Lecture 03a Introd to Assignment 1
Contents
1. digital format Matlab input file by email to brianha at math uio no Brian Hayman 06 09 2010 MEK4540 2010 3a 3 UNIVERSITETET IOSLO The Matlab script 1 Script for Assignment 1 MEK4540 Autumn 2010 Brian Hayman 2010 The material properties and laminate lay ups must be replaced with the correct data clear all Sets all variables to zero Material data to be replaced by correct values EL 40000 ET 7700 vLT 20 25 GLT 2800 t 0 5 Thickness of one UD ply Ply orientations to be replaced by correct lay ups R 45 0 45 3 14159 180 ply angles in radians alternative is R 45 0 45 rad h 1 5 t 0 5 t 0 5 t 1 5 t z coordinates for top and bottom surfaces of plies as defined in AB amp C Fig 6 5 Compliance 5 matrix 5 1 1 1 EL 5 2 2 1 ET 5 1 2 2 vLT EL 5 3 3 21 GLT 5 2 1 5 1 2 Stiffness Q matrix 1 5 The procedure shown here uses tensor shear strains You may keep to engineering shear strains 1f you prefer but then you need the T1 and T2 matrices as defined in AB amp C Q 3 3 22 Q0 3 3 convert from engineering to tensor shear strains MEK4540 2010 3a 4 UNIVERSITETET 5 OSLO The Matlab script 2 A 1 3 1 3 20 B 1 3 1 3 20 D 1 3 1 3 20 for 1 1 length R Calculate T and Q for each ply Assemble A B and D Transformation matrix T matrix T 1 1 cos R 1 2 T 2 2 cos R 1 2 T 12. 2 2s1n R 1 2 T 2 1 s1n R 1 2 T 3 1 2 san R 1 cos R 1 2 T 3 2 s1n R 1 cos R 1 T 1 3 22 s1n R 1 cos R 1 T 2 3 2 2 s1n R 1 cos R 1 T 3 3 2cos R 1 2 s1n R 1 2 Qk 1 1nv T Q T Stiffness matrix for tensor strains following rotation Qk 3 1 2Qk 3 15 2 Convert back to engineering shear strains A AtOK C 7 h 1 1 h 1 Calculate A matrix B 6 5 QkC 71 Ch 1 1 42 h 1 42 Calculate B matrix D D41 3 Qk 1 5 h 141 3 h 1 3 5 Calculate D matrix en A B D Assemble total stiffness matrix for the laminate This gives the relation between stresses and strains with engineering shear strains Qtot A B B D Places contributions A B D with B D rows below B MEK4540 2010 3a 5 j UNIVERSITETET UP 1 OSLO How to run Matlab at UiO e f you are logged on to a Linux machine in the Science Faculty at UiO just write the command matlab or matlab amp e f you are using a Windows PC somewhere else e g your own laptop Make sure you have an internet connection then use Accessories Communications Remote desktop connection Alogin box will appear Type windows ifi uio no and press Connect You will then be faced with a normal UiO login box Log in to UIO with your UiO user and password Click on the Linux penguin icon to open a Linux login box log in on this with your UiO user and password then you will get a Linux
3. window Proceed as described above e You can also purchase a student Matlab CD and licence at the bookshop MEK4540 2010 3a 6 j UNIVERSITETET UP 1 OSLO Matlab some basic principles e Use the help function to find out how each type of command works e Matlab also contains some tutorials for beginners e Matlab is specially designed for matrix operations e It uses scalars vectors and matrices e Matrix operations are simple to write e g Invert matrix A to give matrix B B inv A Transpose matrix to give matrix B transpose A Pre multiply vector V by matrix A to give vector W W e Basic input file is filename m e This can call up subroutine files but this facility is not needed for this assignment e Comments ignored by program are preceded by 96 sign can be separate line or end of line e The result of each line will be written to the command window unless it ends with sign e Values of varables are retained unless set to zero by clear command MEK4540 2010 3a 7 f FHA UNIVERSITETET 1 OSLO Matlab some basic principles Open Matlab You will see an empty command window e Use File Open to open the m file e You can edit this file as you wish e Save it then press the green arrow button to run it e Results will appear the command window e You can copy any part of the command window and p
4. Explain briefly how these matrices express the relationship between stress and strain for a single ply and indicate clearly whether you are using the tensor shear strain or the engineering shear strain MEK4540 2010 3a 2 UNIVERSITETET 5 I OSLO Assignment no 1 contd d Study the Matlab script provided and modify it to calculate the A B and D matrices for laminates consisting of the above plies in the four lay ups 0 0 45 0 45 45 0 0 45 45 90 iv 90 45 45 0 and v 0 45 45 0 Comment on the differences identifying any special properties displayed by the lay ups Note The Matlab script may also be used to check the individual ply stiffness matrices Q calculated in part c e Calculate the total thickness of each of the laminates 11 and 111 Modify the same Matlab script to calculate the strains for each of these two laminates when they are exposed to a tensile stress in the 0 direction of 1 MPa which must first be converted to a force per unit length Hence find the effective E modulus Ey and Poisson s ratio for each of these two laminates By similar means find the effective E and Comment on the differences between the results for the two laminates The Matlab script that is developed to solve parts d and e is to be handed in together with the solution Even if the main solution is handed in on paper the script should be sent in
5. aste into a text file Further notes e Matlab script files are simply text files They can be edited either within Matlab as above or by use of a text editor such as Notepad or Wordpad in Windows e Much information is available from the web page of MAT1110 including a user manual in Norwegian but also some links to internet websites MEK4540 2010 3a 8
6. f UNIVERSITETET I OSLO MEK4540 Komposittmaterie Composite mater Introduction to Assignment no 1 4540 2010 3a 1 UNIVERSITETET 5 I OSLO Assignment no 1 MEK 4540 Autumn 2010 Compulsory Assignment no 1 To be submitted by 10 15 on 04 10 2010 by one of the following means e directly by email to brianha at math uio no e placed in Brian s mail pigeon hole on the 7th Floor e delivered by hand at lecture on 30 September or 4 October A glass fibre laminate consists of the following materials Glass fibres E modulus E 72 4 GPa Poisson s ratio 0 2 Density 2 54 g em Epoxy E modulus E 3 5 GPa Poisson s ratio v 0 35 Density p 1 2 g cm The fibre fabric in each unidirectional ply weighs 200 g m After a burn off test on 5 g laminate 3 55 of glass 15 left a Calculate the density of the composite the fibre volume fraction and the thickness of a single 200 g m ply b Estimate Ez Er and vzr Use the simple combination laws and where appropriate also the Halpin Tsai formulae Explain the differences With the elastic properties derived in b above taking the Halpin Tsai values for Er and Grr set up the stiffness matrix in the L T axes Use the transformation matrix T as defined in the lectures or the matrices T and T as defined in the text book to calculate the stiffness matrices in directions 0 90 45 and 45
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