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MAtlabcode :

%chapter 4 micromechanics

Vf=0.5; Vm=0.6;

E1=37.9; E2=11.3 G12=3.3; neu12=0.3

%___________________________________________________________

%chapter 5 ply mechanics : %__________________ %compincematrix : %inputs :sigma1 , sigma2, sigma6 %outputs: e1,e2,gamma6 e: strain sigma1=1.4*10^6; sigma2=1.2*10^6; sigma6=0.8*10^6;

e1=(sigma1/E1)-((neu12*sigma2)/E1); e2=((-neu12*sigma1)/E1)+(sigma2/E2); gamma6=(sigma6/G12); S=[1/E1 -neu12/E1 0; neu12/E1 1/E2 0; 0 0 1/G12]; delta=1-(neu12*neu12);

Q=[E1/delta (neu12*E2)/delta 0; (neu12*E2)/delta E2/delta 0; 0

0 G12];

%S', Q'

theta = 90; Q11dash

=(Q(1,1)*(cosd(theta))^4)+2*((Q(1,2)+2*Q(3,3))*(sind(theta))^2*(cosd(theta))^

2)+Q(2,2)*(sind(theta))^4; Q12dash =((Q(1,1)+Q(2,2)-

4*Q(3,3))*(sind(theta))^2*(cosd(theta))^2)+(Q(1,2)*((sind(theta))^4+(cosd(the

ta))^4)); Q22dash

=(Q(1,1)*(sind(theta))^4)+2*((Q(1,2)+2*Q(3,3))*(sind(theta))^2*(cosd(theta))^

2)+Q(2,2)*(cosd(theta))^4; Q16dash =(((Q(1,1)-Q(1,2)-2*Q(3,3))*(sind(theta))*(cosd(theta))^3)+(Q(1,2)-

Q(2,2)+2*Q(3,3))*(sind(theta))^3*cosd(theta));

Q26dash =(((Q(1,1)-Q(1,2)-2*Q(3,3))*(sind(theta))^3*(cosd(theta)))+(Q(1,2)-

Q(2,2)+2*Q(3,3))*(sind(theta))*(cosd(theta))^3); Q66dash =((Q(1,1)+Q(2,2)-2*Q(1,2)-


ta))^4)); Qdash=[Q11dash Q12dash Q16dash ; Q12dash Q22dash Q26dash ;

Q16dash Q26dash Q66dash];

S11dash=(S(1,1)*(cosd(theta))^4)+((2*S(1,2)+S(3,3))*(sind(theta))^2*(cosd(the

ta))^2)+S(2,2)*(sind(theta))^4; S12dash=((S(1,1)+S(2,2)-

S(3,3))*(sind(theta))^2*(cosd(theta))^2)+(S(1,2)*((sind(theta))^4+(cosd(theta

))^4)); S22dash=(S(1,1)*(sind(theta))^4)+((2*S(1,2)+S(3,3))*(sind(theta))^2*(cosd(the

ta))^2)+S(2,2)*(cosd(theta))^4; S16dash=((2*S(1,1)-2*S(1,2)-S(3,3))*sind(theta)*(cosd(theta))^3)-((2*S(2,2)-

2*S(1,2)-S(3,3))*(sind(theta))^3*cosd(theta)); S26dash=((2*S(1,1)-2*S(1,2)-S(3,3))*(sind(theta))^3*(cosd(theta)))-

((2*S(2,2)-2*S(1,2)-S(3,3))*(sind(theta))*(cosd(theta))^3); S66dash=((2*(2*S(1,1)+2*S(2,2)-4*S(1,2)-

S(3,3))*(sind(theta))^2*(cosd(theta))^2))+(S(3,3)*((sind(theta))^4+(cosd(thet

a))^4)); Sdash=[S11dash S12dash S16dash ; S12dash S22dash S26dash ;

S16dash S26dash S66dash]; %Machrommechanics :

for t3=0:0.1:1 for i=1:length(t3)

t1=0.3 ;%thickness of 0 layer t2=0.8 ;%thickness of 45 layer %t3=0.4 %thickness of 90 layer % t=1.5 %total thickness t(i)=t1+t2+t3(i); alpha(i)=t1/t(i); beta(i)=t2/t(i); gamma(i)=t3(i)/t(i); A1190(i)=(Q11dash*alpha(i))+(Q11dash*beta(i))+(Q11dash*gamma(i)); A1290(i)=(Q12dash*alpha(i))+(Q12dash*beta(i))+(Q12dash*gamma(i)); A2290(i)=(Q22dash*alpha(i))+(Q22dash*beta(i))+(Q22dash*gamma(i)); A1690(i)=(Q16dash*alpha(i))+(Q16dash*beta(i))+(Q16dash*gamma(i)) ; A2690(i)=(Q26dash*alpha(i))+(Q26dash*beta(i))+(Q26dash*gamma(i)); A6690(i)=(Q66dash*alpha(i))+(Q66dash*beta(i))+(Q66dash*gamma(i)); z1(i)=-((alpha(i)/2)+(beta(i)/2)); z2(i)=-beta(i)/2; z3(i)=-beta(i)/6; z4(i)=beta(i)/6; z5(i)=beta(i)/2; z6(i)=((beta(i)/2)+(gamma(i)/2)); z7(i)=((beta(i)/2)+gamma(i));

%

B1190=(Q11dash*alpha(i)*(z1(i)+z2(i)))+(Q11dash*beta(i)*(z3(i)+z4(i)+z5(i)))+

(Q11dash*gamma(i)*(z6(i)+z7(i)))

%


(Q12dash*gamma(i)*(z6(i)+z7(i))) %








(Q66dash*gamma(i)*(z6(i)+z7(i)))

%

D1190=(Q11dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q11dash*(((beta/3)*(z

3^2+z4^2+z5^2))+(beta^3/108)))+(Q11dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48)

)) %



)) %



)) %



)) %



)) %



))

theta = 0; Q11dash




ta))^4)); Q22dash



Q(2,2)+2*Q(3,3))*(sind(theta))^3*cosd(theta)); Q26dash =(((Q(1,1)-Q(1,2)-2*Q(3,3))*(sind(theta))^3*(cosd(theta)))+(Q(1,2)-

Q(2,2)+2*Q(3,3))*(sind(theta))*(cosd(theta))^3);

Q66dash =((Q(1,1)+Q(2,2)-2*Q(1,2)-







))^4)); S22dash=(S(1,1)*(sind(theta))^4)+((2*S(1,2)+S(3,3))*(sind(theta))^2*(cosd(the






S16dash S26dash S66dash]; %_________ %chapter 6 %Machrommechanics : %t1=0.3 %thickness of 0 layer %t2=0.8 %thickness of 45 layer %t3=0.4 %thickness of 90 layer % t=1.5 %total thickness % alpha=t1/t; %beta=t2/t; %gamma=t3/t; A110(i)=(Q11dash*alpha(i))+(Q11dash*beta(i))+(Q11dash*gamma(i)); A120(i)=(Q12dash*alpha(i))+(Q12dash*beta(i))+(Q12dash*gamma(i)); A220(i)=(Q22dash*alpha(i))+(Q22dash*beta(i))+(Q22dash*gamma(i)); A160(i)=(Q16dash*alpha(i))+(Q16dash*beta(i))+(Q16dash*gamma(i)) ; A260(i)=(Q26dash*alpha(i))+(Q26dash*beta(i))+(Q26dash*gamma(i)); A660(i)=(Q66dash*alpha(i))+(Q66dash*beta(i))+(Q66dash*gamma(i));

%

B110=(Q11dash*alpha*(z1+z2))+(Q11dash*beta*(z3+z4+z5))+(Q11dash*gamma*(z6+z7)

) %


) %


) %


) %


)

%


)

%

D110=(Q11dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q11dash*(((beta/3)*(z3

^2+z4^2+z5^2))+(beta^3/108)))+(Q11dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48))

) %



) %



) %



) %



) %



)

theta = 45; Q11dash




ta))^4)); Q22dash



Q(2,2)+2*Q(3,3))*(sind(theta))^3*cosd(theta)); Q26dash =(((Q(1,1)-Q(1,2)-2*Q(3,3))*(sind(theta))^3*(cosd(theta)))+(Q(1,2)-

Q(2,2)+2*Q(3,3))*(sind(theta))*(cosd(theta))^3); Q66dash =((Q(1,1)+Q(2,2)-2*Q(1,2)-







))^4));

S22dash=(S(1,1)*(sind(theta))^4)+((2*S(1,2)+S(3,3))*(sind(theta))^2*(cosd(the






S16dash S26dash S66dash] %_________ %chapter 6

A1145(i)=(Q11dash*alpha(i))+(Q11dash*beta(i))+(Q11dash*gamma(i)); A1245(i)=(Q12dash*alpha(i))+(Q12dash*beta(i))+(Q12dash*gamma(i)); A2245(i)=(Q22dash*alpha(i))+(Q22dash*beta(i))+(Q22dash*gamma(i)); A1645(i)=(Q16dash*alpha(i))+(Q16dash*beta(i))+(Q16dash*gamma(i)) ; A2645(i)=(Q26dash*alpha(i))+(Q26dash*beta(i))+(Q26dash*gamma(i)); A6645(i)=(Q66dash*alpha(i))+(Q66dash*beta(i))+(Q66dash*gamma(i));

%B1145=(Q11dash*alpha*(z1+z2))+(Q11dash*beta*(z3+z4+z5))+(Q11dash*gamma*(z6+z

7)) %B1245=(Q12dash*alpha*(z1+z2))+(Q12dash*beta*(z3+z4+z5))+(Q12dash*gamma*(z6+z





7))

%D1145=(Q11dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q11dash*(((beta/3)*(

z3^2+z4^2+z5^2))+(beta^3/108)))+(Q11dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48

))) %D1245=(Q12dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q12dash*(((beta/3)*(










)))

A11t(i)=(4*A1145(i))+(2*A1190(i))+(2*A110(i)); A12t(i)=(4*A1245(i))+(2*A1290(i))+(2*A110(i)); A22t(i)=(4*A2245(i))+(2*A2290(i))+(2*A220(i)); A16t(i)=(4*A1645(i))+(2*A1690(i))+(2*A160(i)); A26t(i)=(4*A2645(i))+(2*A2690(i))+(2*A260(i)); A66t(i)=(4*A6645(i))+(2*A6690(i))+(2*A660(i));

%B11t=(4*B1145)+(2*B1190)+(2*B110) %B12t=(4*B1245)+(2*B1290)+(2*B120) %B22t=(4*B2245)+(2*B2290)+(2*B220) %B16t=(4*B1645)+(2*B1690)+(2*B160) %B26t=(4*B2645)+(2*B2690)+(2*B260) %B66t=(4*B6645)+(2*B6690)+(2*B660)

%D11t=(4*D1145)+(2*D1190)+(2*D110) %D12t=(4*D1245)+(2*D1290)+(2*D120) %D22t=(4*D2245)+(2*D2290)+(2*D220) %D16t=(4*D1645)+(2*D1690)+(2*D160) %D26t=(4*D2645)+(2*D2690)+(2*D260) %D66t=(4*D6645)+(2*D6690)+(2*D660) K=[A11t(i) A12t(i) A16t(i); A12t(i) A22t(i) A26t(i) ; A16t(i) A26t(i)

A66t(i)]

Ex(i)=((K(1,1).*K(2,2))-(K(1,2).^2))/(t(i).*K(2,2))

plot(gamma,Ex) gridon

end end

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