Solution to Example 1.6 First use periodic microstructure micromechanics (6.8) to obtainthe lamina properties (in MPa).E1 = 145; 880 G12 = 4; 386 12 = 13 = 0:263E2 = 11; 590 G23 = 3; 767 23 = 0:538Then, compute the compliance matrix [S0] using (1.91), the rotation matrix [T] using(1.34), the compliance [S] in laminate coordinate system using (1.53), and the stiness[C] = [S]??1 in the laminate coordinate system for each lamina. Then, average them using(1.102), invert the average, and nally using (1.105) getEx = 75; 924 Gxy = 38; 048 xy = 0:370Ey = 44; 913 Gyz = 3; 999 yz = 0:394Ez = 15; 119 Gxz = 4; 154 xz = 0:276This example can be solved with the following MATLAB code:function Ex106% Example 1.6 laminate stiffness as per section 1.15clc% Lamina properties calculated with PMM in cadec-online% Cprime (1.92) calculated with% http://www.cadec-online.com/Chapters/Chapter5/3DConstitutiveEquations% /StiffnessMatrix.aspxCprime = [149395.9113 6754.740801 6754.740801 0 0 0;6754.740801 16627.00749 9093.208855 0 0 0;6754.740801 9093.208855 16627.00749 0 0 0;0 0 0 3766.899318 0 0;0 0 0 0 4385.907534 0;0 0 0 0 0 4385.907534;]theta = [0,90,30,-30];thickness = [1,1,1,1]*1.5; % mmlaminateThickness = sum(thickness);C = zeros(6);for i=1:length(theta)[T,Tbar] = RotationMatrix3D(theta(i));C = C + Tbar*Cprime*Tbar*thickness(i)/laminateThickness; % (1.102)PRxy=-S(2,1)/S(1,1)PRyz=-S(3,2)/S(2,2)PRxz=-S(3,1)/S(1,1)end