n n What force axial length will cause web peel off h Irrelevant for ISOGRID configuration Wanted here is the force per axial length of stringer required to peel half of each stringer web and faying flange away from the panel skin Half the stringer web means half of the thickness It is assumed that each half of the stringer web consists of layers that start as part or all of the faying flange on either side of the stiffener These layers turn a corner to become the stringer web Tensile forces in the plane of the web normal to the stringer axis will therefore tend to peel the web halves from the faying flanges from which they derive In the post local buckling regime such forces develop in each stringer web These are calculated by PANDA2 and a constraint condition is formulated that indicates whether or not stringer popoff will occur because of web peel off caused by post local buckling deformations The force required here depe
146. de 1 the number of layers through the thickness of the group 2 whether the winding angles can ever be decision variables 3 layer indices for each layer 4 whether the layer is a new type of layer 5 if it is a new type of layer thickness winding angle and material type corresponding to that layer index Is the next group of layers to be a default group 12 layers n n Module with T shaped stiffener Seg No 4 Segment No 3 gt Seg No 2 h Seg No l 7 Seg No 5 A V same as Seg 1 lt b2 gt lt Module width stiffener spacing b gt number of layers in the next group in Segment no 1 1 1 Can winding layup angles ever be decision variables h The term winding angle is used throughout PANDA2 However PANDA2 assumes that the composite laminates are laid up layer by layer with each layer having a distinct and constant angle between the axial direction normal to the screen and the direction of the fibers high modulus direction Hence the composite structure is not wound but built up layer by layer Fig 2 of the journal article on PANDA shows the geometry See the article PANDA interactive program for minimum weight design of stiffened cylindrical panels and shells Computers and Structures vol 16 pp 167 185 1983 Use with caution Please note that weight does not change with winding angle so that if you plan to optimize something and
147. dex no 5 RNG seg 4 layer 1 Kk k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k kk k k kkk k kkk k k kkkk kkkkkkkkkkkkkkkk DESIGN OBJECTIVE kkk kkk kkk kkk kkk kkk kkk kkk kkk k kkk kkk kkk kk CORRESPONDING VALUE OF THE OBJECTIVE FUNCTION VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 0 0 1 221E 04 WEIGHT OF THE ENTIRE PANEL KKK KR RRR KE KKK KKK KERR RRR REE kkkk kkkk kkkkkkkkkkkk DESIGN OBJECTIVE kkk kkk kkk kkk kkk Kk k k k k k k k k k k k k k k k k k k k k k k k k k k k kk k k kk k k kk k k kk kk kkk kk kkk end of the abridged list of the cylstif OPP file PART 1 9 Execute the PANDA2 processor called CHOOSEPLOT in order to choose what to plot Next execute CHOOSEPLOT bush gt chooseplot Please enter PANDA2 case name cylstif kkkxkxkkkkkkkkkkkkk CHOOSEPLOT kkkkkkkkkkkkkkkkkkk The purpose of CHOOSEPLOT is to permit you to choose 1 Which design variables decision variable candidates are to be plotted v design iterations ITYPE 1 2 Which behaviors to plot v load steps ITYPE 3 3 Which sensitivity plots to obtain ITYPE 4 4 At which locations to plot extreme fiber strains ITYPE 3 5 Which design margins are to be plotted v design iterations ITYPE 1 or load steps ITYPE 3 or design variable ITYPE 4 or load combo ITYPE 5 6 For which load steps to plot the deformed panel module ITYPE 3 7 Whether or not t
148. e EIGMNC 2 72E 00 2 72E 00 3 79E 00 6 72E 00 1 00E 17 2 72E 00 1 00E 17 SLOPEX 0 00E 00 0 00E 00 0 00E 00 0 00E 00 0 00E 00 0 00E 00 0 00E 00 MWAVEX 1 1 2 4 0 1 1 NWAVEX 3 3 3 5 0 3 0 lines skipped to save space Buckling load factor before t s d 2 7174E 00 After t s d 2 4489E 00 lines skipped to save space Number of circumferential halfwaves in buckling pattern 3 0000E 00 Buckling load factor BEFORE knockdown for smeared stringers 2 4489E 00 Buckling load factor AFTER knockdown for smeared stringers 2 2966E 00 General buckling load factor before and after knockdown EIGGEN before modification by 5 factors below 2 2966E 00 Knockdown factor from modal imperfection s 1 0000E 00 Knockdown factor for smearing rings on cyl shell 9 0000E 01 Knockup factor to avoid twice accounting for t s d 1 0000E 00 lst modifying factor FKNMOD 1 or 1 EIG9X FMDKD9 1 0000E 00 2nd modifying factor EIGMR9 1 or EIGGNX EIGGEN 1 0000E 00 After knockdn EIGGEN FKNOCK 9 RNGKNK SHRFCT FKNMOD EIGMR9 2 0669E 00 Get a plot of the general buckling mode bush gt bosorplot Please enter the BIGBOSOR4 case name cylstif Do you want to use Xgraph or create a PostScript file Choose X or P p etc etc as above end of obtaining the plot file metafile ps bush gt cp metafile ps plot2 ps bush gt gv plot2 ps gv means ghost view you will see the buckling mode on your screen Take a scree
149. e metafile ps bush gt cp metafile ps plotl ps bush gt gv plotl ps gv means ghost view you will see the buckling mode on your screen Take a screen shot of this buckling mode and store it in the file 3 cylstif localbuck panel png PART 2 6 Execute the PANDA2 processor called PANEL and the BIGBOSOR4 processors bigbosorall and bosorplot in order to obtain a plot of the critical GENERAL buckling mode and load factor eigenvalue Next get a plot from BIGBOSOR4 of buckling of the entire shell from a BIGBOSOR4 model generated via the PANDA2 processor called PANEL In this BOSOR4 model the T rings are smeared out and the T stringers are modeled as flexible shell segments 180 degrees of the cylindrical shell are included in the model The axial length of the model is 300 inches The prismatic shell BIGBOSOR4 model is used bush gt panel Please enter PANDA2 case name cylstif The correct input for the PANEL processor follows input cylstif PAN for PANEL for general buckling model to be analyzed with BIGBOSOR4 n Do you want a tutorial session and tutorial output 314 1600 Panel length in the plane of the screen L2 0 Enter control 0 or 1 for stringers at panel edges 2 Enter control l sym 2 s s for boundary condition 1 Enter ILOCAL 0 or 1 or 1 or 2 Type H elp ILOCAL 1 Number of halfwaves in the axial direction see H elp NWAVE
150. e prebuckling and the buckling phases of the analysis Panel length normal to the plane of the screen Ll h This is the axial length of the panel For a cylindrical panel this is the length of the generator of the panel This is the x direction Panel length normal to the plane of the screen L1 300 300 Panel length in the plane of the screen L2 h For a cylindrical panel this is the arc length along the circumference of the entire panel A complete cylindrical shell can be modelled by using L2 pi radius Then the number of half waves over this circumferential length is the same as the number of full waves around the complete 360 degree circum ference If you are analyzing a complete cylindrical shell especially one with loads that vary around the circumference it will probably be best to divide it into panels Then analyze the panel as a structure subjected to multiple sets of uniform loads See the paper PANDA2 program for minimum weight design of stiffened composite locally buckled panels for an example Computers and Structures Vol 25 pp 570 574 Fig 79 Panel length in the plane of the screen L2 314 16 314 1600 The stiffened panel is considered to be divided into several identical modules as follows For a module you will be asked to provide the following data 1 width b of the module same as stiffener spacing 2 width b2 of the thickened region at the base of the stiffener shown as above 3
151. e cases This was the old help paragraph corresponding to the original question Answer Y or N If you answer Y the response of the local single module model to uniform normal pressure is calculated from a nonlinear theory in which the two edges normal to the screen located at the symmetry planes midway between stringers are allowed to approach eachother as the panel skin deforms locally under the uniform normal pressure no in plane hoop load develops in the panel skin as it deforms under the pressure Generally designs obtained with in plane movable edges are more conservative than those obtained with in plane fixed edges because a the maximum stresses are higher with in plane movable edges because there is more bending in this case b No in plane tension develops in the panel skin with in plane movable edges which means that local buckling load factors will be lower in this case Are you feeling well today type H lt enter gt Y Is there a maximum allowable deflection due to pressure h Answer Y or N If your answer is Y then you will be asked to provide the maximum deflection allowed A constraint condition will be introduced into the design process This constraint condition has the form WPGMAX WPG AMPLIT gt 1 in which WPGMAX is the maximum allowable deflection WPG is the normal deflection at the midlength of the panel due to pressure without any effect of in plane applied loads and AMPLIT is an amplitude
152. e decision variables layer index 1 2 for layer no 1 Is this a new layer type thickness for layer index no 4 winding angle deg for layer index no 4 material index 1 2 for layer index no 4 Any more layers or groups of layers in Segment no 3 Is the next group of layers to be a default group 12 layers number of layers in the next group in Segment no 4 Can winding layup angles ever be decision variables layer index 1 2 for layer no 1 Is this a new layer type thickness for layer index no 5 winding angle deg for layer index no 5 material index 1 2 for layer index no 5 Any more layers or groups of layers in Segment no 4 choose external 0 or internal 1 rings Is the panel curved in the plane of the screen Y for cyls Radius of curvature cyl rad in the plane of screen R Is panel curved normal to plane of screen answer N Is this material isotropic Y or N Young s modulus E 1 Poisson s ratio NU 1 transverse shear modulus G13 1 Thermal expansion coeff ALPHA 1 residual stress temperature positive TEMPTUR 1 Want to supply a stress strain curve for this mat l H Want to specify maximum effective stress Maximum allowable effective stress in material type 1 Do you want to take advantage of bending overshoot weight density greater than 0 of material type 1 Is lamina cracking permitted along fibers type H elp
153. ed at the tips of the stringer webs all stringer segments are modeled as shell branches stringer faying flange is modeled as beam 210 elements but stringer web and stringer outstanding flange are modeled as shell branches 5 the stringers are replaced by enforcement of a constraint that the normal displacement w be constant along the generator where the stringer would be attached to the cylindrical shell Stringer model 1 or 2 or 3 or 4 or 5 Type H elp 3 3 Ring model 1 or 2 or 3 or 4 or 5 Type H elp 3 3 Reference surface of cyl l outer O middle 1l inner h Choose either 1 or 0 or 1 If the stringers are external you may want to choose 1 If the stringers are internal you may want to choose 1 If the height of the stringers is large compared to the thickness of the cyl shell you should choose 0 If you are planning to use fasteners please choose 0 Reference surface of cyl l outer O middle 1l inner 0 0 Do you want to use fasteners they are like rigid links h Usually you should answer N However if at the optimum design the height of the stringers is not large compared to the thickness of the cylindrical shell and if you answered 0 to the previous question about location of the reference surface of the cylindrical shell then you might want to answer Y Note that the use of fasteners approximately numerically doubles the size of the case Fasteners are used to permit a gap between the reference surface
154. ed out Number of nodes in the Y direction NODEY 101 101 You will next be asked to provide loads for Load Set A Nx Ny Nxy p followed by loads for Load Set B Nx0 Ny0 p0 for the STAGS finite element model Now provide loads Nx Ny Nxy p for Load Set A Resultant e g lb in normal to the plane of screen Nx h What is wanted is the applied line load in the Ll axial direction in units of force length Negative for compression If this axial load varies in the L2 circumferential direction use the largest compressive value applied to that edge of the panel What is wanted now is the axial load in Load Set A that is the eigenvalue load the load to be multiplied by the critical load factor the eigenvalue in computations of the critical applied load Resultant e g lb in normal to the plane of screen Nx 25000 25000 00 Resultant e g lb in in the plane of the screen Ny 50000 50000 00 In plane shear in load set A Nxy 0 0 000000 Normal pressure in STAGS model in Load Set A p h If the panel is curved the normal pressure p must be consistent with the applied hoop resultant Ny p r Ny in which r cylindrical shell radius r is always positive Normal pressure in STAGS model in Load Set A p h There is no more help Do your best Normal pressure in STAGS model in Load Set A p 500 500 0000 Next provide loads for Load Set B Nx0 Ny0 p0 in the STAGS finite element model Resulta
155. eg cylindrical shell Thus the PANDA2 analysis of a panel spanning 180 deg is equivalent to an analysis of a complete 360 deg cylindrical shell Buckling choose 0 simple support or l clamping 0 0 28 fixed parameters have now been identified 99 fixed parameters are permitted 71 additional fixed parameters are allowed DESCRIPTION OF FILES GENERATED BY THIS CASE cylstif NAM This file contains only the name of the case cylstif BEG Summary of interactive session you have just completed This file can be edited and used for future runs of BEGIN cylstif CBL Contains part of cylstif data base cylstif OPB Output from BEGIN Please list this file and inspect it and the cylstif BEG file carefully before proceeding For further information about files generated during operation of PANDA2 give the command HELPAN FILES Next give a command CHANGE or CHOOSETEMP or SETUP end of the interactive BEGIN session The files that now exist in the working directory are as follows rw r r 1 bush bush 5604 Feb 21 11 18 cylstif BEG rw r r 1 bush bush 182500 Feb 21 11 18 cylstif CBL rw r r 1 bush bush 30 Feb 21 11 18 cylstif NAM rw r r 1 bush bush 12112 Feb 21 11 18 cylstif OPB The user provided input data supplied during the interactive BEGIN session are saved in the file cylstif BEG A list of cylstif BEG follows n Do you want a tutorial session and tutorial output 30
156. el Do you want stringer s with a high nodal point density n n Do you want ring s with a high nodal point density n n You will next be asked if the material in the STAGS model can go plastic For comparison with PANDA2 you will usually answer N no However occasionally you may want to answer Y yes If you answer Y you will be asked to provide a stress strain curve for the material and the number of integration points thru the wall thickness NOTE Answer Y only if the panel and stiffeners are all made of only one isotropic material This plasticity option does not work for panels made of more than one material The plasticity option WILL work provided that all the materials specified in BEGIN BEG file have the same isotropic properties ANOTHER NOTE The FIRST stress strain coordinates you provide MUST agree with the elastic modulus you provided in BEGIN that is first stress value first strain value E Is there plasticity in this STAGS model n n Do you want to use the least squares model for torque h Usually you should answer y In STAGSUNIT models torque is always applied at x 0 There are two choices 1 STAGSUNIT can simply apply the appropriate value of Nxy at x 0 as one of the loading components in Shell Unit No 1 2 STAGSUNIT can apply a torque about what the STAGS manual calls a user defined point This user defined point is always located at the origin of the global coordinate
157. el in Load Set B p0 1 000000 Starting load factor for Load System A STLD 1 0 000000 Load factor increment for Load System A STEP 1 1 000000 Maximum load factor for Load System A FACM 1 0 Starting load factor for Load System B STLD 2 0 Load factor increment for Load System B STEP 2 0 Maximum load factor for Load System B FACM 2 1 How many eigenvalues do you want NEIGS 480 Choose element type 480 or 410 or 940 n Have you obtained buckling modes from STAGS for this case 62 Number of stringers in STAGS model of 360 deg cylinder 10 Number of rings in the STAGS model of the panel y Are there rings at the ends of the panel 1 Number of finite elements between adjacent stringers 3 Number of finite elements between adjacent rings 3 Stringer model 1 or 2 or 3 or 4 or 5 Type H elp 3 Ring model 1 or 2 or 3 or 4 or 5 Type H elp 0 Reference surface of cyl l outer O middle 1l inner n Do you want to use fasteners they are like rigid links n Are the stringers to be smeared out n Are the rings to be smeared out 5 Number of nodes over height of stiffener webs NODWEB 5 Number of nodes over width of stringer flange NDFLGS 5 Number of nodes over width of ring flange NDFLGR n Do you want stringer s with a high nodal point density n Do you want ring s with a high nodal point density n Is there plasticity in this STAGS model y Do you want to use the least squares model for t
158. el in which bending is significant and if PANDA2 predicts many axial halfwaves in the local buckling pattern more than 10 for example then you might answer N You will then be asked further questions about the distribution of nodal points in the axial direction x If local buckling occurs only near the midlength of the panel because of bending under pressure for example then you might want to concentrate nodal points in that region If local buckling might occur both near the midlength of the panel and near the ends bending of a clamped panel under pressure for example then you might want to concentrate nodal points near the midlength and near one or both ends of the panel Is the nodal point spacing uniform along the stringer axis y y Number of nodes in the X direction NODEX h NODEX must be an odd integer It may be changed later The X direction is the direction along the stringer axis You should have at least three nodes per axial halfwave of the local buckling pattern This input datum is not used if there are rings Number of nodes in the X direction NODEX 51 51 Number of nodes in the Y direction NODEY h NODEY must be an odd integer It may be changed later The Y direction is the direction around the circumference You should have at least three nodes per circumferential halfwave of the general or inter ring buckling pattern This input datum is not used if there are stringers that are not to be smear
159. er index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 12 12 Lower bound of variable no 12 01 0 1000000E 01 Upper bound of variable no 12 1 1 000000 Any more decision variables Y or N y y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness fo
160. er index no 5 2 3 4 Want to change any other parameters in this set y Y PARAMETERS WHICH CAN BE CHANGED VAR STR SEG LAYER NO RNG 1 2 STR 3 STR 4 STR 5 SKN 6 STR 7 STR 8 9 RNG 10 RNG 11 RNG 12 RNG 13 RNG Number of parameter to change 1 5 New value of the parameter 0 76896 0 7689600 NO SBPWRWNHOBWE BWNO NO FPrROODOOORFFRFOOCOCO CURRENT VALUE 1 011E 01 3 370E 00 7 817E 00 2 534E 00 7 690E 01 2 038E 01 8 450E 02 3 185E 01 0 000E 00 9 783E 00 4 304E 00 5 673E 01 9 452E 01 CHOOSE ONE OF THE FOLLOWING DEFINITION B STR stiffener spacing b STR seg NA B2 STR width of stringer base b2 must H STR height of stiffener type H for s W STR width of outstanding flange of st T 1 SKN thickness for layer index no 1 T 2 STR thickness for layer index no 2 T 3 STR thickness for layer index no 3 B RNG stiffener spacing b RNG seg NA B2 RNG width of ring base b2 zero is a H RNG height of stiffener type H for s W RNG width of outstanding flange of st T 4 RNG thickness for layer index no 4 T 5 RNG thickness for layer index no 5 2 3 5 Want to change any other parameters in this set y Y PARAMETERS WHICH CAN BE CHANGED VAR STR SEG LAYER NO RNG 1 2 STR 3 STR 4 STR 5 SKN 6 STR 7 STR 8 9 RNG 10 RNG 11 RNG 12 RNG 13 RNG Number of parameter to change 1 6 New value of the parameter 0 20380 0 2038000 NO
161. ers in STAGS model of 360 deg cylinder 4 Number of rings in the STAGS model of the panel y Are there rings at the ends of the panel 3 Number of finite elements between adjacent stringers 9 Number of finite elements between adjacent rings 3 Stringer model 1 or 2 or 3 or 4 or 5 Type H elp 3 Ring model 1 or 2 or 3 or 4 or 5 Type H elp 0 Reference surface of cyl l outer O middle 1l inner n Do you want to use fasteners they are like rigid links n Are the stringers to be smeared out n Are the rings to be smeared out 5 Number of nodes over height of stiffener webs NODWEB 5 Number of nodes over width of stringer flange NDFLGS 5 Number of nodes over width of ring flange NDFLGR n Do you want stringer s with a high nodal point density n Do you want ring s with a high nodal point density n Is there plasticity in this STAGS model y Do you want to use the least squares model for torque n Is stiffener sidesway permitted at the panel edges y Do you want symmetry conditions along the straight edges 0 Edges parallel to screen 0 in plane deformable 1 rigid 0 Stringer web axial displacement index IBCXOXL 0 or 1 end of the cylstif STG file The STAGS index ILIN is set equal to unity that is 1 Nonlinear 0 or linear 1 kinematic relations ILIN in order to filter out unwanted buckling eigenvalues that correspond to local deformation of
162. esponding to general instability less than unity you need either to include the wide column model as a constraint or increase the factor of safety Do you want wide column buckling to constrain the design n n xxkk k WARNING WARNING WARNING We are now in SUBROUTINE LOADSX Load Set No 1 YOU HAVE CHOSEN THAT WIDE COLUMN BUCKLING WILL NOT CONSTRAIN THE DESIGN THE WIDE COLUMN MODEL IS ONE IN WHICH THE PART OF THE PANEL BETWEEN ADJACENT RINGS IS ASSUMED TO BE FLAT UNLESS THE DISTANCE BETWEEN RINGS IS RATHER LONG OR THE STRINGERS ARE NOT DEEP WHEN STRINGERS ARE PRESENT IT IS USUALLY A GOOD IDEA TO ANSWER YES TO THE WIDE COLUMN QUESTION IN ORDER TO AVOID UNCONSERVATIVE DESIGNS YOU MAY WANT TO FORCE THE WIDE COLUMN BUCKLING ANALYSIS TO CONSTRAIN THE DESIGN SINCE THE PANEL IS STIFFENED BY STRINGERS IN YOUR NEXT RUN YOU SHOULD SERIOUSLY CONSIDER CHANGING YOUR ANSWER TO THE WIDE COLUMN QUESTION FROM NO TO YES THIS WARNING IS BASED ON PREVIOUS EXPERIENCE WITH STRINGER STIFFENED PANELS xx x END WARNING END WARNING END WARNING Next please provide the fixed stress resultants Nx0 and Ny0 These constitute part of the in plane loads in Load Set B Note that no fixed in plane shear resultant Nxy0 is permitted The fixed stress resultants Nx0 and Ny0 are not multiplied by the eigenvalue eigenvalue load factor determined in bifurcation buckling analyses In the absence of normal pressure the cr
163. essor called DECIDE in order to choose decision variables upper and lower bounds equality constraints inequality constraints and escape variables Execute the PANDA2 processor called MAINSETUP in order to establish loading and solution strategies Execute the PANDA2 processor called SUPEROPT in order to search for a global optimum design Reset the upper bound of the stringer spacing in the file cylstif DEC and restart from scratch Execute the PANDA2 processor called SUPEROPT in order to search for a global optimum design Execute the PANDA2 processor called CHOOSEPLOT in order to choose what to plot 1 10 Execute the PANDA2 processor called DIPLOT in order to generate Postscript files for plotting 1 11 Execute the PANDA2 processors called SUPEROPT and DIPLOT again in order to 1 search for a global optimum design that may weigh less than the optimum design determined so far and 2 to plot the objective versus design iterations 1 12 Execute the PANDA2 processor called MAINSETUP again in order to set up a run for a fixed design ITYPE 2 the optimum design with the weight 1 178E 04 1b 1 13 Execute the PANDA2 processor called PANDAOPT for the analysis of the fixed optimized design 1 14 Inspect the output from PANDAOPT the cylstif OPM file 5 Execute the PANDA2 processor called CHANGE in order to archive the optimized design 1 16 Execute the PANDA2 processors called SETUP
164. f OPM file Next inspect the file cylstif OPM which is the list of output from PANDAOPT A somewhat abridged version of the file cylstif OPM follows abridged version of the file cylstif OPM lines skipped to save space kkkeKKKAKEE AUGUST 2010 VERSION OF PANDA2 ke eRe x x x BEGINNING OF THE cylstif OPM FILE lines skipped to save space MARGINS FOR MAR MARGIN NO VALUE 1 3 18E 03 2 3 18E 03 3 1 99E 01 4 1 97E 02 5 2 96E 02 6 8 83E 01 7 1 21E 02 8 5 86E 01 9 1 82E 02 10 1 23E 01 11 6 96E 00 12 1 31E 00 13 7 03E 00 14 7 86E 01 15 5 89E 01 16 1 71E 01 17 1 61E 01 18 8 73E 01 19 1 91E 02 20 1 69E 01 21 3 89E 01 22 1 05E 00 23 6 93E 02 CURRENT DESIGN LOAD CASE NO 1 SUBCASE NO DEFINITION Local buckling from discrete model 1 M Bending torsion buckling M 1 FS 1 1 1 1 axial halfwaves FS 1 1 eff stress matl 1 SKN Dseg 2 node 6 layer 1 z 0 3845 MID FS 1 m 1 lateral torsional buckling load factor FS 1 FS 1 1 circ halfwaves FS 1 1 circ halfwaves FS 1 1 eff stress matl 1 RNG Iseg 4 allnode layer 1 z 0 4726 MID FS 1 Inter ring bucklng discrete model n 32 Lo n Ring sidesway discrete model n 1 buckling margin stringer Iseg 3 Local halfwaves 4 buckling margin stringer Iseg 4 Local halfwaves 4 7C 0 buckling stringer Iseg 4 as beam on foundation buckling margin ring Iseg 3 Local halfwaves 32 buckling stringer Isegs 3 4 together M 4
165. f OPP FILE AFTER EACH OPTIMIZATION RUN OR BETTER YET RUN SUPEROPT xx NOTE It is almost always best to set the number of xx iterations per execution of PANDAOPT equal to 5 RRKK x in response to the following prompt in MAINSETUP How many design iterations permitted in this run 5 to 25 xx Hence the OPT file should almost always have the x following line in it RRKK 5 How many design iterations in this run 5 to 25 end of MAINSETUP interactive session The files now existing in the working directory are the following rw r r 1 bush bush 76 Feb 21 12 44 cylstif 010 rw r r 1 bush bush 2046 Feb 21 11 27 cylstif AL2 rw r r 1 bush bush 2058 Feb 21 11 27 cylstif AL3 rw r r 1 bush bush 2058 Feb 21 11 27 cylstif ALL rw r r 1 bush bush 5604 Feb 21 11 18 cylstif BEG rw r r 1 bush bush 110324 Feb 21 11 27 cylstif BL1 rw r r 1 bush bush 110324 Feb 21 11 27 cylstif BL2 rw r r 1 bush bush 110324 Feb 21 11 27 cylstif BL3 rw r r 1 bush bush 110324 Feb 21 11 27 cylstif BL4 rw r r 1 bush bush 481 Feb 21 11 27 cylstif BOS rw r r 1 bush bush 182500 Feb 21 11 48 cylstif CBL rw r r 1 bush bush 3126 Feb 21 11 48 cylstif DEC rw r r 1 bush bush 30 Feb 21 11 18 cylstif NAM rw r r 1 bush bush 12112 Feb 21 11 18 cylstif OPB rw r r 1 bush bush 7934 Feb 21 11 48 cylstif OPD rw r r 1 rw r r 1 rw r r 1 rw r r 1 rw
166. f ring no 10 5 00001 S m 1 ISHELL IGLOBE NROWS NCOLS NLAYS NFABS 2 97848E 02 3 02152E 02 0 00000E 00 3 60000E 02 8 98325E 01 m 2 X1 X4 th1 th2 r 7 0 90 0 0 000E 00 0 0 O m 5 IWALL IWIMP ZETA ECZ ILIN IPLAS IRAMP 480 0 00 0 0 0 n 1 KELT NNX NNY IRREG IUGRID INTEG IPENL C C Input for b c and loading 3 3 3 3 0 p 1 IBLN i i 1 4 IBOND b c C 2 0 0 0 0 q 1 NSYS NICS NAMS NUSS NHINGE loading C Load Set A Ring No 10 1 4 0 q 2 ISYS NN USRLD C C Drilling freedoms suppressed in ring 10 outstanding flange 0 1 6 1 1 0 124 0 01 q 3 P LT LD LI LJ LAX NX 0 16 2 1 0 124 0 01 q 3 P LT LD LI LJ LAX NX 0 1 6 4 1 0 124 0 01 q 3 P LT LD LI LJ LAX NX 0 1 6 5 10124 0O 0 1 q 3 P LT LD LI LJ LAX NX C Load Set B Ring No 10 2 4 0 q 2 ISYS NN USRLD C C Drilling freedoms suppressed in ring 10 outstanding flange C Output contro 0000000 0 16 1 10 12400 1 q 3 P LT LD LI LJ LAX NX 0 16 2 10 12400 1 q 3 P LT LD LI LJ LAX NX 0 16 4 10 12400 1 q 3 P LT LD LI LJ LAX NX 0 16 5 10 12400 1 q 3 P LT LD LI LJ LAX NX Tere 0 0 0000 r 1 output end unit145 aa A finite element unit is needed for the torque at x 0 10000 0 0 111 111 s 1 Point of torque application 10000041 u 1 One least squares loading case 1 1 u 2 torque in Load Set A 1 record needed C The torque at x 0 is given by TORQUE Nxy 2 pi r 2 0 000000E 00 1 4 1 u 3 P LT LD LI torque at userpoint 1 in ru se
167. f the screen 2 means simple support conditions applied at the edges of the panel normal to the plane of the screen Enter control l sym 2 s s for boundary condition 2 2 Enter ILOCAL 0 or 1 or 1 or 2 Type H elp ILOCAL h ILOCAL 0 panel buckling means that tangent stiffnesses will be used for the wall stiffnesses The Nx Ny Nxy distributions over the panel module cross section are those calculated in the Koiter branch of PANDA2 that is Nx Ny Nxy are for the locally postbuckled panel You will generally select NWAVE 1 axial halfwaves when you are asked to supply a value for NWAVE The axial length of the shell is the length between adjacent rings ILOCAL 1 local buckling means that original stiffnesses will be used for the wall stiffnesses of the various segments in the panel module The Nx Ny Nxy distributions over the panel module cross section are those calculated from SUBROUTINE FORCEX that is Nx Ny Nxy are for the panel with no local buckling You will generally select NWAVE number of axial halfwaves that corresponds to the minimum local buckling load factor EIGOLD computed by PANDA2 See the OPM file The axial length of the shell is the length between adjacent rings ILOCAL 1 general buckling The original stiffnesses are used for the shell skin with smeared rings CY i j 5 The tangent stiffnesses are used for the stringer segments The axial length of the shell model is the total length of the
168. flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Want to use default for thickness decision variables type H elp h It is sometimes best to answer Y if you have a lot of different layer types However it is a bit tricky and YOU MUST BE CAREFUL You answer Y or N Your answer means N means you choose thickness decision variables one by one Y means that for a certain range of layer index types to be specified by you the following will happen 1 the thickness of any layer type for which the winding angle is either 0 or 90 deg will be a decision variable 2 the thickness of any layer type will be a decision variable regardless of winding angle if the winding angle of any previous layer type within the given range of layer types is not equal to minus the winding angle of the current layer type 3 If the current winding angle is minus some previous winding angle within the given range of layer types the current thickness will be linked to that previous thickness and the link
169. g factor FKNMOD 1 or 1 EIG9X FMDKD9 1 0000E 00 2nd modifying factor EIGMR9 1 or EIGGNX EIGGEN 1 0000E 00 After knockdn EIGGEN FKNOCK 9 RNGKNK SHRFCT FKNMOD EIGMR9 2 0669E 00 lines skipped to save space N lope 0 FS 14 2 06690E 00 buckling load factor simp support general buck M 1 N 3 s Margin 8 7900E 01 buck SAND simp support general buck M 1 N 3 slope 0 FS 1 1 lines skipped to save space Inter ring buckling with smeared stringers and ring rolling is not recorded as a margin because this type of buckling has been superseded by the results from the discretized inter ring module model for which inter ring buckling load factors have been computed in the range from n 1 ton 117 circumferential halfwaves The critical inter ring buckling with ring rolling model has 20 circ half waves which lies within this range lines skipped to save space Margin 4 1833E 01 buck SAND rolling only of stringers M 8 N 0 slope 0 FS 1 4 lines skipped to save space Margin 1 2841E 00 buck SAND hiwave roll of stringers M 54 N 0 slope 0 FS 1 2 lines skipped to save space Ring rolling without participation of the panel skin is not recorded as a margin because this type of buckling has been superseded by the results from the discretized skin ring module model for which buckling load factors have been computed in the range from n 1 ton 117 circ halfwaves The critical ring rolling without participatio
170. h as 1K 1L etc These designations occur in Reference 1 of the following paper ANOTHER NOT The string t s d occurs t s d transverse shear deformation Bushnell D Optimization of an axially compressed ring and stringer stiffened cylindrical shell with a general buckling modal imperfection AIAA Paper 2007 2216 48th AIAA SDM Meeting Honolulu Hawaii April 2007 lines skipped to save space CHAPTER 1 Compute the 6 x 6 constitutive matrices C for individual model segments and various combinations thereof skin with smeared stiffener sets 1A See Section 8 in 1A Eq 8 1 on p 495 of 1A lines skipped to save space CHAPTER 2 Do PANDA type 1B general buckling analysis to get Donnell factors for later use if appropriate lines skipped to save space CHAPTER 3 Do various PANDA type 1B general buckling analyses needed for later computation of effective length of the panel Compute the effective length lines skipped to save space CHAPTER NEW Compute wide column buckling from discretized skin stringer module model Figs 20b c amp 22b c in 1A with only Nx Ny 0 Nxy 0 The purpose is to obtain a knockdown factor WIDKNK for smearing the stringers in an inter ring buckling mode lines skipped to save space CHAPTER NEW1 Compute distribution of loads in panel module skin stringer segments neglecting redistribution due to initial buckling modal imperfections See Section 10 of
171. h bush 30290 Feb 21 18 30 cylstif 5 ps This plot contains the objective versus design iterations during the SUPEROPT execution In order to see the plot on your screen type the following command gv cylstif 5 ps gv means ghost view a utility for reading Postscript files and producing the plot image on your screen A screen snapshot of the plot is taken and stored in the file l cylstif superoptl objective png All the png files are appended at the bottom of this file PART 1 11 Execute the PANDA2 processors called SUPEROPT and DIPLOT again in order to 1 search for a global optimum design that may weigh less than the optimum design determined so far and 2 to plot the objective versus design iterations Next run SUPEROPT again Maybe there is a FEASIBLE or ALMOST FEASIBLE design with a smaller weight than that found in PART 1 8 and listed at the end of PART 1 8 1 221E 04 1b bush gt superopt The purpose of SUPEROPT is to launch the batch run which performs multiple executions of the panda2 processors in the order autochange setup pandaopt pandaopt pandaopt The processor autochange automatically changes the decision variables as follows y i x i 1 dx i i 1 2 3 no of dec var in which x i is the old value of the ith decision variable y i is the new value and dx i is a random number between 0 5 and 1 5 The purpose of the successive cycles of autochange setup pandaopt pandaopt pa
172. he lack of in plane shear Nxy loading and anisotropy in discretized BOSOR4 type models See Section 11 in 1A lines skipped to save space CHAPTER 12 Obtain prebuckled state of the initially imperfect and loaded and bent panel or shell This section includes the redistribution of Nx Ny Nxy in the various segments of the stiffened shell structure lines skipped to save space CHAPTER 13 Get prebuckling stress resultants Nx Ny needed for the discretized single module skin stringer model used for local buckling and bending torsion buckling BOSOR4 type model see Figs 18 20 22 97 and 98 of 1A for examples of the discretized single skin stringer BOSOR4 type module model lines skipped to save space CHAPTER 14 Compute local buckling from BOSOR4 type discretized skin stringer single module model See Section 12 2 upper table on p 511 and Figs 46c and 98b in 1A for examples BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DISCRETIZED MODEL skin stringer discretized module of local buckling AXIAL BUCKLING KNOCKDOWN FOR KNOCKDOWN FOR BUCKLING HALF LOAD FACTOR TRANSVERSE SHEAR IN PLANE SHEAR LOAD FACTOR WAVES BEFORE KNOCKDOWN DEFORMATION LOADING AND OR AFTER KNOCKDOWN ANISOTROPY M EIGOLD KSTAR KNOCK EIGOLD KSTAR KNOCK 3 2 43710E 00 1 00000E 00 1 00000E 00 2 43710E 00 4 2 22611E 00 1 00000E 00 1 00000E 00 2 22611E 00 5 2 13420E 00 1 00000E 00 1 00000E 00 2 13420E 00 6 2 22328E 00 1 00000E 00 1 00000E 00 2 22328E 00
173. he linking expression Y or N n n Any more linked variables Y or N n n Next establish inequality relations among variables of the two forms 1 0 lt vl1l v2 v3 or 1 0 gt vl1l v2 v3 in which the expression f vl v2 v3 has the form f v1 v2 v3 CO Cl v1l D1 C2 v2 D2 C3 v3 D3 etc up to max of 10 terms up to 10 cross product terms of the form C i j v i v j The variables vl v2 v3 can be any of the variables that are decision variables or potential candidates for decision variables or linked variables Any inequality relations among variables type H n n Any escape variables Y or N h An escape variable is a variable that when increased drives the design toward the feasible region For example in designs which are buckling critical local and general instability represent two constraint conditions that bound the feasible region Increasing the thicknesses of any parts while keeping all other dimensions the same drives the design toward the feasible region makes buckling less critical Hence a thickness should always be chosen as an escape variable Other variables such as winding angles should not be used as escape variables since their increase might well result in a decrease in the buckling load hence driving the design toward the infeasible region Any escape variables Y or N y y Want to have escape variables chosen by default h Generally answe
174. he parameter n Want to change any other parameters in this set n Do you want to change values of fixed parameters n Do you want to change values of allowables end of the STAGS worthy cylstif CHG file PART 3 2 Execute the PANDA2 processors called CHANGE and SETUP Next we execute CHANGE and SETUP bush gt change Please enter PANDA2 case name cylstif KKKKKKKKKKKKKKKKKE CHANGE kkkkxkkkkkkkkkkkkxkkk You use CHANGE to change parameters without having to go back to BEGIN The parameters you can change are segregated into three groups 1 parameters elegible to be decision variables 2 parameters not elegible to be decision variables 3 allowables for example max strain Your interactive input is saved on a file called cylstif CHG in which cylstif is the same name you used for BEGIN SETUP etc A summary of the output from CHANGE is stored in cylstif OPC kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Are you correcting adding to or using an existing file y The interactive CHANGE session zips by on your screen bush gt setup Enter case name cylstif The output from SETUP zips by on your screen Next give the command DECIDE or MAINSETUP PART 3 3 Execute the PANDA2 processors called MAINSETUP and PANDAOPT bush gt mainsetup Please enter PANDA2 case name cylstif kkkkkkkkkkkkkkkxkk MAINSETUP kkkkkkkkkkkkkk kk The purpose of this p
175. he sign of Wimpgl is significant Otherwise Wimpgl will have the same sign as Wimpg2 in the calculations in PANDA2 b overall buckling modal imperfection amplitude Wimpg2 NOTE If the panel is stiffened the sign of the overall buckling modal imperfection Wimpg2 is important because it affects how the panel skin and stiffener cross sections of the imperfect panel become loaded under the applied loads Type H elp for a discussion of this when you are prompted for Wimpg2 c if there are rings inter ring buckling modal imperfection amplitude Wpan NOTE The sign of Wpan is important for the same reason given in Paragraph b d local buckling modal imperfection amplitude Wloc The sign of Wloc is NOT significant Out of roundness Wimpgl Max diameter Min diam 4 Wimpgl 1 0 0 000000 Initial buckling modal general imperfection amplitude Wimpg2 1 h In PANDA2 the general imperfection is assumed to have the same shape as the general buckling mode obtained from a PANDA type closed form analysis of the cylindrical panel IMPORTANT NOTES If the panel has axial stiffeners stringers and no rings and if the analysis model IQUICK 0 then You should consider optimizing with both negative and positive Wimpg2 Under axial loading negative Wimpg2 gives rise to more compression in the skin than in the tips of the stringers The opposite is true for positive Wimpg2 You can optimize for both positive and negative Wimpg2 by
176. idth of stringer base b2 must H STR height of stiffener type H for s W STR width of outstanding flange of st T 1 SKN thickness for layer index no 1 T 2 STR thickness for layer index no 2 T 3 STR thickness for layer index no 3 B RNG stiffener spacing b RNG seg NA B2 RNG width of ring base b2 zero is a H RNG height of stiffener type H for s W RNG width of outstanding flange of st T 4 RNG thickness for layer index no 4 T 5 RNG thickness for layer index no 5 2 3 12 Want to change any other parameters in this set y y PARAMETERS WHICH CAN BE CHANGED VAR STR SEG LAYER NO RNG 1 2 STR 3 STR 4 STR 5 SKN 6 STR 7 STR 8 9 RNG 10 RNG 11 RNG 12 RNG 13 RNG Number of parameter to change 1 13 New value of the parameter 0 94524 0 9452400 NO BPWHRWNHOKBWE BWNO NO FPrROOOOrRFFOOCOOCOO CURRENT VALUE 1 011E 01 3 370E 00 7 817E 00 2 534E 00 7 690E 01 2 038E 01 8 450E 02 3 185E 01 0 000E 00 9 783E 00 4 304E 00 5 673E 01 9 452E 01 CHOOSE ONE OF THE FOLLOWING DEFINITION B STR stiffener spacing b STR seg NA B2 STR width of stringer base b2 must H STR height of stiffener type H for s W STR width of outstanding flange of st T 1 SKN thickness for layer index no 1 T 2 STR thickness for layer index no 2 T 3 STR thickness for layer index no 3 B RNG stiffener spacing b RNG seg NA B2 RNG width of ring base b2 zero is a H
177. iffness Want to include effect of transverse shear deformation y Y IQUICK quick analysis indicator 0 or 1 h IQUICK 0 means discrete BOSOR4 type model will be treated IQUICK 1 means only closed form types of models will be included except for prediction of the static response of the entire panel and of the panel module to normal pressure For a panel with stringers almost always use IQUICK 0 It may be advisable to start out with IQUICK 1 and to refine the design later with the longer IQUICK 0 type of analysis However don t overdo the IQUICK 1 option it might easily lead to unconservative designs You must use IQUICK 0 at least once to check that the design is feasible You must use IQUICK 0 if you want to include any effects of local buckling of panel skin or stringer parts With TRUSS CORE SANDWICH construction it is best to use IQUICK 1 although IQUICK 0 is available IQUICK quick analysis indicator 0 or 1 0 0 Do you want to vary M for minimum local buckling load h M is the number of axial half waves between rings in the local buckling mode The developer of PANDA2 always answers Y Don t worry about computer time as described below That paragraph was written many years ago when computers were much slower Computer time can be saved if you are confident that the number of axial halfwaves M that you next choose is truly the critical value for local skin buckling Generally answer this
178. inear overall static response of a stiffened panel to uniform normal pressure Much of the BOSOR4 preprocessor software is used to do this Therefore in order to use PANDA2 you must have available to you the most recent version of BOSOR4 DESCRIPTION OF FILES GENERATED BY THIS CASE cylstif ALL Input data for BOSOR4 type of preprocessor correponding to discretized single panel module cylstif BOS Input data for BOSOR4 type of preprocessor correponding to discretized entire panel with smeared stiffeners cylstif CBL Contains part of cylstif data base For further information about files generated during operation of PANDA2 give the command HELPAN FILES The next module will cause to be generated matrix templates for solution of the local and general buckling eigenvalue problems in which the cross section of the panel module is discretized and in which the entire panel cross section is discretized smeared stiffeners according to the conventions used in BOSOR4 Normal termination setup still processing Please wait Executing setup2 kkkkkkkkkkkkkx k SETUP2 kkkkkkkkkkkkk kk The purpose of SETUP2 is to set up an input data file called NAME AL2 in which NAME is your name for this case This file NAME AL2 is a BOSOR4 type of input data file It is used as input for B4READ SETUP2 is for skin ring module kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxkkk GENERATING BOSOR4 TYPE DISCRETIZED MODEL FOR A SINGLE PANEL
179. ing Iseg 3 Local halfwaves 32 RNGS FS 1 13 1 06E 01 buckling ring Iseg 4 as beam on foundation M 67 RNGS FS 1 2 14 1 76E 01 buck SAND rolling with smear rings M 93 N 1 slope 0 FS 1 1 15 4 18E 01 buck SAND rolling only of stringers M 8 N 0 slope 0 FS 1 4 16 1 28E 00 buck SAND hiwave roll of stringers M 54 N 0 slope 0 FS 1 2 17 6 12E 01 buck SAND rolling only axisym rings M 0 N 0 slope 0 FS 1 4 18 6 93E 01 buck SAND STRINGERS web buckling M 4 N 1 slope 0 FS 1 19 1 42E 00 buck SAND RINGS web buckling M 26 N 1 slope 0 FS 1 20 6 93E 02 Max allowable ave axial strain ave axial strain 1 FS 1 KKAKKKKKAKEK ALL 1 LOAD SETS PROCESSED KRKKKK end of abridged cylstif OPM file for perfect shell Compare with the margins listed previously for the optimized imperfect shell See PART 1 14 PART 1 19 Selected output from the cylstif OPM file obtained when the output index NPRINT 2 in the cylstif OPT file This section is quite long but it is important as it demonstrates 1 What sort of calculations PANDA2 performs and 2 What the predictions are obtained from certain of the CHAPTERS as listed next Here follows some selected output contained in the cylstif OPM file for the perfect shell included when the print index NPRINT 2 in the OPT cylstif OPT file OPT input for MAINSETUP NOTE There appear below some references to previously published papers notations suc
180. ing constant C will be 1 0 NOTE You must choose lowest and highest layer indeces from a GIVEN SEGMENT in the module cross section NOT from the entire module and a skin stringer module must be done separately from a skin ring module You MUST answer N if winding angles are decision variables Want to use default for thickness decision variables type H elp n n Choose a decision variable 1 2 3 h Use an index from the left hand column of the table above Choose a decision variable 1 2 3 1 Lower Te of variable no 1 10 Upper P of variable no 1 50 Any E E variables Y or N y Y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO RNG NO NO 1 0 0 VALUE 3 000E 01 DEFINITION B STR stiffener spacing b STR PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN seg NA VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of s
181. inger base b2 must STR STR SKN STR STR 3 4 5 6 7 8 9 RNG 10 RNG 11 RNG 12 RNG 13 RNG Number of parameter to change 1 11 New value of the parameter 4 3037 4 303700 BPWKRWNHOKBWE BW FPRrRODOOORFRFRFOO 7 817E 00 2 534E 00 7 690E 01 2 038E 01 8 450E 02 3 185E 01 0 000E 00 9 783E 00 4 304E 00 5 673E 01 9 452E 01 H STR height of stiffener type H for s W STR width of outstanding flange of st T 1 SKN thickness for layer index no 1 T 2 STR thickness for layer index no 2 T 3 STR thickness for layer index no 3 B RNG stiffener spacing b RNG seg NA B2 RNG width of ring base b2 zero is a H RNG height of stiffener type H for s W RNG width of outstanding flange of st T 4 RNG thickness for layer index no 4 T 5 RNG thickness for layer index no 5 2 3 11 Want to change any other parameters in this set y Y PARAMETERS WHICH CAN BE CHANGED VAR STR SEG LAYER NO RNG 1 2 STR 3 STR 4 STR 5 SKN 6 STR 7 STR 8 9 RNG 10 RNG 11 RNG 12 RNG 13 RNG Number of parameter to change 1 12 New value of the parameter 0 56729 0 5672900 NO BPW KBWNHOKBWE BWNO NO rFPROOOORFRFOGCOCO CURRENT VALUE 1 011E 01 3 370E 00 7 817E 00 2 534E 00 7 690E 01 2 038E 01 8 450E 02 3 185E 01 0 000E 00 9 783E 00 4 304E 00 5 673E 01 9 452E 01 CHOOSE ONE OF THE FOLLOWING DEFINITION B STR stiffener spacing b STR seg NA B2 STR w
182. initial buckling modal imperfections have the unknown shapes of the local inter ring and general buckling modes the user cannot know ahead of time whether or not a given imperfection amplitude is too large An imperfection of given amplitude is easier to detect if it has a shape that has short axial and circumferential wavelengths than if it has long wavelengths because it is the wall out of plane rotations that are most likely to be detected These out of plane rotations increase inversely with the critical buckling modal wavelengths The user does not know in advance what the various wavelengths of the critical buckling modes are An answer N means STRATEGY 1 in 17 is followed An answer Y means STRATEGY 2 in 17 is followed If you answer Y PANDA2 will take the following three steps Step 1 Use the critical buckling mode shape m n Slope axial halfwaves circ halfwaves nodal line slope corresponding to the PERFECT rather than the IMPERFECT geometry if the axial halfwavelength of the critical buckling mode of the IMPERFECT geometry is less than or equal to half the user specified axial halfwavelength of the imperfection Step 2 Change the amplitude of whatever imperfection results from Step 1 by the factor ratio axial halfwavelength of the critical buckling mode user specified axial halfwavelength of the imperfection Step 3 Reduce the buckling modal imperfection amplitude remaining after Steps 1 and 2
183. introduction of two load cases in MAINSETUP with everything the same in each except the sign of Wimpg2 With IQUICK 1 optimization with both positive and negative Wimpg2 is automatically performed within a single load case If the panel is clamped for buckling has stringers and is flat the effective simply supported length may be less than the actual length L eff LENMOD L where LENMOD is computed by PANDA2 In this case the Wimpg2 that you provide should be given by Wimpg2 your input Wimpg2 actual 2 LENMOD 2 You can obtain LENMOD by running PANDAOPT with ITYPE 2 NPRINT 2 and search the resulting OPM file for the string LENMOD Initial buckling modal general imperfection amplitude Wimpg2 1 0 5 ie A modal inter ring imperfection amplitude Wpan 1 0 eres ceed imperfection amplitude must be positive Wloc 1 0 Soa A PANDA2 to change imperfection amplitudes see H elp 1 h Default is Y If you answer Y then PANDA2 may automatically reduce the amplitude of one or more of the buckling modal imperfections that it judges to be larger than that which would be easily detectable by the most casual inspection and therefore greater than that represented by a reasonable tolerance It was necessary to allow PANDA2 to do this in order a to try to avoid extreme oscillations of design margins from design iteration to iteration and b to avoid production of optimum designs that are too conservative Since the
184. itical load can be calculated from Nx crit Nx0 T Nx0 eigenvalue Factor of safety Nx Ny crit Ny0 T Ny0 eigenvalue Factor of safety Ny Nxy crit eigenvalue Factor of safety Nxy in which Nx0 T and Ny0 T are resultants generated by curing and or temperature loading variation from segment to segment considered in the above equations to be part of Load Set B the thermal loading can be part of Load Set A however Note that the fixed loads are added to any stress resultants that are generated by thermal loading of a composite panel The loads that you are now asked to provide are fixed applied loads Resultant e g lb in normal to the plane of screen Nx0 1 0 0 Resultant e g lb in in the plane of the screen Ny0O 1 0 0 Axial load applied along the 0 neutral plane l panel skin h Choose 0 or 1 0 means that the axial load is applied at the neutral surface that is the axial load causes no axial bending of a panel with axial stiffeners The writer almost always uses this choice 1 means that the axial load is applied along the middle surface of the panel skin A simply supported panel with axial stiffeners will bend when loaded in this way PANDA2 includes this axial bending bowing effect Please use 0 if the panel is clamped Generally use 0 Axial load applied along the 0 neutral plane l panel skin 0 0 Uniform applied pressure positive upward See H elp p 1 h NOTE This pressure i
185. itical mode 1 8127E 00 6 Compare with PANDA2 CHAPTERS 22 amp 26 2 2312E 00 8 From PANDA2 CHAPTER 22 of the cylstif OPM file Margin 5 8244E 01 lLo n Ring sidesway discrete model n 4 circ halfwaves FS 1 1 The corresponding buckling load factor is given by buckling load factor factor of safety x Margin 1 0 buckling load factor 1 1 x 0 58244 1 0 1 7407 PART 3 15 Produce and run a different STAGS model one with smeared stringers and smeared rings Run a STAGS model yet again this time with the use of different input data in cylstif STG Now both the stringers and the rings are smeared out The purpose of this run is to obtain the general buckling load factor and mode shape The new cylstif STG file follows cylstif STG file input for STAGSUNIT n Do you want a tutorial session and tutorial output 1 Choose type of STAGS analysis 1 3 4 5 6 INDIC 0 Restart from ISTARTth load step 0 lst nonlinear soln ISTART 1 155000 Local buckling load factor from PANDA2 EIGLOC y Are the dimensions in this case in inches 0 Nonlinear 0 or linear 1 kinematic relations ILIN 1 Type 1 for closed 360 deg cyl shell 0 otherwise ITOTAL 300 X direction length of the STAGS model of the panel XSTAGS 628 3185 Panel length in the plane of the screen L2 y Is the nodal point spacing uniform along the stringer axis 51 Number of nodes in the X direction NODEX 101 N
186. kip the KOITER local postbuckling analysis y Y Do you want wide column buckling to constrain the design h The wide column model refers to the portion of the panel between adjacent rings If there are no rings the wide column model refers to the entire panel If the portion of the panel between rings is unstiffened or truss core sandwich or isogrid you should always answer N For these configurations the wide column model is too conservative Otherwise If the inter ring portion is flat you should probably answer Y If the panel is cylindrical curvature in the plane of the screen the wide column buckling load may be too conservative leading to unnecessarily heavy designs If for a curved panel you answer Y then you will not have to worry as much about the effect of initial imperfections as you would if you answer N because the wide column buckling load is not sensitive to initial geomtrical imperfections if there is little or no interaction between local and general buckling This is a difficult and not very well understood area in the field of shell buckling Actually I recommend that you design a panel first with use of the wide column model of general instability and then without this model In any case check your general instability load when you finish optimizing by running PANEL which sets up a discretized model of the entire panel width with stringers treated as shell branches If this PANEL model has a load factor corr
187. kk PART 1 1 Activate the PANDA2 commands bush gt panda2log PANDA2 commands have been activated PANDA2 commands are begin you provide a starting design material properties boundary conditions choosetemp choose temparature dependence setup PANDA2 generates BOSOR4 type matrix skylines for use by PANDA2 decide you choose decision variables lower and upper bounds linking relationships mainsetup you provide loading imperfection amplitudes fact of safety analysis type strategy pandaopt launch run of mainprocessor for a single set of design iterations superopt launch run for multiple sets of design iterations obtain a global optimum design change assign new values to parameters or save an optimum design autochange assign new vector of decision variables randomly used in the superopt process chooseplot choose which variables margins to plot diplot generate amp print PostScript file containing plots panel generate BOSOR4 input for a skin stringer multi module model panel2 generate BOSOR4 input for a skin ring multi module model panel3 generate BOSOR4 input for a skin stringer weld land multi module model stagsmodel generate STAGS input for panel element unit no rings stagsunit generate STAGS input for panel shell units both rings and stringers permitted cleanpan delete temporary case specific files A typical PANDA2 runstream is begin setup decide mainsetup superopt or panda
188. kkkkkkkkk Are you correcting adding to or using an existing file n n Do you want a tutorial session and tutorial output n n Now you start to provide input data You will be prompted by short questions If you need help just type H as an answer to the prompt instead of the datum called for In most instances you will then be given more information on the datum you must provide It may be a good idea to run the tutorial option if you are a new user of PANDA2 Overall panel dimensions 1 length normal to the plane of the screen L1 2 length in the plane of the screen L2 SOME ADVICE ON MODELING WHEN NORMAL PRESSURE IS PRESENT If you are designing a panel that has both stringers and rather large rings and you expect that in the prebuckling phase there may be significant bending between these large rings due to the pressure then set up models in which there are stringers only or stringers and weak rings weak implies that the normal pressure does not cause significant local axial bending between them The entire axial length of each model must be equal to the spacing of the large rings The boundary conditions along the edges where the large rings are supposed to be should be clamped for the prebuckling phase and simply supported for the buckling phase of the analysis if the stringers are not tapered in the neighborhoods of the large rings If the stringers are tapered near the large rings then use simple support for both th
189. kkkkkkkkkkkkkkkkkk PART 3 0 Processing with CHANGE STAGSUNIT and STAGS kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk PART 3 1 Edit the file cylstif CHG See PART 1 15 in order to create dimensions that are STAGS worthy integral numbers of stringer spacings amp ring spacings over the circumference and length of the cylindrical shell Next we wish to set up STAGS models of the optimized T ring and T stringer stiffened cylindrical shell First we must use the PANDA2 processor CHANGE to make sure that there are an integral number of stringers over 360 degrees of circumference and an integral number of rings over the 300 inch length Accordingly we do the following We first edit the file cylstif CHG changing the optimized values of B STR 10 110 B2 STR 3 3697 and B RNG 31 85 inches to B STR 10 13417 B2 STR 3 3777 and B RNG 33 3333 With B STR 10 13417 inches there are exactly 62 stringers over 360 degrees of circumference and with B RNG 33 3333 inches there are exactly 9 ring spacings over the length 300 inches The new cylstif CHG file follows cylstif CHG file for STAGS worthy shell n Do you want a tutorial session and tutorial output y Do you want to change any values in Parameter Set No 1 1 Number of parameter to change 1 2 3 10 13417 New value of the parameter y Want to change any other parameters in this set 2 Number of
190. l 1 or 2 or 3 or 4 or 5 Type H elp 0 Reference surface of cyl l outer O middle 1l inner n Do you want to use fasteners they are like rigid links NOTE gt y Are the stringers to be smeared out n Are the rings to be smeared out 5 Number of nodes over height of stiffener webs NODWEB 5 Number of nodes over width of stringer flange NDFLGS 5 Number of nodes over width of ring flange NDFLGR n Do you want stringer s with a high nodal point density n Do you want ring s with a high nodal point density n Is there plasticity in this STAGS model y Do you want to use the least squares model for torque n Is stiffener sidesway permitted at the panel edges NOTE gt 0 Edges parallel to screen 0 in plane deformable 1 rigid NOTE gt 0 Stringer web axial displacement index IBCXOXL 0 or 1 f the new cylstif STG file STAGS is run as described above and the following lines now appear in the cylstif out2 from the STAGS file cylstif out2 CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 1 CRITICAL LOAD FACTOR COMBINATION NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF 1 1 709327E 00 1 709327E 00 0 000000E 00 71745 end of fragment from the STAGS file cylstif out2 Use STAPL to obtain a plot of the critical buckling mode The input in this case for STAPL is as follows cylstif pin file input for STAPL linear buckli
191. l and inter ring bending of imperfect panel Additional Nx in base of ring GNx 0 0000E 00 Additional Nx at webtip of ring dNx 0 0000E 00 Additional Nx in flange of ring dNx 0 0000E 00 LABEL NO IN STRUCT 9560 lines skipped to save space CHAPTER 25 Compute buckling load factors from PANDA type theory for the vari a ring Typical buc Figs 5 and 6 of Re lines skipped to save space Prebuck resultant along string At root of web 2 9376E 03 lines skipped to save space Margin 6 9253E 01 buckling lines skipped to save space Margin 2 5027E 01 buckling lines skipped to save space Margin 2 0179E 01 buckling lines skipped to save space Margin 8 7729E 00 buckling lines skipped to save space Prebuck resultant along ring At root of web 2 2922E 04 Knockdown factor to account fo any anisotropic properties o lines skipped to save space Margin 1 4368E 00 buckling lines skipped to save space Margin 1 0614E 01 buckling lines skipped to save space CHAPTER 26 Compute local inte factors from PANDA alternative doub expansion models ous segments of a stringer and kling modes are displayed in f 1B er axis at root and tip of web At tip of web 2 9376E 03 margin stringer Iseg 3 Local halfwaves 4 MID FS 1 margin stringer Iseg 4 Local halfwaves 4 MID FS 1 stringer Isegs 3 4 together M 4 C 0 MID FS 1 4 stringer Iseg 4 as beam on foundation M 369 MID FS 1 2 axis at r
192. l pressure should have FSPAN 1 4 Cylinders under uniform torsion in plane shear should have FSPAN 1 3 If you plan to use the wide column model you can use a smaller factor of safety here than would otherwise be the case In fact you can probably get away with using a factor FSPAN 1 0 NOTE The above are general guidelines only For more details consult the extensive NASA literature ASME Code Case N 284 and run PANDA with the option to get interaction curves for imperfect shells Also see COMPUTERIZED BUCKLING ANALYSIS OF SHELLS by David Bushnell Nijhoff and Co The Netherlands 1985 Occasionally you may want to use FSPAN 0 999 You do this in order to prevent PANDA2 from automatically increasing FSPAN to 1 1 which it does if FSPAN 1 0 For example you might wamt to use FSPAN 0 999 in a case for which you intend to compare results from PANDA2 with results from some other analysis Factor of safety for panel between rings instability FSPAN 1 1 1 000000 FACTOR OF SAFETY FOR PANEL INSTABILITY FSPAN 1 HAS BEEN CHANGED TO FSPAN 1 1 TO AVOID SINGULARITY Minimum load factor for local buckling Type H for HELP FSLOC 1 h Local buckling here means buckling of the panel skin between adjacent stringers and rings The factor FSLOC is NOT included in load factors for local buckling of stringer parts A different factor FSBSTR governs local buckling of stringer parts Factors of safety for local buckling of ri
193. led MAINSETUP However note that if you change certain of the input values there may occur different prompts following the prompt corresponding to that change and that therefore an edited version of the OPT file may not represent valid input for MAINSETUP For example if you change IQUICK from 0 to 1 the three prompts that follow the prompt for IQUICK no longer occur PART 1 6 Execute the PANDA2 processor called SUPEROPT in order to search for a global optimum design bush gt superopt The purpose of SUPEROPT is to launch the batch run which performs multiple executions of the panda2 processors in the order autochange setup pandaopt pandaopt pandaopt The processor autochange automatically changes the decision variables as follows y i x i 1 dx i i 1 2 3 no of dec var in which x i is the old value of the ith decision variable y i is the new value and dx i is a random number between 0 5 and 1 5 The purpose of the successive cycles of autochange setup pandaopt pandaopt pandaopt is to try to find a global optimum design by redesigning in each cycle from a different starting point The user should use a small maximum number of design iterations such as 5 in the file case OPT where case is the user specified name of the case Enter case name cylstif Enter number of executions of pandaopt for each execution of autochange 5 or 6 or 7 or 8 or 9 or 10 5 B background F foreground or Q N
194. lll fnxrng 2 eltab iwalll eps2 ty 3 3 0 0000E 00 1 0000E 07 0 0000E 00 5 6729E 01 ring outflange iwalll fnxrng 3 eltab iwalll eps2 ty 4 4 0 0000E 00 1 0000E 07 0 0000E 00 9 4524E 01 EQUILIBRIUM FOR LOAD SET B Check for axial equilibrium with nominal stringer web height H 1 7 8167E 00 FNX Applied axial resultant Nx FNXTOT Computed value FNXSTR 1 1 FNXSTR 2 1 FNXSTR 3 I1 Nx in stringer fayflange web outflange FNXSKN I Nx in skin smeared stringers FNX FNXTOT FNXSKN I FNXSTR 1 I FNXSTR 2 I FNXSTR 3 I 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 Substringer axial Nx height 0 0000E 00 0 0000E 00 Check for hoop equilibrium with nominal ring web height H 2 9 7830E 00 FNY Applied hoop resultant Ny FNYTOT Computed value FNXRNG 1 1 FNXRNG 2 1 FNXRNG 3 I Ny in ring fayflange web outflange FNYSKN I Ny in skin smeared rings FNY FNYTOT FNYSKN I FNXRNG 1 I FNXRNG 2 I FNXRNG 3 I 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 Subring axial Nx height 0 0000E 00 0 0000E 00 Axial equilibrium Nx added over x cross section off by 0 0000E 00 per cent Hoop equilibrium Ny added over y cross section off by 0 0000E 00 per cent Major stringer logic ILOGST T Column numbers of major stringer web skin junctions ICOLST i 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95
195. long the length L2 where L2 is the arc length of the panel in the plane of the screen Identify type of stiffener along L2 N T J Z R A t t Module with T shaped stiffener Seg No 4 Segment No 3 gt Seg No 2 h Seg No l 5 Seg No 5 k V same as Seg 1 lt b2 gt lt Module width stiffener spacing b gt stiffener spacing b 50 50 00000 width of ring base b2 zero is allowed 0 0 height of stiffener type H for sketch h h The height of the stiffener is measured from the surface of the stiffener base to the middle surface of the stiffener flange as shown in the sketch below lt middle surface of stiffener flange gt flange material stiffener web gt h stiffener height stiffener base V panel skin height of stiffener type H for sketch h 10 10 00000 width of outstanding flange of stiffener w 10 10 00000 Are the rings cocured with the skin n n Module with T shaped stiffener Seg No 4 Segment No 3 gt Seg No 2 h Seg No 1 Seg No 5 V same as Seg 1 lt b2 gt lt Module width stiffener spacing b gt Next provide the properties of Segment 3 3 3 3 Beevers Is the next group of layers to be a default group 12 layers n n number of layers in the next group in Segment no
196. lots of the critical RING SIDESWAY and INTER RING buckling modes and load factors eigenvalues from BIGBOSOR4 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk PART 3 0 Processing with CHANGE STAGSUNIT and STAGS kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk PART 3 1 Edit the file cylstif CHG See PART 1 15 in PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART PART 3 19 3 20 3 21 order to create dimensions that are STAGS worthy integral numbers of stringer spacings amp ring spacings over the circumference and length of the cylindrical shell Execute the PANDA2 processors called CHANGE and SETUP Execute the PANDA2 processors called MAINSETUP and PANDAOPT Inspect the cylstif OPM file Execute the PANDA2 processor called STAGSUNIT in order to generate valed input files bin amp inp for STAGS In this first STAGSUNIT case we include the entire cylindrical shell in the STAGS model with the T rings and T stringers all modeled with flexible shell segments Shell units in STAGS jargon Scroll upward on your screen in order to view the following output from STAGSUNIT STAGSUNIT produces the file cylstif STG which is valid input for the PANDA2 processor STAGSUNIT STAGSUNIT produces two files cylstif bin and cylstif inp that are valid input files for the STAGS general purpose finite element comp
197. lstif OPD cylstif OPD contains a summary of optimization parameters If you choose the tutorial option cylstif OPD contains a complete list of the interactive session including prompting questions all help paragraphs your responses to the prompting questions and evolving lists of optimization parameters as they are chosen by you kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Are you correcting adding to or using an existing file y The DECIDE interactive session rolls by fast Not reproduced here in order to save space Next give either command CHOOSETEMP or MAINSETUP bush gt mainsetup Please enter PANDA2 case name cylstif kkkkkkkkkkkkkkk kk MAINSETUP kkkkkkkkkkkkkkkk The purpose of this processor is to permit you to choose loads and initial imperfections Nx Ny Nxy Mx My Nxo Nyo p T iseg Wimp global Wimp local up to 5 sets of them safety factors for general instability panel instability local instability panel skin local instability stiffener parts and stress and strategy parameters for subsequent batch execution of an optimization analysis analysis type 1 or an analysis of a fixed design at fixed load levels analysis type 2 or an analysis of a fixed design for a single load set for monotonically increasing load levels test simulation analysis type 3 Results of the interactive session in MAINSETUP are saved on a file called cylstif OPT which will appear at the beginning
198. lution model generated automatically by the PANDA2 processor called PANEL2 250 Umetormed Deformed cylstif R Z_EIGENMODE_1 N_30 300 350 250 Axial Station 150 100 50 0 50 100 150 200 250 300 Radius 6 cylstif interring panel2 png Inter ring buckling from a BIGBOSOR4 shell of revolution model generated automatically by the PANDA2 processor called PANEL2 Ox 35 84 l y 13 14 iia 7 Model geometry all units Oz 3563 cylstif STAGS INPUT FOR STIFFENED CYL STAGSUNIT SHELL UNITS ba 7 cylstif stagsunit model png STAGS model generated automatically by the PANDA2 processor called STAGSUNIT The shell has previously been optimized by PANDA2 figure AOR es GERI SY yen Pt ee cr 4 ERA A Ne anes 7 XA i Om ee F eee 7 Be eer Fee eg A ag Canetti solution scale 0 2076E 02 mode 1 per 0 10305E 01 step 0 eigenvector deformed geometry linear buckling of perfect shell from STAGS 9 cylstif stagsunit eigl png curved edges can undergo Ox 35 84 O y 13 14 2z 35 63 in plane warping N Paes ae Ft 3 an ra E Nee a A a TE a Cs ra a A ENS A pe GT ae ee fis KSA te tee i OE see a ez A n OEE solution scale 0 2132E 02 mode 1 per 0 11868E 01 Ox 35 84 7 ee e a a o O y 13 14 J step 0 eigenvector deformed geometry Oz 3563 NG linear buckling of perfect shell from STAGS 10 cylstif s
199. maximum inner fiber effective stress of 51010 psi not far above the prediction from PANDA2 PART 3 20 Outer fiber effective stresses from the 5 x 3 bay STAGS model We obtain a fringe plot of the distribution of the outer fiber effective stress via the STAGS post processor STAPL The input for STAPL is as follows cylstif pin input for STAPL for the outer fiber effective stress distribution over the entire model nonlinear effective stress outer fiber same view a linear buckling mode 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 2 0 7 1 00001 2 PL 3 KPLOT VIEW ITEM STEP MODE IFRNG COLOR ICOMP 0 0 3 0 0 0 0 0 0 PL 5 DSCALE NROTS LWSCALE RNGMIN RGMAX 1 0 35840000E 02 SPL 6 IROT ROT 2 0 13140000E 02 SPL 6 IROT ROT 3 0 35630001E 02 SPL 6 IROT ROT end of cylstif pin file The fringe plot is contained in the following cylstif stagsunit outerfibstress 5x3 png We want to see the outer fiber effective stress in the skin only The appropriate input for the STAGS post processor STAPL is as follows cylstif pin input for STAPL for the inner fiber effective stress distribution over the panel skin only nonlinear effective stress outer fiber same view a linear buckling mode 1 0 1 0 PL 2 NPLOT IPREP IPRS KDEV 2 1 7 1 0000 1 2 PL 3 KPLOT VIEW ITEM STEP MODE IFRNG COLOR ICOMP 1 0 0 3 0 0 0 0 0 0 PL 5 DSCALE NROTS LW
200. me general buckling mode The input for the STAGS postprocessor STAPL follows cylstif pin file input for STAPL linear buckling of perfect shell from STAGS 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 1 0 4 0 1 PL 3 KPLOT NUNIT ITEM STEP MODE 3 PL 5 DSCALE NROTS 1 0 0 SPL 6 IROT ROT 2 90 0 SPL 6 IROT ROT 3 0 0 SPL 6 IROT ROT end of cylstif pin file The end view of the critical buckling mode is shown in the plot 14 cylstif stagsunit genbuck eigl endview png PART 3 16 Compare with the predictions from BIGBOSOR4 and PANDA2 Compare the latest STAGS eigenvalue 2 507291E 00 with the eigenvalues that correspond to general buckling obtained from BIGBOSOR4 and PANDA2 General buckling load factor from BIGBOSOR4 BUCKLING LOADS FOLLOW AXIAL HALF WAVE NUMBER N 1 EIGENVALUES 2 88019E 00 3 62711E 00 4 75444E 00 xx CRITICAL EIGENVALUE AND WAVENUMBER EIGCRT 2 8802E 00 NO OF AXIAL HALF WAVES NWVCRT 1 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk The general buckling load factor obtained from BIGBOSOR4 is unconservative because BIGBOSOR4 does not account for transverse shear defomation t s d General buckling load factor from CHAPTER 26 of the PANDA2 file cylstif OPM general buckling smeared stiffeners C11 1 0238E 07 radius R 1 0000E 02 lines skipped to save space EIGMNC 2 72E 00 2 72E 00 3 79E 00 6 72E 00 1 00E 17 2 72E 00 1 00E 1
201. ment No 3 gt Seg No 2 h Seg No l Seg No 5 A V same as Seg 1 lt b2 gt lt Module width stiffener spacing b gt Next provide the properties of Segment 4 4 4 4 Are be Is the next group of layers to be a default group 12 layers n auber of layers in the next group in Segment no 4 1 Can ee A layup angles ever be decision variables n Teger index 1 2 for layer no 1 3 Is this a new layer type y Y thickness winding angle material for layer index thickness for layer index no 3 1 0 1000000 winding angle deg for layer index no 3 0 0 material index 1 2 for layer index no 3 1 1 Any more layers or groups of layers in Segment no 4 n n choose external 0 or internal 1 stringers h If the panel is flat choose external 0 If the panel is cylindrical choose either 0 or 1 See Fig 8 p 490 of the long 1987 PANDA2 paper for geometry If you choose 0 external then the radius of curvature of the panel will be regarded as positive Referring to the sketch of the single panel module the concave surface of the panel skin will be the bottom surface If you choose 1 internal then the radius of curvature of the panel will be regarded as negative The bottom surface in the panel module sketch will be convex choose external 0 or internal 1 stringers 0 Next you will be asked to provide input data for stiffeners a
202. n of the panel skin model has 4 circ half waves which lies within this range lines skipped to save space Margin 6 1151E 01 buck SAND rolling only axisym rings M 0 N 0 slope 0 FS 1 4 lines skipped to save space Margin 6 9253E 01 buck SAND STRINGERS web buckling M 4 N 1 slope 0 FS 1 lines skipped to save space Margin 1 4222E 00 buck SAND RINGS web buckling M 26 N 1 slope 0 FS 1 lines skipped to save space Margin 6 9276E 02 Max allowable ave axial strain ave axial strain 1 FS 1 lines skipped to save space CHAPTER 27 Compute the objective function e g WEIGHT xxxk k k BEGIN SUBROUTINE OBJECT OBJECTIVE FUNCTION Objective weight of PANDA2 model of panel OBJ 1 1778E 04 xkKKKK END SUBROUTINE OBJECT OBJECTIVE FUNCTION end of presentation of the abridged cylstif OPM file for the optimized perfect T ring and T stringer stiffened cylindrical shell kkkkkkkkkkkkkkkkkkkkkkkkkkk kkkkkkkkkkkkkkkkkkkkkkkkkk PART 2 0 Processing with PANEL PANEL2 and BIGBOSOR4 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxk PART 2 1 Execute the PANDA2 processor called PANEL in order to produce a valid input file cylstif ALL for BIGBOSOR4 for a prismatic model for LOCAL buckling Next get a plot from BIGBOSOR4 of buckling of the portion of the shell between rings from a BIGBOSOR4 model generated via the PANDA2 pr
203. n shot of this buckling mode and store it in the file 4 cylstif genrlbuck panel png PART 2 7 Execute the PANDA2 processor called PANEL2 and the BIGBOSOR4 processors bigbosorall and bosorplot in order to obtain plots of the critical RING SIDESWAY and INTER RING buckling modes and load factors eigenvalues from BIGBOSOR4 Next get plots from BIGBOSOR4 of buckling of the entire shell from a BIGBOSOR4 model generated via the PANDA2 processor called PANEL2 In this BOSOR4 model the T stringers are smeared out and the T rings are modeled as flexible shell segments The shell is modeled as a cylindrical shell not as a prismatic shell as is the case when the PANDA2 processor called PANEL is used bush gt panel2 Please enter PANDA2 case name cylstif The correct input for PANEL2 is as follows input file cylstif PAN for PANEL2 n Do you want a tutorial session and tutorial output 300 Length of the ring stiffened cylindrical shell Ll 1 Choose BOSOR4 model INDIC 1 or INDIC 4 INDIC 25000 00 Axial resultant Nx in Load Set A Nx 0 Axial resultant Nxo in Load Set B Nxo 500 0000 Normal pressure p 1 IABP 1 if pressure in Load Set A IABP 0 otherwise IABP 2 Enter control l sym 2 s s 3 clamp for buckling b c 2 Starting number of circumferential waves see H elp N0B 40 Ending number of circumferential waves see H elp NMAXB 2 Increment in number of circumferential waves INCRB
204. name OPM in which casename is the name of the case You will want to examine casename OPM as soon as PANDAOPT is finished Enter case name cylstif B background F foreground or Q NQS network queue system f Running PANDA2 pandaopt case cylstif Executing main Normal termination main still processing Please wait Executing store Normal termination store still processing Please wait cylstif mainprocessor run completed successfully Menu PANDAOPT CHOOSEPLOT MAINSETUP CHANGE Please examine the files cylstif OPM cylstif OPP and cylstif OPI If ITYPE 1 print the file called cylstif OPP If ITYPE 3 or 4 print the file called cylstif OPI Run PANDAOPT several times for optimization PART 3 4 Inspect the cylstif OPM file Inspect the new cylstif OPM file The new design margins are not much different from those listed above for the perfect shell MARGINS FOR CURRENT DESIGN LOAD CASE NO 1 SUBCASE NO 1 MAR MARGIN NO VALUE DEFINITION 1 5 98E 02 Local buckling from discrete model 1 M 1 axial halfwaves FS 1 1 2 5 98E 02 Bending torsion buckling M 1 FS 1 1 3 2 64E 01 eff stress matl 1 SKN Dseg 2 node 6 layer 1 z 0 3845 MID FS 1 4 7 66E 02 m 1 lateral torsional buckling load factor FS 1 FS 1 1 5 5 41E 02 Inter ring bucklng discrete model n 29 circ halfwaves FS 1 1 6 5 64E 01 Lo n Ring sidesway discrete model n 4 circ halfwaves FS 1 1 7 2 64E 01 eff stress matl 1 SKN Iseg 2 at n 6 laye
205. nd depth of the rings either of these modes might be critical If you answer N PANDA2 will accept whichever type of general instability mode corresponds to the lowest general instability load factor If you answer Y PANDA2 will set up a constraint condition that forces the general buckling load factor associated with the mode type 2 to be at least 5 per cent higher than that associated with the mode type 1 This special constraint condition may make it difficult to settle on the best optimum With successive PANDAOPTs the designs while feasible may drift away from previously found configurations that weigh less Therefore it is best to start by answering N finding an optimum design then anwering Y and continuing then returning to answering N again and doing more PANDAOPTs NOTE If you answer Y you may want to do a series of optimizations with fixed ring spacing Eliminate the ring spacing as a decision variable More on this item A control integer IHIAXL equals 0 if the user answers N and IHIAXL 1 if the user answers Y ILAMHI is another control integer that depends on the value of IHIAXL and on a third integer IMLOC to be explained next ILAMHI is initially set equal to zero and IMLOC is initially set equal to unity IMLOC is a switch that determines whether or not general buckling load factors are to be saved corresponding to both low and high numbers of axial halfwaves in the buckling mode If yes then IMLOC
206. ndaopt is to try to find a global optimum design by redesigning in each cycle from a different starting point The user should use a small maximum number of design iterations such as 5 in the file case OPT where case is the user specified name of the case Enter case name cylstif Enter number of executions of pandaopt for each execution of autochange 5 or 6 or 7 or 8 or 9 or 10 5 B background F foreground or Q NOS network queue system b H high or L low priority 1 Diagnostics will be mailed to you upon program termination bush gt usr sbin sendmail No such file or directory The abridged cylstif OPP file includes the following optimized design after completion of the second execution of SUPEROPT from the cylstif OPP file VALUES OF DESIGN VARIABLES CORRESPONDING TO BEST FEASIBLE DESIGN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 1 011E 01 B STR stiffener spacing b STR seg NA layer NA 2 STR 2 0 3 370E 00 B2 STR width of stringer base b2 must be gt 0 see Help STR seg 2 lay 3 STR 3 0 7 817E 00 H STR height of stiffener type H for sketch h STR seg 3 layer NA 4 STR 4 0 2 534E 00 W STR width of outstanding flange of stiffener w STR seg 4 layer NA 5 SKN 1 1 7 690E 01 T 1 SKN thickness for layer index no 1 SKN seg 1 layer 1 6 STR 3 1 2 038E 01 T 2 STR thickness for layer index no 2 STR seg 3 layer 1 7
207. nds on what sort of adhesive is used between stringers and skin and its thickness You will probably have to consult peel test data for this input datum Units required are force length A typical value for graphite epoxy is in the range 40 100 lb in Figures 5 and 6 of the paper PANDA2 program for minimum weight design of stiffened composite locally buckled panels show the phenomenon just described and a peel test specimen Figure 7 is a photograph of a graphite epoxy peel test specimen after failure What force axial length will cause web peel off 1000000 1000000 Now you will be asked to provide properties for the panel module on a segment by segment basis starting with the skin which is Segment 1 as shown in the Figure above In each segment of the module the wall is considered to be divided into groups of layers There are two types of groups 1 default groups 12 layers 90 0 45 45 0 90 s all of the same material and initially all of the same thickness If you choose this option winding angles cannot be decision variables Thicknesses can be decision variables 2 just plain groups any number of layers any winding angles any variety of material types and any variety of thickness Winding angles CAN be decision variables For each default group group type 1 you will be asked to give 1 the thickness of one of the layers 2 the material type For each just plain group group type 2 you must provi
208. ng bucklng discrete model n 32 circ halfwaves FS 1 1 lines skipped to save space From CHAPTER 22 of PART 1 19 ring sidesway buckling mode Margin 5 8244E 01 lLo n Ring sidesway discrete model n 4 circ halfwaves FS 1 1 The ring sidesway buckling load factor can be obtained from the Margin as follows factor of safety x Margin 1 0 1 1 x 0 58244 1 0 1 74068 buckling load factor buckling load factor Get plots of the two critical buckling modes bush gt bosorplot Please enter the BIGBOSOR4 case name cylstif Do you want to use Xgraph or create a PostScript file Choose X or P p etc etc as above end of obtaining the plot file metafile ps bush gt cp metafile ps plot4 ps bush gt gv plot4 ps gv means ghost view you will see the buckling mode on your screen Take a screen shot of this buckling mode and store it in the file 5 cylstif ringsidesway panel2 png bush gt bosorplot Please enter the BIGBOSOR case name cylstif Do you want to use Xgraph or create a PostScript file Choose X or P p etc etc as above end of obtaining the plot file metafile ps bush gt cp metafile ps plot30 ps bush gt gv plot30 ps gv means ghost view you will see the buckling mode on your screen Take a screen shot of this buckling mode and store it in the file 6 cylstif interring panel2 png kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
209. ng load factor FS 1 FS 1 1 circ halfwaves FS 1 1 circ halfwaves FS 1 1 eff stress matl 1 RNG Iseg 4 allnode layer 1 z 0 4726 RNGS FS 1 Inter ring bucklng discrete model n 32 Lo n Ring sidesway discrete model n 5 buckling margin stringer Iseg 3 Local halfwaves 4 buckling margin stringer Iseg 4 Local halfwaves 4 7C 0 buckling stringer Iseg 4 as beam on foundation buckling margin ring Iseg 3 Local halfwaves 32 buckling stringer Isegs 3 4 together M 4 FS 1 RNGS FS 1 RNGS FS 1 RNGS FS M 369 RNGS FS 1 2 RNGS FS 1 1 4 buckling ring Iseg 4 as beam on foundation M 67 RNGS FS 1 2 buck SAND rolling with smear rings M 93 N 1 slope 0 FS 1 1 buck SAND rolling only of stringers M 8 N 0 slope 0 FS 1 4 buck SAND hiwave roll of stringers M 54 N 0 slope 0 FS 1 2 buck SAND rolling only axisym rings M 0 N 0 slope 0 FS 1 4 buck SAND STRINGERS web buckling M 4 N 1 slope 0 01 FS 1 buck SAND RINGS web buckling M Max allowable ave axial strain ave axi ALL 1 LOAD SETS PROCESSED xxxx 2 7 7 6 a 1 N 1 slope 0 04 FS strain 1 FS 1 SUMMARY OF INFORMATION FROM OPTIMIZATION ANALYSIS VAR DEC ESCAPE LINK LINKED LINKING LOWER CURRENT UPPER NO VAR VAR VAR TO CONSTANT BOUND VALUE BOUND 1 Y N N 0 0 00E 00 1 00E 01 1 0110E 01 3 00E 01 B STR stiffener spacing b STR seg NA layer NA 2 N N Y 1 3 33E 01 0 00E 00 3 3698E 00 0 00E 00 of stringer base b2
210. ng of perfect shell from STAGS 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 1 0 4 0 1 S PL 3 KPLOT NUNIT ITEM STEP MODE 0 0 0 SPL 5 DSCALE NROTS end of cylstif pin file The latest buckling mode from STAGS is shown in the plot ll cylstif stagsunit smrstr eigl png Because the rings are internal the plot hides most of the rings We wish to obtain a plot of the same mode with the skin with its smeared stringers removed so that we can see the rings The input data for STAPL in this particular is as follows cylstif pin file input for STAPL linear buckling of perfect shell from STAGS 1 0 1 0 S PL 2 NPLOT IPREP IPRS KDEV 1 20 4 0 1 PL 3 KPLOT NUNIT ITEM STEP MODE 2 3456789 10 11 12 13 14 15 16 17 18 19 20 21 0 0 0 PL 5 DSCALE NROTS end of cylstif pin file The buckling mode is displayed in the file 12 cylstif stagsunit smrstr eigl rngs png PART 3 14 Compare with the predictions from BIGBOSOR4 and PANDA2 Compare the latest STAGS eigenvalue 1 709327E 00 with the eigenvalues that correspond to ring sidesway obtained from BIGBOSOR4 PART 2 7 and PANDA2 PART 2 7 From the BIGBOSOR4 model generated with the use of PANEL2 x x CRITICAL EIGENVALUE AND WAVENUMBER EIGCRT 1 6141E 00 NO OF CIRC WAVES NWVCRT 4 ee ee ee xx x k EIGENVALUES AND MODE SHAPES EIGENVALUE CIRC WAVES 1 6929E 00 2 1 6141E 00 4 lt ring sidesway cr
211. ng parts are assigned by PANDA2 you have no control over them FSLOC plays a special role If you do NOT want local buckling to occur you don t want any postbuckling capability then set FSLOC greater than unity minimum of 1 1 as with FSGEN and FSPAN With the IQUICK 0 option PANDA2 assumes the panel between adjacent stringers is flat so that FSLOC 1 1 can be used If you want postbuckling capability but you do not want local buckling to occur at less than a certain fraction of the applied load then set FSLOC equal to that fraction of the load For example suppose the load set Nx Ny Nxy corresponds to an ultimate load that is 1 5 times the design load You may not want local buckling to occur below a limit load that is 1 25 times the design load To enforce this constraint set FSLOC 1 25 1 50 0 8333 If you are not bothered by local buckling at all set FSLOC equal to zero Occasionally you may want to use FSLOC 0 999 You do this in order to prevent PANDA2 from automatically increasing FSLOC to 1 1 which it does if FSLOC 1 0 For example you might wamt to use FSLOC 0 999 in a case for which you intend to compare results from PANDA2 with results from some other analysis Minimum load factor for local buckling Type H for HELP FSLOC 1 1 1 000000 FACTOR OF SAFETY FOR LOCAL INSTABILITY FSLOC 1 HAS BEEN CHANGED TO FSLOC 1 1 TO AVOID SINGULARITY You will next be asked to provide a minimum load fact
212. nse 1146 10 1 u 8a NSOR IUNIT IROW ICOL SCALE torque location 1 1 1 0 u 8b P LU LR LC wgt slave unit row col 100001 v 1 print displacement nodal reaction end of the long STAGS input file cylstif inp The cylstif bin and cylstif inp files are valid input files for STAGS PART 3 9 Execute STAGS Next go to a directory where you want to run STAGS and run STAGS At the writer s facility the correct commands are as follows ftp feynman lt username gt lt password gt cd home bush put cylstif bin put cylstif inp telnet feynman lt username gt lt password gt cd home bush cat stags execute source home weiler stags6 prc initialize Please enter your machine type SSTAGSMACHINE from the list below If your machine is not listed just enter one of the choices alpha DEC Alpha workstation amd64 64 bit machine LINUX Intel compilers gfc64 64 bit machine LINUX gfortran gcc compilers envx Convex C120 or C220 mainframe cray CRAY XMP YMP mainframe crayts CRAY TS super computer dec DEC station 5000 or DEC station 3100 hpo Hewlet Packard 32 bit workstation hp4 HP 64 bit architecture amp code 4 byte integers hp8 HP 64 bit architecture amp code 8 byte integers rs6k IBM RS_6000 workstation 1a64 Intel 64 bit architecture amp code 8 byte integers linux Intel 32 bit architecture amp code 4 byte integers macosx MAC OS X 3
213. nt e g lb in normal to the plane of screen Nx0 0 0 Resultant e g lb in in the plane of the screen Ny0 0 0 Normal pressure in STAGS model in Load Set B p0 0 0 Starting load factor for Load System A STLD 1 h Use 1 0 for INDIC 1 linear buckling analyses For transient restarts from nonlinear static runs that got stuck because of singularities on the primary load path use the load factor corresponding to one or two steps back from the last step converged STAGS does not yet properly store information for the last step successfully completed if the run stopped because of maximum number of cuts in step For example if STAGS could not get a converged solution for Load Step 31 then for some reason Load Step 30 is not properly stored Therefore you should use the load factor corresponding to Load Step 29 or perhaps 28 PANDA2 will automatically supply an appropriate value for the actual load factor to be used in the transient analysis This PANDA2 provided value will be a bit higher than the highest load factor reached by STAGS in the case so that the structure will start to move to a new state Starting load factor for Load System A STLD 1 1 0 1 000000 Load factor increment for Load System A STEP 1 h Use zero for linear buckling analysis INDIC 1 and transient analysis INDIC 6 Load factor increment for Load System A STEP 1 0 0 000000 Maximum load factor for Load System A FACM 1 h Use FACM 1 1 0 for eigenv
214. o plot the layup configuration of the skin stringer panel module ITYPE 3 8 Whether or not to obtain a 3 D plot of the locally post buckled panel module ITYPE 3 The results of the interactive session are saved in a file called cylstif CPL in which cylstif is your name for the case You may find this file useful for future runs of CHOOSEPLOT in which you want to avoid answering many questions interactively CHOOSEPLOT also generates the six files cylstif OPL cylstif PL3 cylstif PL4 cylstif PL5 cylstif PL6 cylstif PL7 cylstif PL8 cylstif PL9 cylstif PL10 which are described briefly at the end of this run If you choose the tutorial option cylstif OPL contains a complete list of the interactive session including prompting questions all help paragraphs your responses to the prompting questions and evolving lists of which parameters are to be plotted as they are chosen by you kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Are you correcting adding to or using an existing file n Do you want a tutorial session and tutorial output n oe design variables to be plotted v iterations Y or N n oe design margins to be plotted Y or N n BS you want a plot of the objective v iterations Y N y Y Do you want to get more plots before your next SUPEROPT n DESCRIPTION OF FILES GENERATED BY THIS CASE cylstif CPL Summary of interactive session you have just completed This file can be edited and used fo
215. ocessor called PANEL In this BIGBOSOR4 model the T stringers are modeled as flexible shell segments and the T rings are replaced by simple supports The axial length of the prismatic shell included in the BIGBOSOR4 model is B RNG the ring spacing Half of the circumference of the cylindrical shell is included in the model The axial length of the model is 10 110 inches which is the optimized ring spacing The prismatic shell BIGBOSOR4 model is used bush gt panel Please enter PANDA2 case name cylstif kkkkkkkkkkkkkxkkk PANEL kkkkxkkkkkkkkkkkk kkk The purpose of PANEL is to set up an input file NAME ALL for a multi module model of a panel NAME is your name for the case The file NAME ALL is a BIGBOSOR4 input deck used by the batch run you launch next via the command BIGBOSORALL kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxk Are you correcting adding to or using an existing file n n Do you want a tutorial session and tutorial output n n Panel length in the plane of the screen L2 314 16 314 1600 Enter control 0 or 1 for stringers at panel edges h 0 means edge is half a stringer spacing away from nearest stringer 1 means there is a stringer at each of the edges of the panel normal to the plane of the screen Enter control 0 or 1 for stringers at panel edges 1 0 Enter control l sym 2 s s for boundary condition h 1 means symmetry conditions applied at the edges of the panel normal to the plane o
216. of fixed parameters n Do you want to change values of allowables t he list of the input file cylstif CHG The file cylstif CHG represents an archive of the optimum design It can be used in the future to re establish that optimum design PART 1 16 Execute the PANDA2 processors called SETUP MAINSETUP and PANDAOPT again in order to verify that the archive file cylstif CHG is correct bush gt setup Enter case name cylstif Output from SETUP rolls by fast on the screen bush gt mainsetup Please enter PANDA2 case name cylstif kkkkkkkkkkkkkkkkk MAINSETUP kkkkkkkkkkkkkkkk The purpose of this processor is to permit you to choose loads and initial imperfections Nx Ny Nxy Mx My Nxo Nyo p T iseg Wimp global Wimp local up to 5 sets of them safety factors for general instability panel instability local instability panel skin local instability stiffener parts and stress and strategy parameters for subsequent batch execution of an optimization analysis analysis type 1 or an analysis of a fixed design at fixed load levels analysis type 2 or an analysis of a fixed design for a single load set for monotonically increasing load levels test simulation analysis type 3 Results of the interactive session in MAINSETUP are saved on a file called cylstif OPT which will appear at the beginning of the cylstif OPM file when the mainprocessor batch run launched by your command PA
217. on zero density to at least one part of the panel 2 means that PANDA2 will find the minimum distortion of the panel due to uniform temperature changes To use this option you must have previously assigned non zero coefficient of thermal expansion to at least one part of the panel and you must have assigned nonzero curing temperature to all parts of the panel that have nonzero coefficients of thermal expansion This curing temperature should be the same in all these parts PANDA2 minimizes the quantity DISTORTION SQRT ET1 2 ET2 2 TEFF 1 ET4 2 TEFF 2 ET5 2 in which ET1 ET2 ET4 ET5 are the thermal strains and changes in curvature due to curing for the panel with smeared stiffeners and TEFF 1 and TEFF 2 are the effective thicknesses of the panel with smeared stiffeners in the axial and circ coordinate directions respectively Index for objective l min weight 2 min distortion lt enter gt 1 FMARG Skip load case with min margin greater than FMARG h Generally use FMARG gt 0 5 FMARG must be greater than 0 1 If you have an optimization problem with many load sets and a lot of computer time is required for design iterations you might want to set FMARG to a number as low as 0 2 or even in extremely long running cases to a number as small as 0 11 You should have as the first load case that which is most likely to generate the most critical design margins In the first design iteration of each PANDAOP
218. oot and tip of web At tip of web 2 2922E 04 r in plane shearing of web and f the web FKNOCK 6 8 3564E 01 margin ring Iseg 3 Local halfwaves 32 MID FS 1 ring Iseg 4 as beam on foundation M 67 MID FS 1 2 r ring general buckling load type models 1B and from le trigonometric series Ref 1G Also compute sandwich wall behavior 1F if applicable Also compute buckl when substiffeners lines skipped to save space general buckling smeared stif lines skipped to save space EIGMNC 2 72E 00 2 72E 00 3 SLOPEX 0 00E 00 0 00E 00 0 MWAVEX 1 1 NWAVEX 3 3 lines skipped to save space Buckling load factor before t ing load factors appropriate are present feners Cll 1 0238E 07 radius R 1 0000E 02 79E 00 6 72E 00 1 00E 17 2 72E 00 1 00E 17 00E 00 0 00E 00 0 00E 00 0 00E 00 0 00E 00 2 4 0 1 1 3 5 0 3 0 s d 2 7174E 00 After t s d 2 4489E 00 lines skipped to save space Number of circumferential halfwaves in buckling pattern 3 0000E 00 Buckling load factor BEFORE knockdown for smeared stringers 2 4489E 00 Buckling load factor AFTER knockdown for smeared stringers 2 2966E 00 General buckling load factor before and after knockdown EIGGEN before modification by 5 factors below 2 2966E 00 Knockdown factor from modal imperfection s 1 0000E 00 Knockdown factor for smearing rings on cyl shell 9 0000E 01 Knockup factor to avoid twice accounting for t s d 1 0000E 00 lst modifyin
219. opt several more pandaopts if the previous command is not superopt chooseplot diplot change superopt or pandaopt etc cleanpan Please consult the files in panda2 doc for more information about PANDA2 Also review the sample cases in panda2 case Also read the published papers listed in the file panda2 doc panda2 ref The file panda2 doc panda2 news contains updates and comments since 1987 Useful annotation appears in the OPM file when NPRINT 2 in the OPT file USEFUL HINT PERTAINING TO THE INTERACTIVE INPUT YOU SHOULD PROVIDE DURING mainsetup After you type the command mainsetup try just hitting ENTER to obtain the default value of any data entry that you are unsure about PANDA2 will provide what its developer usually chooses Generally use 5 iterations pandaopt Generally use NPRINT 0 Generally use superopt Generally choose 5 pandaopts per autochange for superopt runs USEFUL HINT FOR SAVING OPTIMUM DESIGNS FOR FUTURE RUNS Once you have obtained a global optimum design that you are happy with execute the process called change in order to save this global optimum design in a file called CHG Then the global optimum design will be preserved in the CHG file after execution of cleanpan You can then execute change immediately following begin in order to re establish that same global optimum design at any time in the future FILES THAT ARE PRESERVED FOLLOWING EXECUTION OF THE COMMAN
220. or FSBSTR for local buckling of the stringer parts You should probably use a factor of unity If you use a factor less than unity PANDA2 may produce a design in which one or more of the stringer parts buckle locally at a load smaller than the applied load Thus local buckling of the stringer parts would be allowed in your design concept USE WITH CAUTION IF YOU PLAN TO USE A VALUE OF FSBSTR THAT IS LESS THAN UNITY MAKE SURE THAT YOU FIRST READ CAREFULLY ITEMS 37 60 c AND 67 IN PANDA2 NEWS Also read items 19 and 30 of PANDA2 NEWS If the stiffeners are J or T cross sections a factor of 1 4 is applied to the buckling load factor for buckling of both segments 3 and 4 of the stiffener together The factor you next apply is in addition to this so that the total factor is F S 1 4 FSBSTR Minimum load factor for stiffener buckling Type H FSBSTR 1 h Stiffener buckling here means local buckling of the parts of the stiffener with the corners between stiffener parts rotating but not displacing IF YOU PLAN TO USE A VALUE OF FSBSTR THAT IS LESS THAN UNITY MAKE SURE THAT YOU READ CAREFULLY ITEMS 37 60 c AND 67 IN PANDA2 NEWS FSBSTR plays a special role If you do NOT want local buckling to occur you don t want any postbuckling capability of the stiffener parts then set FSBSTR greater than unity Minimum value of 1 1 is suggested The factor of safety for buckling of ring parts is always 1 0 or greater If
221. or which the stringers deflect FSLOC pertains to local instability between adjacent rings and stringers FSBSTR pertains to local buckling of stringer parts FSLOC and FSBSTR play special roles so read this carefully FSSTR is the factor of safety for stress FSGEN and FSPAN should always be greater than or equal to unity The purpose of these two factors is to compensate for initial imperfections and to prevent general instability or panel instability general buckling between rings The values you assign these factors depend on the geometry and loading There is a huge literature on the difficult subject of imperfection sensitivity A recent survey is contained in the book COMPUTERIZED BUCKLING ANALYSIS OF SHELLS by David Bushnell published by Nijhoff and Co The Netherlands in 1985 If you assign a factor of 1 0 to FSGEN and or FSPAN the factor will automatically be changed by PANDA2 to 1 1 in order to avoid the nearly singular behavior that occurs near general or panel buckling abrupt increase in bowing amplitude This singular behavior causes difficulties in convergence of the design during optimization iterations Note During 1993 1994 PANDA2 was upgraded to allow the user to supply amplitudes of the following kinds of initial geometric imperfections in unstiffened and stiffened cylindrical panels and shells 1 Out of roundness 2 General buckling modal imperfection imperfection has the shape of the critical general bu
222. order to save space Next give a command CHANGE or CHOOSETEMP or SETUP a bush gt setup Enter case name cylstif Output from SETUP rolls by fast Not reproduced here in order to save space Pandaread pre processor complete Next give the command DECIDE or MAINSETUP kkkkxkkkkkkkkkkkkkkkkkkkkk NOTE BERK KKKKKKKKKKKKKKKKKKKKKKEKK Next we edit the file cylstif DEC in order to reduce the upper bound of the stringer spacing from 50 inches to 30 inches The part of the cylstif DEC file involved before the edit is as follows 1 Choose a decision variable 1 2 3 10 Lower bound of variable no 1 50 Upper bound of variable no 1 and after the edit is as follows 1 Choose a decision variable 1 2 3 10 Lower bound of variable no 1 30 Upper bound of variable no 1 kkkxkxkkkkkkkkkkkkkkkkxkk END NOTE B RRR KKK KKKKKKKKKKKKKEKKKKKE Then we run DECIDE bush gt decide Please enter PANDA2 case name cylstif kkkkkkkkkkkkkkkkxk DECIDE kkkkxkkkkkkkkkkkkxkkk The purpose of DECIDE is to permit you to choose decision variables linked variables and escape variables for the optimization run or runs to follow The results of the interactive session are saved in a file called cylstif DEC in which cylstif is your name for the case You may find this file useful for future runs of DECIDE in which you want to avoid answering many questions interactively DECIDE also generates a file called cy
223. orque n Is stiffener sidesway permitted at the panel edges NOTE gt 1 Edges parallel to screen 0 in plane deformable 1 rigid NOTE gt 1 Stringer web axial displacement index IBCXOXL 0 or 1 end of the cylstif STG file input for STAGSUNIT In the previous STAGS model the last two lines of the cylstif STG file were as follows 0 Edges parallel to screen 0 in plane deformable 1 rigid 0 Stringer web axial displacement index IBCX0XL 0 or 1 STAGS is run again as described above and the following lines now appear in the cylstif out2 file a fragment from the STAGS file cylstif out2 CONVERGENCE HAS BEEN OBTAINED FOR EIGENVALUES 1 THROUGH 1 CRITICAL LOAD FACTOR COMBINATION NO EIGENVALUE LOAD SYSTEM A LOAD SYSTEM B DOF 1 1 186805E 00 1 186805E 00 0 000000E 00 89555 end of fragment from the STAGS file cylstif out2 In the previous STAGS model the lowest bifurcation buckling eigenvalue was 1 030548E 00 listed above in PART 3 9 Compare the latest STAGS eigenvalue 1 186805E 00 with the eigenvalue from BIGBOSOR4 BUCKLING LOADS FOLLOW AXIAL HALF WAVE NUMBER N 1 EIGENVALUES 1 21180E 00 1 21651E 00 1 22461E 00 x x x CRITICAL EIGENVALUE AND WAVENUMBER EIGCRT 1 2118E 00 NO OF AXIAL HALF WAVES NWVCRT 1 Compare with the eigenvalue from CHAPTER 14 of the PANDA2 file cylstif OPM for the perfect shell BUCKLING LOAD FACTORS FROM BOSOR4 TYPE DI
224. ove Make sure that the margins and weight and values of the decision variables are essentially the same as before NOTE very small margins may differ in the signficant figures but that does not matter as long as they remain very small PART 1 17 Execute the PANDA2 processors called MAINSETUP and PANDAOPT again this time for the perfect shell Next edit the input for MAINSETUP the file cylstif OPT to set the general buckling modal imperfction equal to zero as follows 0 0 Initial buckling modal general imperfection amplitude Wimpg2 1 and run MAINSETUP and PANDAOPT again for the same fixed optimized design Why do we do this Because afterward we intend to run BIGBOSOR4 in order to verify the PANDA2 predictions and BIGBOSOR4 cannot handle non axisymmetric buckling modal imperfection shapes bush gt mainsetup Please enter PANDA2 case name cylstif kkkkkkkkkkkkkkk kk MAINSETUP kkkkkkkkkkkkkk kk The purpose of this processor is to permit you to choose loads and initial imperfections Nx Ny Nxy Mx My Nxo Nyo p T iseg Wimp global Wimp local up to 5 sets of them safety factors for general instability panel instability local instability panel skin local instability stiffener parts and stress and strategy parameters for subsequent batch execution of an optimization analysis analysis type 1 or an analysis of a fixed design at fixed load levels analysis type 2 or an analysis of a fixed design
225. paed stiffeners via PANDA2 1998 SDM Meeting for some guidance Do you want to prevent secondary buckling mode jumping lt enter gt Y Do you want to use the alternative buckling solution h The alternative buckling solution is more accurate but uses much more computer time than the regular solution The regular solution is the PANDA type closed form solution obtained from the assumed displacement field given by Eqs 50 in the paper Theoretical basis Computers and Structures Vol 27 pp 541 563 1987 leading to Eq 57 on p 553 of that paper The alternative solution is obtained via double trig series expansions for buckling modal displacement components u v w It is described in detail in ITEM 438 of panda2 doc panda2 news SUGGESTION Start optimization by answering N Then finalize with use of the answer Y Do you want to use the alternative buckling solution lt enter gt N Next you will be asked for the number of design iterations This is the number of iterations corresponding to a single execution of PANDAOPT not the total number of iterations to be processed for your entire case It is almost always best to use a small number like 5 iterations The best optimization strategy is explained in connection with Fig 83 on p 582 of the long 1987 PANDA2 paper PANDA2 Program for minimum weight design of stiffened composite locally buckled panels Computers amp Structures Vol 25 No
226. parameter to change 1 2 3 3 377856 New value of the parameter y Want to change any other parameters in this set 3 Number of parameter to change 1 2 3 7 816700 New value of the parameter y Want to change any other parameters in this set 4 Number of parameter to change 1 2 3 2 534000 New value of the parameter y Want to change any other parameters in this set 5 Number of parameter to change 1 2 3 0 7689600 New value of the parameter y Want to change any other parameters in this set 6 Number of parameter to change 1 2 3 0 2038000 New value of the parameter y Want to change any other parameters in this set 7 Number of parameter to change 1 2 3 0 8449600E 01 New value of the parameter y Want to change any other parameters in this set 8 Number of parameter to change 1 2 3 33 33333 New value of the parameter Want to change any other parameters in this set 10 Number of parameter to change 1 2 3 9 783000 New value of the parameter y Want to change any other parameters in this set 11 Number of parameter to change 1 2 3 4 303700 New value of the parameter y Want to change any other parameters in this set 12 Number of parameter to change 1 2 3 0 5672900 New value of the parameter Want to change any other parameters in this set 13 Number of parameter to change 1 2 3 0 9452400 New value of t
227. post bifurcation behavior rather than the general instability behavior In such a case you might choose a length XSTAGS that is equal to no more than about 10 axial half waves of the local buckling pattern X direction length of the STAGS model of the panel XSTAGS 300 300 Panel length in the plane of the screen L2 h For a cylindrical panel this is the arc length along the circumference of the entire panel A complete cylindrical shell can be modelled by using L2 pi radius Then the number of half waves over this circumferential length is the same as the number of full waves around the complete 360 degree circum ference If you are analyzing a complete cylindrical shell especially one with loads that vary around the circumference it will probably be best to divide it into panels Then analyze the panel as a structure subjected to multiple sets of uniform loads See the paper PANDA2 program for minimum weight design of stiffened composite locally buckled panels for an example Computers and Structures Vol 25 pp 570 574 Fig 79 Panel length in the plane of the screen L2 628 31854 628 3185 STAGSUNIT MAY HAVE CHANGED YOUR INPUT VALUE OF YSTAGS YOUR INPUT VALUE OF ARC LENGTH OF THE PANEL YSTAGS 6 2832E 02 STAGSUNIT HAS CHANGED THE ARC LENGTH TO YSTAGS 6 2832E 02 WHICH IS EXACTLY EQUAL TO A MULTIPLE OF THE STRINGER SPACING Is the nodal point spacing uniform along the stringer axis h Generally answer Y If you have a pan
228. pper bound to 30 inches Then we will start over from the beginning of the case by first cleaning up the cylstif files cleanpan and then executing the PANDA2 processors BEGIN SETUP DECIDE MAINSETUP SUPEROPT as follows bush gt cleanpan Enter the case name cylstif You now have the following case cylstif files in your directory cylstif BEG cylstif DEC cylstif OPT bush gt begin Please enter PANDA2 case name cylstif kkkkkkkkkkkkkxkkk BEGIN kkkkkkkkkkkkkkkk kk Purpose of BEGIN is to permit you to provide a starting design in an interactive mode You give starting dimensions material properties allowables The interactive session is stored on a file called cylstif BEG in which cylstif is a name that you have chosen for the case cylstif must remain the same as you use all the PANDA2 processors In future runs of the same or a slightly modified case you will find it convenient to use the file cylstif BEG as input Rather than answer all the questions interactively you can use cylstif BEG or an edited version of cylstif BEG as input to BEGIN BEGIN also generates an output file called cylstif OPB cylstif OPB lists a summary of the case and if you choose the tutorial option the questions helps and your answers for each input datum kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Are you correcting adding to or using an existing file y The BEGIN interactive session rolls by fast Not reproduced here in
229. question Y Note however that there may be cases when you will want to do preliminary optimization runs in which M is fixed at a value that you know is near the critical value for plates with aspect ratios fairly close to that of your current design In this way you can save a lot of computer time and perhaps come up with a good preliminary optimum design You can always later allow M to vary thereby checking your intuition and further improving the design Do you want to vary M for minimum local buckling load y Y Do you want to choose a starting M for local buckling h M is the number of axial halfwaves between rings or if there are no rings along the entire axial length of the panel If you answer N for no PANDA2 starts with M calculated from the formula M S RT C 5 5 C 4 4 axial length of panel between rings stringer spacing stringer base width 2 which is based on experimental observations that local buckles of uniformly axially compressed long narrow isotropic plates are almost square However from previous experience on this and other similar cases you may wish to use a different starting value for M Generally answer this question N for no Do you want to choose a starting M for local buckling n n Do you want to perform a low axial wavenumber search h What is being referred to here is a search over the number of axial halfwaves between rings to determine the critical local buckling lo
230. r future runs of CHOOSEPLOT cylstif CBL Contains the cylstif data base cylstif OPL Output from CHOOSEPLOT Please list this file and inspect it and the cylstif CPL file carefully before proceeding cylstif PL3 File for margin plots via DIPLOT cylstif PL4 File for design variable plots ITYPE 1 or behavior v load plots ITYPE 3 or in plane load interaction curves ITYPE 5 via DIPLOT cylstif PL5 File for objective plot ITYPE 1 or undeformed and deformed panel module ITYPE 3 or in plane load combinations ITYPE 5 via DIPLOT cylstif PL6 File for plot of layup of skin stringer module ITYPE 3 cylstif PL7 File for 3 D plot of locally post buckled panel module ITYPE 3 cylstif PL8 File for plot of AXIAL or 45deg extreme fiber strains v a selected load component ITYPE 3 cylstif PL9 File for plot of HOOP or 45deg extreme fiber strains v a selected load component ITYPE 3 cylstif PL10 File for plot of SHEAR strains at 0deg or 45deg v a selected load component ITYPE 3 For further information about files generated during operation of PANDA2 give the command HELPAN FILES NEXT INSPECT THE FILE cylstif OPL AND THEN IF ALL IS OKAY GIVE THE COMMAND DIPLOT The interactive CHOOSEPLOT session produces the following file Do you want a tutorial session and tutorial output Any design variables to be plotted v iterations Y or N Any design margins to be plotted Y or N Do you want
231. r r 1 rw r r 1 The user provided session are saved follows 25000 00 50000 00 0 000000 1 000000 1 000000 1 000000 1 000000 1 000000 n Y n 0 0 0 500 000 Y Y 0 Y n 0 000000 0 5000000 0 000000 0 000000 Y 300 0000 Y 1 000000 KBBBBBKDB ZKK e O m AY UE gt UU UP NUNN NNNUNN NNN NUNON NNNUNN NNNUNN NNNUNN NNNNNNNN bush bush 0 Feb 21 11 49 cylstif OPM bush bush 4547 Feb 21 12 44 cylstif OPT bush bush 33792 Feb 21 11 27 cylstif RN1 bush bush 36864 Feb 21 11 27 cylstif RN2 bush bush 33792 Feb 21 11 27 cylstif RN3 bush bush 33792 Feb 21 11 27 cylstif RN4 input data from the MAINSETUP interactive in the file cylstif OPT A list of that file Do you want a tutorial session and tutorial output Resultant e g lb in normal to the plane of screen Nx 1 Resultant e g lb in in the plane of the screen Ny 1 In plane shear in load set A Nxy 1 Does the axial load vary in the L2 direction Applied axial moment resultant e g in lb in Mx 1 Applied hoop moment resultant e g in lb in My 1 Want to include effect of transverse shear deformation IQUICK quick analysis indicator 0 or 1 Do you want to vary M for minimum local buckling load Do you want to choose a starting M for local buckling Do you want to perform a low axial wavenumber search Factor of safety for general instability FSGEN 1 Factor of safety for panel between rings instability FSPAN
232. r 1 z 0 3845 MID FS 1 8 7 13E 01 buckling margin stringer Iseg 3 Local halfwaves 4 MID FS 1 9 2 55E 01 buckling margin stringer Iseg 4 Local halfwaves 4 MID FS 1 10 2 16E 01 buckling stringer Isegs 3 4 together M 4 C 0 MID FS 1 4 11 8 85E 00 buckling stringer Iseg 4 as beam on foundation M 369 MID FS 1 2 12 1 41E 00 buckling margin ring Iseg 3 Local halfwaves 32 MID FS 1 13 1 05E 01 buckling ring Iseg 4 as beam on foundation M 67 MID FS 1 2 14 8 24E 01 buck SAND simp support general buck M 1 N 3 slope 0 FS 1 1 15 1 69E 01 buck SAND rolling with smear rings M 93 N N 1 slope 0 FS 1 1 16 4 30E 01 buck SAND rolling only of stringers M 8 N 0 slope 0 FS 1 4 17 1 30E 00 buck SAND hiwave roll of stringers M 54 N 0 slope 0 FS 1 2 18 5 92E 01 buck SAND rolling only axisym rings M 0 N 0 slope 0 FS 1 4 19 7 13E 01 buck SAND STRINGERS web buckling M 4 N 1 slope 0 FS 1 20 1 39E 00 buck SAND RINGS web buckling M 26 N 1 slope 0 FS 1 21 6 99E 02 Max allowable ave axial strain ave axial strain 1 FS 1 L PART 3 5 Execute the PANDA2 processor called STAGSUNIT in order to generate valed input files bin amp inp for STAGS In this first STAGSUNIT case we include the entire cylindrical shell in the STAGS model with the T rings and T stringers all modeled with flexible shell segments Shell units in STAGS jargon Next in order to generate the STAGS model execute the PANDA2 processor called STAG
233. r PANDA2 case name cylstif kkkkkkkkkkkkkkkkk MAINSETUP kkkkkkkkkkkkkkkk The purpose of this processor is to permit you to choose loads and initial imperfections Nx Ny Nxy Mx My Nxo Nyo p T iseg Wimp global Wimp local up to 5 sets of them safety factors for general instability panel instability local instability panel skin local instability stiffener parts and stress and strategy parameters for subsequent batch execution of an optimization analysis analysis type 1 or an analysis of a fixed design at fixed load levels analysis type 2 or an analysis of a fixed design for a single load set for monotonically increasing load levels test simulation analysis type 3 Results of the interactive session in MAINSETUP are saved on a file called cylstif OPT which will appear at the beginning of the cylstif OPM file when the mainprocessor batch run launched by your command PANDAOPT has been completed NOTE JUST HIT RETURN FOR DEFAULT VALUE OF INPUT DATUM IF PANDA2 REQUIRES AN INPUT IT WILL SAY PLEASE SAY SOMETHING KKK KK KKK KKK KKK KKK KKK KKK KKK kkk KKK KKK KKK RKKK RKKK RKKK K Are you correcting adding to or using an existing file n n Do you want a tutorial session and tutorial output n n x x NOTE NOTE NOTE NOTE NOTE NOTE Your applied loads should correspond to the ULTIMATE load condition in contrast to LIMIT loads or OPERATING loads xxx END NOTE END NOTE END
234. r Y PANDA2 will then automatically choose as escape variables all of the thicknesses that are decision variables This is usually the best strategy and use of the default option saves you the trouble of doing it interactively Want to have escape variables chosen by default y y ESCAPE VARIABLES FOR THE OPTIMIZATION PROBLEM VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer 6 STR 3 1 1 000E 01 T 2 STR thickness for layer 7 STR 4 1 1 000E 01 T 3 STR thickness for layer 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer DESCRIPTION OF FILES GENERATED BY THIS CASE index index index index index no 1 no 2 no 3 no 4 no 5 ed cylstif DEC Summary of interactive session you have just completed This file can be edited and used for future runs of DECIDE cylstif CBL Contains part of cylstif data base cylstif OPD Output from DECIDE Please list this file and inspect it and the cylstif DEC file carefully before proceeding For further information about files generated during operation of PANDA2 give the command HELPAN FILES Next give either command CHOOSETEMP or MAINSETUP The user provided input data supplied during the DECIDE interactive session are saved in the file cylstif DEC A list of cylstif DEC follows cylstif DEC file input for DECIDE n
235. r layer index no 4 PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 13 13 Lower bound of variable no 13 01 0 1000000E 01 Upper bound of variable no 13 1 1 000000 Any more decision variables Y or N n n 11 decision variables have now been identified 40 decision variables are permitted 29 additional decision variables are allowed Next choose linked variables A linked variable is a variable that is not a decision variable but is expressed in terms of decision variables thus linked variable Cl1 decision variable no jl C2 decision variable no j2 C3 decision variable no j3 etc up to max of 5 terms C0 in which C1 C2 and C0 are constants For example material layers with ALPHA degree orientation are usually matched with layers with ALPHA degree orientation Suppose for a certain layer with winding angle ALPHA this winding angle is chosen as a decision variable You want another layer in the same laminate to have the winding angle ALPHA Then for this other layer winding angle 1 0 winding angle of the layer with ALPHA The winding angle on the left hand side of the above equation is called a linked variable because its value is
236. r selected ending value 5 means that margins and interaction curves will be calculated for a user selected in plane load combination N1 N2 Nx Ny or Nx Nxy or Ny Nxy for a user selected number of values of N1 and N2 Choose type of analysis ITYPE 1 or 2 or 3 or 4 or 5 1 1 Do you want to prevent secondary buckling mode jumping h Secondary Buckling means mode jumping or post post local buckling Mode jumping is initiated by local bifurcation buckling in a panel skin which has already been loaded well beyond initial local buckling Mode jumping might cause material failure especially for composite walls that delaminate relatively easily Example of secondary buckling Suppose you have an axially stiffened panel under pure axial compression For axial loads well above that corresponding to local buckling of the panel skin between stringers the internal axial resultant Nx in the skin becomes concentrated near the stringers The question is under the redistributed Nx does local bifurcation buckling occur for a load factor less than unity If so then mode jumping is possible NOTE Your panel may become a lot heavier if you elect to prevent mode jumping It may be a good idea to obtain optimum designs both with Y and N answers to this question See the papers AIAA 97 1141 Optimization of stiffened panels in which mode jumping is accounted for 1997 SDM Meeting and AIAA 98 1990 Optimization of panels with riveted z sh
237. ress and a means allowable The quantity f is a bending overshoot factor which might be different for as many as five different conditions 1 S membrane is axial tensile 2 S membrane is axial compressive 3 S membrane is hoop tensile 4 S membrane is hoop compressive 5 S membrane is in plane shear stress Accordingly you will next be prompted whether or not you want to take advantage of bending overshoot If you answer Y and the current material does NOT have a single maximum allowable effective stress you will then be prompted for the following five bending overshoot factors fxt fxc fyt fyc fxy each greater than unity 1 f axial tensile fxt 2 f axial compressive fxc 3 hoop tensile fyt 4 hoop compressive fyc 5 in plane shear fxy hoop means normal to the axial direction in the plane of the panel module segment the s or y coordinate in Fig 9 of the long 1987 PANDA2 paper in Computers and Structures pp 469 605 If you have previously indicated that the material has a single maximum effective stress in the von Mises sense then you will simply be prompted for one quantity f which is the single bending overshoot factor greater than unity NOTE IF YOU ELECT TO TAKE ADVANTAGE OF THE BENDING OVERSHOOT YOU MUST TREAT THIS MATERIAL AS A DIFFERENT MATERIAL IF THE SAME MATERIAL APPEARS ELSEWHERE IN A MULTILAYER SEGMENT Do you want to take advantage of bending over
238. restart from ISTARTth load step BEGIN D 1 rec 3500 NSEC number of CPU seconds before run termination 5 NCUT number of times step size may be cut 20 NEWT number of refactorings allowed 1 NSTRAT 1 means path length used as independent parameter 0 0001 DELX convergence tolerance 0 WUND 0 means initial relaxation factor 1 END D 1 rec 0 1 0 NPATH 0 Riks method NEIGS no of eigs NSOL 0 contin ET 1 end of cylstif bin file a The STAGS output file cylstif out2 includes the following beginning of fragment from the STAGS output file cylstif out2 BEGIN ITERATIONS FOR LOAD STEP 1 DETA 0 292884E 02 PA 0 100000E 01 PB 0 000000E 00 ITERATION RNORM DNORMO PA ENERGY DOF RESIDUAL DETRM EXP NEGRT RFACT 1 0 315580E 01 0 703508E 01 0 100000E 01 0 605530E 06 10218 0 105888E 05 0 157628E 01 165011 82 0 1000E 01 2 0 660142E 02 0 668540E 02 0 100000E 01 0 603607E 06 10076 0 203753E 04 0 120615E 01 165009 82 0 1000E 01 3 0 615675E 03 0 253234E 02 0 100000E 01 0 603792E 06 27629 0 110176E 02 0 297926E 01 165008 82 0 1000E 01 4 0 121575E 04 0 302363E 05 0 100000E 01 0 603819E 06 27473 0 177187E 01 0 292803E 01 165008 82 0 1000E 01 CP SEC 46 480 I O REQSTS 14429 WORDS USED 3290795 WORDS TRANSFD 7 49911E 07 ISTEP ITNMAX TMAX DETA 1 1868 1 461046860444531E 02 29 22589528856226 Convergence obtained for load step 1
239. riginal long PANDA2 paper PANDA2 program for minimum weight design Computers and Structures vol 25 469 605 1987 for local buckling of the panel skin between rings This discretized module model is used for local buckling if the user selected analysis control integer IQUICK 0 Generally you should answer Y as this will lead to conservative designs However there may be times when neglecting the curvature of an axially stiffened cylindrical panel during computations of local buckling of the skin stringer module leads to results that are too conservative This would happen for example if the stringers were spaced at intervals that are not very small compared to the shell radius The default answer is Y A Y answer generates IICURV 0 and a N answer generates IICURV 1 in which IICURV is the control index used in PANDA2 IICURV 0 means no curvature 1 means yes curvature It would be a good idea to optimize panels with this choice taken first one way then the other way Please see panda2 news Item No 530 for more information Do you want flat skin discretized module for local buckling n n Do you want to skip the KOITER local postbuckling analysis h You answered the previous question N Therefore the index IICURV 1 and your PANDA2 discretized single skin stringer module model retains the curvature of the cylindrical panel skin However the local postbuckling KOITER theory used in PANDA2 is still
240. rocessor is to permit you to choose loads and initial imperfections Nx Ny Nxy Mx My Nxo Nyo p T iseg Wimp global Wimp local up to 5 sets of them safety factors for general instability panel instability local instability panel skin local instability stiffener parts and stress and strategy parameters for subsequent batch execution of an optimization analysis analysis type 1 or an analysis of a fixed design at fixed load levels analysis type 2 or an analysis of a fixed design for a single load set for monotonically increasing load levels test simulation analysis type 3 Results of the interactive session in MAINSETUP are saved on a file called cylstif OPT which will appear at the beginning of the cylstif OPM file when the mainprocessor batch run launched by your command PANDAOPT has been completed NOTE JUST HIT RETURN FOR DEFAULT VALUE OF INPUT DATUM IF PANDA2 REQUIRES AN INPUT IT WILL SAY PLEASE SAY SOMETHING KKK KKK KKK KKK KKK KKK KKK KKK RRR KKK RK KKK KRKK RKKK RKKK KRKK Are you correcting adding to or using an existing file y The interactive MAINSETUP session zips by on your screen Next give the command CHOOSETEMP or PANDAOPT or SUPEROPT bush gt pandaopt The purpose of PANDAOPT is to launch the batch run which performs optimization or buckling according to the strategy parameters established the last time you did a MAINSETUP Output from PANDAOPT is stored in a file called case
241. s inequality constraints and escape variables bush gt decide Please enter PANDA2 case name cylstif kkkkkkkkkkkkkkkkxk DECIDE kkkkxkkkkkkkkkkkkxkkk The purpose of DECIDE is to permit you to choose decision variables linked variables and escape variables for the optimization run or runs to follow The results of the interactive session are saved in a file called cylstif DEC in which cylstif is your name for the case You may find this file useful for future runs of DECIDE in which you want to avoid answering many questions interactively DECIDE also generates a file called cylstif OPD cylstif OPD contains a summary of optimization parameters If you choose the tutorial option cylstif OPD contains a complete list of the interactive session including prompting questions all help paragraphs your responses to the prompting questions and evolving lists of optimization parameters as they are chosen by you kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Are you correcting adding to or using an existing file n n Do you want a tutorial session and tutorial output n n PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s 4 STR 4 0 1 000E 01 W STR width of outstanding
242. s are on the same side of the skin as the stringers If stringers and rings are on opposite sides of the skin the ring cross section will lie below the panel skin If the panel is cylindrical b If there are no stringers the radius of curvature will be positive that is the concave surface of the panel skin will be the bottom surface See panel module sketch c If there are stringers the sign of the panel curvature is governed by whether they are external or internal and the location of the ring cross section is governed by a above choose external 0 or internal 1 rings 1 1 13 decision variable candidates have now been identified 50 decision variable candidates are permitted 37 additional decision variable candidates are allowed Is the panel curved in the plane of the screen Y for cyls h We are referring here to the module cross section Is the skin curved as we look at the module cross section If this is a cylindrical panel rather than a flat panel your answer should be Y Is the panel curved in the plane of the screen Y for cyls y y Radius of curvature cyl rad in the plane of screen R 100 100 0000 Is panel curved normal to plane of screen answer N n n You will next be asked to provide material properties corres ponding to the material types that you have already indicated MATERIAL PROPERTIES FOR MATERIAL TYPE 1 Is this material isotropic Y or N y Y Young s modulus E 1 10 E
243. s assumed UNIFORM over entire panel Positive pressure always pushes upward Please refer to the sketches of the panel module for physical picture of what upward means See Fig 8 p 490 of Computers and Structures Vol 25 1987 If there are no stringers or if you specified that the stringers are external and if the panel is curved then positive upward pressure pushes on the concave surface of the panel is internal If you specified that the stringers are internal and if the panel is curved then positive upward pressure pushes on the convex surface of the panel Figure 8 of the PANDA2 paper shows the sign convention for pressure and curvature NOTE If the panel is curved the value of p must be consistent with the value of hoop resultant that you supplied earlier for cylindrical panels Ny p r Uniform applied pressure positive upward See H elp p 1 500 500 0000 THE PANEL IS CURVED Radius of curvature R 1 0000E 02 INPUT DATA FOR LOAD SET NO I NORMAL PRESSURE positive acting upward p 5 0000E 02 CURRENTLY APPLIED AXIAL RESULTANTS Nx load set A 2 5000E 04 Nxo load set B 0 0000E 00 CURRENTLY APPLIED HOOP RESULTANTS Ny load set A 5 0000E 04 Nyo load set B 0 0000E 00 Is the pressure part of Load Set A h Load Set A is the eigenvalue load set that is Critical load Load Set B eigenvalue Load Set A If you are concerned with a cylindrical panel or shell and the pressure is internal
244. s or make panel module flat 4 if this message occurs at the end of a SUPEROPT run that bombed see the ERR file use CHANGE to save the best design so far look at the end of OPP and execute SETUP MAINSETUP and SUPEROPT again 5 read Item 675 of panda2 doc panda2 news 6 possibly introduce an inequality constraint in DECIDE that forces B STR lt cylinder radius 3 xxxk k k MODEL CHANGE REQUIRED end of part of the cylstif ERR file This type of bomb is described in Item No 580 of the file panda2 doc panda2 news dated September 2004 The initial part of that news item is as follows from the panda2 doc panda2 news file 580 September 2004 Occasionally a run bombs during a SUPEROPT execution When this happens do the following Please read this entire news item before proceeding SUMMARY of what to do 1 look at the OPP file 2 Look at the OPM file especially the end of it 3 Look at the ERR file especially the end of it end of small part of panda2 news PART 1 7 Reset the upper bound of the stringer spacing in the file cylstif DEC and restart from scratch In this case we will follow the alternative no 2 listed above 2 make stringer spacing less than cylinder radius 3 We will do this by setting the upper bound of the stringer spacing to less than radius 3 We reset that u
245. s this edge and is uniform in the direction normal to the plane of the screen NOTE It may in some cases be beneficial to answer this question Y and then provide the same Nx at the beginning and end of the axially loaded edge thus providing a uniform axial load Please see ITEM No in PANDA2 NEWS and read the handout entitled BUCKLING OF UNSTIFFENED PERFECT AND IMPERFECT UNSTIFFENED CYLINDRICAL SHELLS WITH PANDA2 dated 25 November 1988 If you answer N the axial load will be uniform over the entire panel Does the axial load vary in the L2 direction n n Applied axial moment resultant e g in lb in Mx 1 0 0 Applied hoop moment resultant e g in lb in My 1 0 0 Want to include effect of transverse shear deformation h If you answer Y reduction factors are computed for various kinds of general semi general and local instability and crippling These factors reduce the eigenvalues computed from classical normals remain normal shell theory The reduction factors are based on Timoshenko beam theory See pp 132 136 of Timoshenko and Goodier 2nd edition That is a typical reduction factor has the form k 1 1 n Nx Lambda t G13 in which n is a shape factor 1 2 is now used Nx is the local stress resultant lb in for example Lambda is the critical eigenvalue computed from normals remain normal theory t is the local effective thickness of the wall and G13 is the local effective transverse shear st
246. shoot n n weight density greater than 0 of material type 1 0 1 0 1000000 Is lamina cracking permitted along fibers type H elp h If this material is isotropic or cloth or has fibers running in both directions answer N If you answer Y two things will happen in PANDA2 1 Cracking due to tension normal to the fiber direction will not be treated as failure Instead if PANDA2 perceives that the allowable stress for tension normal to the fibers in a lamina is exceeded the allowable for compression along the fibers in that material at that particular location in the laminate will be reduced by half and the allowable for in plane shear will be reduced by 20 per cent 2 If during design changes the thickness of any layer made of this material becomes less than a quarter of that which you give as the minimum thickness such as 005 in the layer will disappear If you answer N even though the material is unidirectional cracking due to tension normal to the fibers will be treated as failure and the layer will never disappear no matter how thin it gets during optimization iterations Is lamina cracking permitted along fibers type H elp n n 26 fixed parameters have now been identified 99 fixed parameters are permitted 73 additional fixed parameters are allowed SOME ADVICE ON MODELING WHEN NORMAL PRESSURE IS PRESENT If you are designing a panel that has both stringers and rather large rings and you expect that
247. sign iterations such as 5 in the file case OPT where case is the user specified name of the case Enter case name cylstif Enter number of executions of pandaopt for each execution of autochange 5 or 6 or 7 or 8 or 9 or 10 5 B background F foreground or Q NOS network queue system b H high or L low priority 1 Diagnostics will be mailed to you upon program termination bush gt usr sbin sendmail No such file or directory The SUPEROPT execution requires only about 12 minutes for about 470 design iterations The tail end of the cylstif OPP file which is output from SUPEROPT has the following abridged information near the end of the cylstif OPP file SUMMARY OF STATE OF THE DESIGN WITH EACH ITERATION ITERA WEIGHT FOR EACH LOAD SET ANY ABRUPT CHANGES IN MODE TION OF IQUICK NO OF CRITICAL MARGINS SLOPE CHANGE m n CHANGE NO PANEL LOAD SET NO gt 1 2 3 4 5 EIG RATIOS EIG RATIOS LOAD SET NO gt 1 2 3 1 2 3 SUBCASE NO gt 121212 121212 See Items 525 and 596 in panda2 news PANDAOPT 1 1 2211E 04 FEASIBLE 0 9 0 0 0 0 0 0 0 0 000000N000000 2 1 2134E 04 NOT FEASIBLE 0 11 0 0 0 0 0 0 0 0 000000N000000 3 1 2478E 04 FEASIBLE 0 3 0 0 0 0 0 0 0 0 000000N000000 4 1 2200E 04 NOT FEASIBLE 0 9 0 0 0 0 0 0 0 0 000000N000000 5 1 2420E 04 FEASIBLE 0 3 0
248. stiffness of the interior stiffeners The purpose of this STAGS model is to be able to capture the local buckling load factor and mode shape with the use of a relatively dense mesh so that we have a converged prediction The new cylstif STG file follows cylstif STG file input for STAGSUNIT n Do you want a tutorial session and tutorial output 1 Choose type of STAGS analysis 1 3 4 5 6 INDIC 0 Restart from ISTARTth load step 0 lst nonlinear soln ISTART 1 155000 Local buckling load factor from PANDA2 EIGLOC y Are the dimensions in this case in inches 0 Nonlinear 0 or linear 1 kinematic relations ILIN 0 Type 1 for closed 360 deg cyl shell 0 otherwise ITOTAL 100 X direction length of the STAGS model of the panel XSTAGS 50 67085 Panel length in the plane of the screen L2 Is the nodal point spacing uniform along the stringer axis 51 Number of nodes in the X direction NODEX 101 Number of nodes in the Y direction NODEY 25000 00 Resultant e g lb in normal to the plane of screen Nx 50000 00 Resultant e g lb in in the plane of the screen Ny 0 000000 In plane shear in load set A Nxy 500 0000 Normal pressure in STAGS model in Load Set A p 0 Resultant e g lb in normal to the plane of screen Nx0 0 Resultant e g lb in in the plane of the screen Ny0 0 Normal pressure in STAGS model in Load Set B p0 1 000000 Starting load factor for Load System A
249. system Xg Yg Zg 0 0 0 in STAGS models created via STAGSUNIT Given the choice of one of the two options STAGSUNIT automatically generates the proper input data for STAGS The user of STAGSUNIT does not need to worry about the details of the modeling Option 2 is preferred because simple application of Nxy to the skin of the cylindrical shell at x 0 generates in nonlinear analyses a small spurious hoop tension in a circumferential band of width approximately equal to a boundary layer width of about 2 0 SQRT r t adjacent to x 0 When you choose Option 2 STAGSUNIT automatically sets up a user defined node at Xg Yg Zg 0 0 0 and sets up a finite element unit containing the torque which is equal to Nxy 2 pi r 2 Do you want to use the least squares model for torque y Y Is stiffener sidesway permitted at the panel edges h In the PANDA2 model it is assumed that stringer sidesway is permitted at the axially loaded ends of the panel provided that the discretized skin stringer module model is used This is in order to obtain conservative designs In STAGSMODEL and in STAGSUNIT you can choose whether or not this mode of deformation can occur By stiffener sidesway is meant a mode of deformation in which the tip of the stiffener can deflect sideways in the y direction in Fig 9 on p 492 of the long PANDA2 paper in COMPUTERS AND STRUCTURES 1987 In tests of panels stringer sidesway is usually prevented by
250. t 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 3 3 Lower bound of variable no 3 0 5 0 5000000 Upper bound of variable no 3 20 20 00000 Any more decision variables Y or N y Y DECISION VARIABLES CHOSEN SO FAR VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 3 000E 01 B STR stiffener spacing b STR seg NA 3 STR 3 0 1 000E 01 H STR height of stiffener type H for s PARAMETERS FROM WHICH A DECISION VARIABLE MUST NOW BE CHOSEN VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 2 STR 2 0 1 000E 01 B2 STR width of stringer base b2 must 4 STR 4 0 1 000E 01 W STR width of outstanding flange of st 5 SKN 1 1 1 000E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 1 000E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 1 000E 01 T 3 STR thickness for layer index no 3 8 0 0 5 000E 01 B RNG stiffener spacing b RNG seg NA 10 RNG 3 0 1 000E 01 H RNG height of stiffener type H for s 11 RNG 4 0 1 000E 01 W RNG width of outstanding flange of st 12 RNG 3 1 1 000E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 1 000E 01 T 5 RNG thickness for layer index no 5 Choose a decision variable 1 2 3 4 Lower bound of variable no 4 0 5 0 5000000 Upper bound of variable no 4 10 10 00000 Any more decision variables Y or N
251. t the general buckling mode resembles that from the BIGBOSOR4 model shown in the figure 4 cylstif genrlbuck panel png solution scale 0 6079E 0 ye 15 cylstif stagsunit locbuck 5x3bay eigl png sub domain model generated automatically by j1 0 11817E eigenvector defo linear buckling of perfect she mode 1 per step x 35 84 y 13 14 Oz 35 63 med geometry I from STAGS This model captures local buckling All the stiffener segments are modeled as flexible shell units the PANDA2 processor called STAGSUNIT 5 786E 04 5 403E 04 5 020E 04 4 637E 04 4 254E 04 3 871E 04 3 488E 04 3 105E 04 2 722E 04 2 339E 04 1 956E 04 1 573E 04 1 190E 04 8 067E 03 4 237E 03 4 063E 02 solution scale 0 1544E 02 PA 1 00000E 00 PB 0 00000E 00 PX 0 00000E 00 ey Taal y z step 1 fabrication system seff layer 1 inner fiber Oz 3563 7 nonlinear effective stress inner fiber same view a linear buckling mode Minimum value 4 06309E 02 Maximum value 5 78611E 04 32446401 16 cylstif stagsunit innerfibstress 5x3 png inner fiber stress in psi from the 5 stringer bay x 3 ring bay sub domain model generated automatically by STAGSUNIT solution scale 0 1475E 02 PA 1 00000E 00 PB 0 00000E 00 PX 0 00000E 00 DS ae step 1 fabrication system seff layer 1 inner fiber a 35 63 nonlinear effective stress inner fiber same view a linear buckling mode Minimum value 3 60
252. ta for example hundreds of stress margins generated for multilayered composite panels that you don t really need to see Try MAXMAR 1 to 5 The bigger the case more variables more load sets more iterations the smaller MAXMAR should be Note that MAXMAR must be greater than or equal to 1 MAXMAR Plot only those margins less than MAXMAR Type H lt enter gt 1 000000 Do you want to reset total iterations to zero Type H h PANDA2 accumulates results from all iterations from the start of the case These results can be plotted via the processors CHOOSEPLOT and DIPLOT It is possible that you may no longer want to plot results from previous runs you may want to make a fresh start but with use of the current design state rather than the original design state from the NAME BEG file You can do this by answering Y to this question Then ITRTOT will be set to zero Likely occasions to reset ITRTOT to zero are 1 If you started from a very bad design state 2 If you are changing IQUICK the integer that points to the type of analysis that you are doing 3 If you are changing one or more load sets or edge conditions 4 If you already have lots of iterations and plotting is too time consuming Do you want to reset total iterations to zero Type H lt enter gt N Index for objective l min weight 2 min distortion h 1 means that PANDA2 will find the minimum weight of the panel You must have previously assigned n
253. tagsunit eigl rigidends png no in plane warping of the curved edges N FENA EA o d A RNA zA may eo oe ie A FF 353 Aa San ps lt lt Ree Cn Vaan sat se TS lt gt eS ver Wen he tots shi as eg wae ato eS ae Soe EE AF T 1 eae xe moe cat are a oor ENSA cS oo ae A a sa Sede Fi eee a lt Ka z ao solution scale 0 1953E 02 mode 1 per 0 17093E 01 Ox 24 00 f y 22 00 step O eigenvector deformed geometry ot 30 00 x linear buckling of perfect shell from STAGS l 6 001601 4 z 11 cylstif stagsunit smrstr eigl png stringers are smeared out ae Pf eats PE ke Fe TE ee iy 7 3 r 3 se Tr gt F i p solution scale 0 1953E 02 mode 1 per 0 17092E 01 Ox 24 00 e i ee a y 22 00 step 0 eigenvector deformed geometry z 30 00 linear buckling of perfect shell from STAGS 12 cylstif stagsunit smrstr eigl rngs png same as previous except no skin shows x 35 84 y 13 14 Oz 35 63 og 2 f step 0 ing of perfect shell from STAGS linear buck 13 cylstif stagsun it genbuck eigl png both stringers solution scale 0 1020E 02 mode 1 per 0 25073E 01 step 0 eigenvector deformed geometry linear buckling of perfect shell from STAGS 14 cylstif stagsunit genbuck eigl endview png end view of same general buckling mode as that shown in the previous figure Note tha
254. tagsunit locbuck 5x3bay eigl png 5 x 3 bay model There is very good agreement between STAGS BIGBOSOR4 and PANDA2 for the prediction of local buckling PART 3 18 Find the maximum effective stress from the same STAGS sub domain model used in the previous PART Next find the maximum effective stress at load factor 1 0 from the same 5 x 3 bay STAGS model In order to do this we run a STAGS nonlinear equilibrium run INDIC 3 The input file cylstif inp is the same as for the linear bifurcation run INDIC 1 However the input file cylstif bin is now as follows cylstif bin file for nonlinear equilibrium optimized imperfect shell nonlinear theory INDIC 3 INDIC 1 is bifur buckling INDIC 3 is nonlinear BEGIN B 1 IPOST 1 means save displacements every IPOSTth step ILIST 0 means normal batch oriented output ICOR 0 means projection in 1 means not in IMPTHE index for imperfection theory IOPTIM 0 means bandwith optimization will be performed IFLU 0 means no fluid interaction ISOLVR 0 means original solver 1 new solver END B 1 rec 0 STLD 1 starting load factor System A BEGIN C 1 rec 5 STEP 1 load factor increment System A FACM 1 maximum load factor System A 00E 00 STLD 2 starting load factor System B 00E 00 STEP 2 load factor increment System B 000E 00 FACM 2 maximum load factor System B ITEMP 0 means no thermal loads END C 1 rec 0 ISTART
255. ten stays constant for a rather large range in load above the initial local buckling load especially in cases where axial compression Nx predominates and the applied in plane shear load Nxy is small Does the postbuckling axial wavelength of local buckles change lt enter gt Y Next you will be asked Want to suppress general buckling mode with many axial waves You should usually answer N Your answer affects the results only for ring stiffened cylindrical panels subjected to external pressure In such cases there may be two types of general buckling buckling of skin and stiffeners together 1 general buckling in a mode with one axial halfwave 2 general buckling in a mode with many axial halfwaves If you answer Y PANDA2 may set up a constraint condition that forces Mode Type 2 to have a load factor that is at least 5 per cent higher than that associated with Mode Type 1 NOTE THIS SPECIAL DESIGN CONSTRAINT SOMETIMES CAUSES THE DESIGN TO DRIFT AWAY FROM THE OPTIMUM CONFIGURATION THEREFORE ANSWER Y ONLY IF YOU HAVE FIRST FOUND AN OPTIMUM WITH A N ANSWER Answer H elp for further explanation in particular under what loading conditions the many axial halfwave buckling mode is to be suppressed Want to suppress general buckling mode with many axial waves h Both types of buckling modes generally have several halfwaves over the circumference of the cylindrical deep panel or shell Depending on the spacing a
256. tep 0 lst nonlinear soln ISTART 1 155000 Local buckling load factor from PANDA2 EIGLOC y Are the dimensions in this case in inches NOTE gt 1 Nonlinear 0 or linear 1 kinematic relations ILIN 0 Type 1 for closed 360 deg cyl shell 0 otherwise ITOTAL 100 X direction length of the STAGS model of the panel XSTAGS 60 80502 Panel length in the plane of the screen L2 y Is the nodal point spacing uniform along the stringer axis 51 Number of nodes in the X direction NODEX 101 Number of nodes in the Y direction NODEY 25000 00 Resultant e g lb in normal to the plane of screen Nx 50000 00 Resultant e g lb in in the plane of the screen Ny 0 000000 In plane shear in load set A Nxy 500 0000 Normal pressure in STAGS model in Load Set A p 0 Resultant e g lb in normal to the plane of screen Nx0 0 Resultant e g lb in in the plane of the screen Ny0 0 Normal pressure in STAGS model in Load Set B p0 1 000000 Starting load factor for Load System A STLD 1 0 000000 Load factor increment for Load System A STEP 1 1 000000 Maximum load factor for Load System A FACM 1 0 Starting load factor for Load System B STLD 2 0 Load factor increment for Load System B STEP 2 0 Maximum load factor for Load System B FACM 2 1 How many eigenvalues do you want NEIGS 480 Choose element type 480 or 410 or 940 n Have you obtained buckling modes from STAGS for this case 62 Number of string
257. ters and Structures pp469 605 1987 With IFREE 1 the same displacement functions are used but only the linear theory is used and the in plane resultants Nx p Ny p are assumed to be zero for a flat panel For a curved panel Nx p is zero and Ny p is calculated from the condition that no horizontal force develops along the straight edges Please note that if IFREE 1 movable edges are permitted only in the global model of the entire panel under uniform normal pressure unless you specify otherwise The IFREE 0 condition is applied in the local model single module model unless you specify otherwise in the following prompt If IFREE 1 any overall axial resultant that develops from pressure being applied to the local model is automatically cancelled by PANDA2 s application of an equal and opposite axial resultant thus maintaining the condition that no axial load develops if the edges are free to approach eachother as the pressure is applied If you are in doubt please just hit ENTER Then PANDA2 will supply the default value which is unity Choose in plane immovable IFREE 0 or movable IFREE 1 b c 1 lt enter gt 1 Are you feeling well today type H h This question used to read Local model Are the edges in plane movable See H elp See ITEM 156 of PANDA2 NEWS for the reason it was modified A silly question was added so that people with old cases already set up would not run into problems upon re running thes
258. the following output from STAGSUNIT The following stuff zips by on your screen at the end of the interactive STAGSUNIT session beginning of stuff that zips by on your screen NODEX 55 AXIAL NODAL SPACING DX 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 5 5556E 00 Row numbers of major ring locations IROWRG i 1 7 13 19 25 31 37 43 49 55 Axial stations of major rings XRINGX i 0 0000E 00 3 3333E 01 6 6667E 01 1 0000E 02 1 3333E 02 1 6667E 02 2 0000E 02 2 3333E 02 2 6667E 02 3 0000E 02 Column numbers of major stringer locations ICOLST i 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 103 105 107 109 111 113 115 117 119 121 123 Circumferential stations of major stringers YSTRGX i 0 0000E 00 5 8065E 00 1 1613E 01 1 7419E 01 2 3226E 01 2 9032E 01 3 4839E 01 4 0645E 01 4 6452E 01 5 2
259. the stringers with little or no participation the panel skin It is difficult to find the critical inter ring buckling mode from STAGS because that mode is hidden within a cluster of stringer buckling modes The following is a series of STAGS runs for which there are two purposes 1 Obtain the critical lowest buckling load factor for the sub domain model with 6 x 3 bays with both T stringers and T rings modeled as flexible shell segments shell units and plot the mode shape See the plot represented by the file 22 cylstif stagsunit 6x3 eigl png This is local buckling essentially the same buckling load factor and mode shape computed by PANDA2 eigenvalue 1 195 see the plot represented by the file 3 cylstif localbuck panel png and by BIGBOSOR4 eigenvalue 1 21 see the plot represented by the same file 3 cylstif localbuck panel png 2 Search for and find the lowest buckling load factor and mode shape that correspond to inter ring buckling that is shape that is analogous to that plotted for the 6 x 3 bay model See the plot in the file 21 cylstif stagsunit 6x3 smrstr eig5 png eigenvalue 2 035 The inter ring buckling eigenvalue for the more elaborate STAGS model in which the stringers are modeled as flexible shell units was found The mode shape is represented by the two files 23 cylstif stagsunit 6x3 eig43 png and 24 cylstif stagsunit 6x3 eig43 skin png 43rd eigenvalue 6 per cent decrease in the predicted
260. ther information about files generated during operation of PANDA2 give the command HELPAN FILES Next give the command BIGBOSOR4LOG followed by BIGBOSORALL BIGBOSOR4 to be used to find buckling of the panel with all stringer parts modelled as flexible shell segments The buckling load factors from this rather elaborate model should be compared with those calculated from PANDA2 The input for PANEL is saved in the file cylstif PAN The cylstif PAN file is as follows cylstif PAN file input for PANEL n Do you want a tutorial session and tutorial output 314 1600 Panel length in the plane of the screen L2 0 Enter control 0 or 1 for stringers at panel edges 2 Enter control l sym 2 s s for boundary condition 1 Enter ILOCAL 0 or 1 or 1 or 2 Type H elp ILOCAL 1 Number of halfwaves in the axial direction see H elp NWAVE 3 How many eigenvalues get at least 3 do you want end of cylstif PAN file for PANEL The valid input file for BIGBOSOR4 cylstif ALL now exists rw r r 1 bush bush 167939 Feb 22 11 16 cylstif ALL This is a long file and is not listed here to save space PART 2 2 Execute BIGBOSOR4 using the file cylstif ALL as input in this particular run a prismatic model for LOCAL buckling Next we must run BIGBOSOR4 We copy the file cylstif ALL to another working directory and execute BIGBOSOR4 there cd to new working directory cp
261. ther parameters in this set 3 Number of parameter to change 1 2 3 7 816700 New value of the parameter y Want to change any other parameters in this set 4 Number of parameter to change 1 2 3 2 534000 New value of the parameter y Want to change any other parameters in this set 5 Number of parameter to change 1 2 3 0 7689600 New value of the parameter y Want to change any other parameters in this set 6 Number of parameter to change 1 2 3 0 2038000 New value of the parameter y Want to change any other parameters in this set 7 Number of parameter to change 1 2 3 0 8449600E 01 New value of the parameter y Want to change any other parameters in this set 8 Number of parameter to change 1 2 3 31 85000 New value of the parameter Want to change any other parameters in this set 10 Number of parameter to change 1 2 3 9 783000 New value of the parameter y Want to change any other parameters in this set 11 Number of parameter to change 1 2 3 4 303700 New value of the parameter Want to change any other parameters in this set 12 Number of parameter to change 1 2 3 0 5672900 New value of the parameter Want to change any other parameters in this set 13 Number of parameter to change 1 2 3 0 9452400 New value of the parameter n Want to change any other parameters in this set n Do you want to change values
262. thout having to go back to BEGIN The parameters you can change are segregated into three groups 1 parameters 2 parameters 3 allowables elegible to be decision variables not elegible to be decision variables for example max strain Your interactive which cylstif is A summary of the input is saved on a file called cylstif CHG in the same name you used for BEGIN SETUP etc output from CHANGE is stored in cylstif OPC kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Are you correcting n Do you want a tutorial session and tutorial output n n adding to or using an existing file n This program permits you to change certain quantities without starting over from the beginning without having to use BEGIN Parameters that you can change are segregated into three sets 1 parameters that are elegible to be decision variables 2 parameters that are always considered to be fixed during design iterations they are not elegible to be decision variables 3 parameters that are allowables such as max stress You will next be asked if you want to change any parameters in set no 1 and if so which then you will be asked the same questions relative to set no 2 and finally the same questions relative to set no 3 Do you want to change any values in Parameter Set No 1 y Y PARAMETERS WHICH CAN BE CHANGED CHOOSE ONE OF THE FOLLOWING STR seg NA VAR STR SEG LAYER CURRENT NO RNG NO NO VA
263. ts and with the stringers smeared out Next use a new sub domain model to determine from STAGS the lowest buckling load factor that corresponds to inter ring buckling In this sub domain model the stringers are smeared out and the rings are modeled with little flexible shell segments shell units in STAGS jargon The STAGS model is generated by STAGSUNIT with the following input data cylstif STG file cylstif STG input data for STAGSUNIT for a STAGS model the purpose of which is to search for inter ring buckling n Do you want a tutorial session and tutorial output a Choose type of STAGS analysis 1 3 4 5 6 INDIC 0 Restart from ISTARTth load step 0 lst nonlinear soln ISTART 1 155000 Local buckling load factor from PANDA2 EIGLOC y Are the dimensions in this case in inches 0 Nonlinear 0 or linear 1 kinematic relations ILIN 0 Type 1 for closed 360 deg cyl shell 0 otherwise ITOTAL 100 X direction length of the STAGS model of the panel XSTAGS 60 80502 Panel length in the plane of the screen L2 Is the nodal point spacing uniform along the stringer axis 51 Number of nodes in the X direction NODEX 101 Number of nodes in the Y direction NODEY 25000 00 Resultant e g lb in normal to the plane of screen Nx 50000 00 Resultant e g lb in in the plane of the screen Ny 0 000000 In plane shear in load set
264. umber of nodes in the Y direction NODEY 25000 00 Resultant e g lb in normal to the plane of screen Nx 50000 00 Resultant e g lb in in the plane of the screen Ny 0 000000 In plane shear in load set A Nxy 500 0000 Normal pressure in STAGS model in Load Set A p 0 Resultant e g lb in normal to the plane of screen Nx0 0 Resultant e g lb in in the plane of the screen Ny0 0 Normal pressure in STAGS model in Load Set B p0 1 000000 Starting load factor for Load System A STLD 1 0 000000 Load factor increment for Load System A STEP 1 1 000000 Maximum load factor for Load System A FACM 1 0 Starting load factor for Load System B STLD 2 0 Load factor increment for Load System B STEP 2 0 Maximum load factor for Load System B FACM 2 1 How many eigenvalues do you want NEIGS 480 Choose element type 480 or 410 or 940 n Have you obtained buckling modes from STAGS for this case 62 Number of stringers in STAGS model of 360 deg cylinder 10 Number of rings in the STAGS model of the panel y Are there rings at the ends of the panel 1 Number of finite elements between adjacent stringers 3 Number of finite elements between adjacent rings 3 Stringer model 1 or 2 or 3 or 4 or 5 Type H elp 3 Ring model 1 or 2 or 3 or 4 or 5 Type H elp 0 Reference surface of cyl l outer O middle 1l inner n Do you want to use fasteners they are like rigid links NOTE gt y Are the stringers to be
265. uniformly spaced rings over the axial length in the STAGS model Alternatively you may Number of 10 Are there y Number of have to change the axial length of the STAGS model rings in the STAGS model of the panel 10 rings at the ends of the panel y finite elements between adjacent stringers h If you are using the 410 finite element make this at least two NOTE If you answer 0 PANDA2 will ask you to provide the number of finite elements in the circumferential direction In such a case the stringers must be smeared out Number of 1 Number of finite elements between adjacent stringers 1 finite elements between adjacent rings h If you are using the 410 finite element make this at least two NOTE If you answer 0 PANDA2 will ask you to provide the number of finite elements in the axial direction In such a case the rings must be smeared out and the nodal point spacing in the axial direction must be uniform Number of 3 Stringer model finite elements between adjacent rings 3 1 or 2 or 3 or 4 or 5 Type H elp h Input must be 1 or 2 or 3 or 4 or 5 1 all stringer segments are modeled as beams 210 elements that are attached to the cyl shell stringer webs are modeled as shell branches 410 or 480 and any faying and or outstanding flanges are modelled as beams 210 elements The faying flanges are attached to the cylindrical shell and the outstanding flanges are attach
266. use FSGEN 0 999 You do this in order to prevent PANDA2 from automatically increasing FSGEN to 1 1 which it does if FSGEN 1 0 For example you might wamt to use FSGEN 0 999 in a case for which you intend to compare results from PANDA2 with results from some other analysis Factor of safety for general instability FSGEN 1 1 1 000000 FACTOR OF SAFETY FOR GENERAL INSTABILITY FSGEN 1 HAS BEEN CHANGED TO FSGEN 1 1 TO AVOID SINGULARITY Factor of safety for panel between rings instability FSPAN 1 h This factor pertains to buckling between rings but with circum ferential wavelengths that are long enough to cause buckling of at least one stringer This factor should account for unknown initial imperfections and the approximate manner in which the general instability load factor is calculated in PANDA2 Panels that buckle locally at loads far below the design load are not particularly sensitive to initial imperfections For such panels use 1 1 lt FSPAN lt 1 4 Panels designed so that local and general instability loads are nearly equal are somewhat sensitive to initial imperfections and FSPAN should be about 1 4 even if the panel is flat Axially stiffened cylinders under axial compression should usually have FSPAN 2 except read on about wide column model Axially compressed monocoque cylinders under axial compression should have FSPAN 4 if r t gt 300 FSPAN 2 if r t lt 100 Cylinders under uniform externa
267. uter program Execute STAGS Execute the STAGS post processor STAPL to get a plot of a bifurcation buckling mode Compare with BIGBOSOR4 and PANDA2 predictions of local buckling Produce and run a slightly different STAGS model Produce and run a different STAGS model one with smeared stringers Compare with the predictions from BIGBOSOR4 and PANDA2 Produce and run a different STAGS model one with smeared stringers and smeared rings Compare with the predictions from BIGBOSOR4 and PANDA2 Produce and run a different STAGS model one which covers only a small sub domain of the entire shell with all stiffener segments modeled as flexible shell units Find the maximum effective stress from the same STAGS sub domain model used in the previous Part Compare with the PANDA2 prediction Outer fiber effective stresses from the 5 x 3 bay STAGS model Produce and run a different STAGS model one which again covers only a small 6 x 3 bay sub domain of the entire shell with all ring segments modeled as flexible shell units and with the stringers smeared out Compare STAGS prediction with those from BIGBOSOR4 and PANDA2 Produce and run a different STAGS model one which covers the same 6 x 3 bay sub domain of the entire shell with all stiffener segments modeled as flexible shell units Note that now the STAGS index ILIN 1 not 0 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk PART 1 0 Processing with PANDA2 kkkkkkkkkkkk kkkkkkkkkkkkkkkkkkk
268. ver each stringer web height in the STAGS model of the panel IBCXOXL 1 u constant is imposed over the height of each stringer web in the STAGS model of the panel There is the following reason for the introduction of the index IBCXOXL The panel is designed to buckle locally at a load less than the design load that is the factor of safety for local buckling FSLOC is less than 0 9 We wish to simulate in the STAGS model the same end conditions that exist in the PANDA2 model for the precollapsed state of the locally postbuckled panel By forcing the axial displacement u to be constant over the heights of the stringer webs we prevent the overall axial bending of the stringer stiffened panel that occurs because of the shift in the neutral axis caused by the axial softening of the panel skin as it deforms in its locally postbuckled state If you have a panel loaded reasonably far into its locally postbuckled state at the design load say FSLOC is less than about 0 7 and if the applied load is equal to the design load and if the STAGS model represents a sub domain of the panel analyzed or optimized by PANDA2 that is XSTAGS is less than the axial length of the panel optimized by PANDA2 then you should probably set IBCXOXL 1 Otherwise set IBCXOXL 0 Stringer web axial displacement index IBCXOXL 0 or 1 0 This is the end of the STAGSUNIT interactive session PART 3 6 Scroll upward on your screen in order to view
269. vided range of loads analogous to the ITYPE 3 analysis test simulation with PANDA2 The user should first run STAGSMODEL or STAGSUNIT with INDIC 1 followed by subsequent runs of STAGSMODEL or STAGSUNIT with INDIC 3 If STAGS cannot continue to obtain solutions for load factors that approach the general instability or wide column buckling load predicted by PANDA then it will be necessary to use a more complex strategy involving the other analysis types INDIC 4 5 and 6 INDIC 4 means bifurcation buckling with nonlinear prebuckling To be used if the user wants a new imperfection shape INDIC 5 means small vibrations with nonlinear prebuckling To be used in order to get appropriate time step for nonlinear transient analyses INDIC 6 means nonlinear transient response analysis see PANDA2 NEWS ITEM 259 and AIAA Paper No 97 1141 Choose type of STAGS analysis 1 3 4 5 6 INDIC 1 1 Restart from ISTARTth load step 0 1st nonlinear soln ISTART h If this is NOT a STAGS POSTPROCESSOR run ISTART 0 Always use ISTART 0 if INDIC 1 ISTART 0 means you are starting the nonlinear analysis and have no previous load steps to start from ISTART gt 0 means you are using the solution at load step number ISTART as a starting solution for the next STAGS run If ISTART gt 0 make sure that the starting load factors STLD 1 and STLD 2 on the C 1 record correspond to load step ISTART If this IS a STAGS POSTPROCESSOR run
270. ween two variations of the local postbuckling theory to be applied in your runs 0 transverse inextensional 0 is the preferred option 1 transverse extensional The 0 option is preferred because it leads to more conservative designs and generally seems to agree better with test results especially with regard to prediction of the number of axial halfwaves in the postbuckling regime Also the nonlinear equations governing the postbuckled state converge more reliably The transverse extensional theory may agree better with tests and other analyses if the edges of the panel normal to the screen cannot deform in the plane of the panel deform in the y direction that is the direction in the plane of the panel and normal to the edges that run parallel to the stringers However Newton method fails to converge more often than is the case for the inextensional theory The transverse inextensional theory is most appropriate if the edges of the panel normal to the screen are free to deform in the plane of the panel This theory is generally conservative as it leads to the prediction of local buckles with larger amplitudes NOTE The projections of the two longitudinal edges edges normal to the screen onto the surface of the undeformed panel are ALWAYS free to move in the y direction as straight lines Choose 0 transverse inextensional l transverse extensional lt enter gt 1 Choose ICONSV 1 or 0 or 1 or H elp ICONSV h
271. when the user wants to take advantage of bending overshoot in stress constraints For details see ITEM No 299 in panda2 doc panda2 news and read carefully messages printed to the screen during the input session xx x END OF IMPORTANT NOTE Is the next group of layers to be a default group 12 layers n ADE of layers in the next group in Segment no 2 1 Can E as layup angles ever be decision variables n laa index 1 2 for layer no 1 1 Is this a new layer type n n Any more layers or groups of layers in Segment no 2 n n Module with T shaped stiffener Seg No 4 Segment No 3 gt Seg No 2 h Seg No 1 Seg No 5 3 V same as Seg 1 lt b2 gt lt Module width stiffener spacing b gt Next provide the properties of Segment 3 3 3 3 Simbu Is the next group of layers to be a default group 12 layers n n number of layers in the next group in Segment no 3 1 1 Can winding layup angles ever be decision variables n n layer index 1 2 for layer no 1 2 2 Is this a new layer type y Y thickness winding angle material for layer index thickness for layer index no 2 1 0 1000000 winding angle deg for layer index no 2 0 0 material index 1 2 for layer index no 2 1 1 Any more layers or groups of layers in Segment no 3 n n Module with T shaped stiffener Seg No 4 Seg
272. which the stringers are smeared Same as for ICONSV 0 Do NOT use computed knockdown factor for smearing rings Knockdown factor for smearing rings 1 0 EXCEPT when there exists significant local deformation in the outstanding flange of the ring in the skin ring single discretized module general buckling model in which case the knockdown factor is computed in the same way as for ICONSV 1 and ICONSV 0 Set the knockdown factor for truncated double trig series expansion altsol models to RFACT 0 95 RFACT 0 85 for altsol models in which there are smeared stiffeners if ICONSV 0 or 1 The user selected shell theory is used in SUBROUTINE STRIMP where imperfection sensitivity is being computed panda2 news Items 620 and 645 are in force that is a non zero slope of buckling nodal lines will probably be set to zero for the computation of Wxx Wyy and Wxy Different from e under ICONSV 0 and ICONSV 1 panda2 news Item 741 is in force that is the effective buckling load for the imperfect shell is given by FMULT2 1 0 IF ICONSV EQ 1 FMULT2 10 0 EIGEFF FACIM1 EILOC9 FACIM2 FMULT2 EILC91 FACIM1 FMULT2 FACIM2 for general buckling and FMULT2 1 0 IF ICONSV EQ 1 FMULT2 10 0 EIGEFF FACIM1 EILOC8 FACIM2 FMULT2 EILC81 FACIM1 FMULT2 FACIM2 for inter ring buckling and FMULT2 1 0 IF ICONSV EQ 1 FMULT2 10 0 EIGEFF FACIM1 EILOC7 FACIM2 FMULT2 EILC71 FACIM1 FMULT2
273. will provide are assumed to be uniform over each segment of the panel module except as follows 1 the panel skin and stringer and ring bases in which the temperature is assumed to vary linearly through the thickness except in the case of truss core for which the temperature in the panel skin is constant through the thicknesses of each of the two face sheets different in the two sheets though 2 the stiffener webs in which the temperature is assumed to vary linearly from the web root to the web tip At the web root the web temperature is the same as that of the panel skin at that point At the web tip the web temperature is assumed to be the same as that of the outstanding flange Is there any thermal loading in this load set Y N n n Next you will be asked Do you want a complete analysis Usually you should respond Y or just hit ENTER This question refers to analysis with stress and buckling constraints generated from both Subcase 1 midlength or midbay and Subcase 2 panel ends or at rings Note that for some loadings the complete analysis has only a single subcase Subcase 1 Then your response to this question although required will not matter Ordinarily you will want the panel to be optimized accounting both for the behavior at its midlength midbay and at its ends at rings However there are doubtless cases for which this conservative approach may generate overly heavy panels For example there may exist
274. x no 3 8 0 0 3 185E 01 B RNG stiffener spacing b RNG seg NA 9 RNG 2 0 0 000E 00 B2 RNG width of ring base b2 zero is a 10 RNG 3 0 9 783E 00 H RNG height of stiffener type H for s 11 RNG 4 0 4 304E 00 W RNG width of outstanding flange of st 12 RNG 3 1 5 673E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 9 452E 01 T 5 RNG thickness for layer index no 5 Number of parameter to change 1 2 3 7 7 New value of the parameter 0 084496 0 8449600E 01 Want to change any other parameters in this set y y PARAMETERS WHICH CAN BE CHANGED CHOOSE ONE OF THE FOLLOWING VAR STR SEG LAYER CURRENT NO RNG NO NO VALUE DEFINITION 1 0 0 1 011E 01 B STR stiffener spacing b STR seg NA 2 STR 2 0 3 370E 00 B2 STR width of stringer base b2 must 3 STR 3 0 7 817E 00 H STR height of stiffener type H for s 4 STR 4 0 2 534E 00 W STR width of outstanding flange of st 5 SKN 1 1 7 690E 01 T 1 SKN thickness for layer index no 1 6 STR 3 1 2 038E 01 T 2 STR thickness for layer index no 2 7 STR 4 1 8 450E 02 T 3 STR thickness for layer index no 3 8 0 0 3 185E 01 B RNG stiffener spacing b RNG seg NA 9 RNG 2 0 0 000E 00 B2 RNG width of ring base b2 zero is a 10 RNG 3 0 9 783E 00 H RNG height of stiffener type H for s 11 RNG 4 0 4 304E 00 W RNG width of outstanding flange of st 12 RNG 3 1 5 673E 01 T 4 RNG thickness for layer index no 4 13 RNG 4 1 9 452E 01 T 5 RNG thickness for layer index
275. xecuting pandaread 4th pass Normal termination pandaread 4 skin substringer panel module templates finished still processing Please wait Executing glbst3 Normal termination glbst3 skin substringer panel module common blocks stored Pandaread pre processor complete Next give the command DECIDE or MAINSETUP The files existing in the working directory after the execution of SETUP are as follows rw r r 1 bush bush 76 Feb 21 12 44 cylstif 010 rw r r 1 bush bush 2046 Feb 21 11 27 cylstif AL2 rw r r 1 bush bush 2058 Feb 21 11 27 cylstif AL3 rw r r 1 bush bush 2058 Feb 21 11 27 cylstif ALL rw r r 1 bush bush 5604 Feb 21 11 18 cylstif BEG rw r r 1 bush bush 110324 Feb 21 11 27 cylstif BL1 rw r r 1 bush bush 110324 Feb 21 11 27 cylstif BL2 rw r r 1 bush bush 110324 Feb 21 11 27 cylstif BL3 rw r r 1 bush bush 110324 Feb 21 11 27 cylstif BL4 rw r r 1 bush bush 481 Feb 21 11 27 cylstif BOS rw r r 1 bush bush 182500 Feb 21 11 48 cylstif CBL rw r r 1 bush bush 30 Feb 21 11 18 cylstif NAM rw r r 1 bush bush 12112 Feb 21 11 18 cylstif OPB rw r r 1 bush bush 33792 Feb 21 11 27 cylstif RN1 rw r r 1 bush bush 36864 Feb 21 11 27 cylstif RN2 rw r r 1 bush bush 33792 Feb 21 11 27 cylstif RN3 rw r r 1 bush bush 33792 Feb 21 11 27 cylstif RN4 PART 1 4 Execute the PANDA2 processor called DECIDE in order to choose decision variables upper and lower bounds equality constraint
276. you set FSBSTR to a value less than 1 0 your value will be used for buckling of stringer parts but 1 0 will be used for buckling of ring parts If you want postbuckling capability but you do not want local buckling of the stringer parts to occur at less than a certain fraction of the applied load then set FSBSTR equal to that fraction of the load For example suppose the load set Nx Ny Nxy corresponds to an ultimate load that is 1 5 times the design load You may not want local buckling to occur below a limit load that is 1 25 times the design load To enforce this constraint set FSBSTR 1 25 1 50 0 8333 If you are not bothered by local buckling of the stringer parts at all set FSBSTR equal to zero IF YOU PLAN TO USE A VALUE OF FSBSTR THAT IS LESS THAN UNITY MAKE SURE THAT YOU READ CAREFULLY ITEMS 37 60 c AND 67 IN PANDA2 NEWS Minimum load factor for stiffener buckling Type H FSBSTR 1 1 1 000000 Factor of safety for stress FSSTR 1 h This factor should account for the fact that the theory used to calculate stress expecially if local buckling of the skin occurs well below the design load is approximate The failure criterion is also approximate Use 1 0 lt FSSTR lt 1 5 Factor of safety for stress FSSTR 1 1 1 000000 Do you want flat skin discretized module for local buckling h This question refers to the discretized skin stringer single module model see for example Fig 20 b p 524 of the o

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