# HW5 - Aerospace Structural Composites I Homework 5 Anirban...

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Aerospace Structural Composites I Homework 5 Anirban Chaudhuri 1. Expand your MATLAB routines to calculate also the B and D matrices and check it on Example 2.4.2, using E 1 = 38.6GPa, E 2 = 8.27GPa, G 12 = 4.14GPa, 12 = 0.26, t = 0.1mm and a laminate with stacking sequence as [(30/(30+90) 2 /30) 2 /(45/-45 2 /45) 2 ] T (taking =30 o ). Solution: A MATLAB code is provided to evaluate the B-matrix and D-matrix along with the A-matrix that was done in homework 3. The main code takes in the input arguments of (material properties) E 1 , E 2 , G 12 , 12 , (thickness) t, (number of plies) n and ply angles. It calls a function that evaluates the A, B, D-matrices using the equations given below. 3 0{ , , } 22 11 1{ , , } 1 2{ , , } 1 3{ , , } ,0, 12 cos2 , , 3 sin 2 , , 3 cos4 , , 3 ABD n kk k k k k k k k k n k k A B D k kkkk k k k A B D h Vh zz z z Vt t z t z z t z t z z t z t         1 4{ , , } 1 sin 4 , , 3 n k n k k A B D k z z t z t … (1) where, t k is the layer thickness, 1 2 k z is the z coordinate of the mid-plane of the k th layer measured from the mid-plane of the laminate. The reduced stiffness matrix or the Q-matrix for the material is obtained by using the equation (2) [Eq. 2.4.8 in book]. 1 11 12 21 2 22 12 21 12 2 12 12 21 66 12 1 1 1 E Q E Q E Q QG  …(2)

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The corresponding U values (material invariants) are given in equation (3) [Eq. 2.4.20 in book]. 11 1 2 2 1 2 6 6 21 1 2 2 31 1 2 2 1 2 6 6 41 1 2 2 1 2 6 6 51 1 2 2 1 2 6 6 1 (3 3 2 4 ) 8 1 () 2 1 (2 4 ) 8 1 (6 4 ) 8 1 4 ) 8 UQ Q Q Q Q Q Q Q Q Q Q Q Q Q    …(3) 12 3 11 11 11 3 0{ , , } 22 22 22 43 1{ , , } 12 12 12 53 2{ , , } 66 66 66 3{ , , 23 16 16 16 26 26 26 00 ,, 0 0 1 0 2 1 0 2 ABD UU U U V V V V        } 4{ , , } V …(4) MATLAB code: % Anirban Chaudhuri % Aerospace Structural Composites I % HW 5 prob 1 close all ;clc;clear all ;format short ;format compact ; % Initial Constants for the given materials (checking with Ex 2.4.2)
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• Spring '08
• PETERIFJU
• Berlin U-Bahn, Coefficient of thermal expansion, Howard Staunton, Anirban Chaudhuri, Aerospace Structural Composites

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HW5 - Aerospace Structural Composites I Homework 5 Anirban...

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