Smart material project number 1
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This document contains Matlab code for analyzing the mechanical properties of composite materials with different fiber orientations. It defines material properties like elastic modulus and Poisson's ratio for different layers. It then calculates the transformed stiffness and compliance matrices for 0°, 45°, and 90° fiber orientations. Finally, it determines the overall stiffness and compliance matrices for a laminate with varying thicknesses of each fiber layer using classical laminate theory equations.
![Smart material
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));](https://image.slidesharecdn.com/smartmaterialprojectnumber1-140520154234-phpapp02/85/Smart-material-project-number-1-1-320.jpg)
![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)-
2*Q(3,3))*(sind(theta))^2*(cosd(theta))^2)+(Q(3,3)*((sind(theta))^4+(cosd(the
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)))](https://image.slidesharecdn.com/smartmaterialprojectnumber1-140520154234-phpapp02/85/Smart-material-project-number-1-2-320.jpg)
![Q66dash =((Q(1,1)+Q(2,2)-2*Q(1,2)-
2*Q(3,3))*(sind(theta))^2*(cosd(theta))^2)+(Q(3,3)*((sind(theta))^4+(cosd(the
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];
%_________
%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)
)
%
B120=(Q12dash*alpha*(z1+z2))+(Q12dash*beta*(z3+z4+z5))+(Q12dash*gamma*(z6+z7)
)
%
B220=(Q22dash*alpha*(z1+z2))+(Q22dash*beta*(z3+z4+z5))+(Q22dash*gamma*(z6+z7)
)
%
B160=(Q16dash*alpha*(z1+z2))+(Q16dash*beta*(z3+z4+z5))+(Q16dash*gamma*(z6+z7)
)
%
B260=(Q26dash*alpha*(z1+z2))+(Q26dash*beta*(z3+z4+z5))+(Q26dash*gamma*(z6+z7)
)](https://image.slidesharecdn.com/smartmaterialprojectnumber1-140520154234-phpapp02/85/Smart-material-project-number-1-4-320.jpg)
![%
B660=(Q66dash*alpha*(z1+z2))+(Q66dash*beta*(z3+z4+z5))+(Q66dash*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))
)
%
D120=(Q12dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q12dash*(((beta/3)*(z3
^2+z4^2+z5^2))+(beta^3/108)))+(Q12dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48))
)
%
D220=(Q22dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q22dash*(((beta/3)*(z3
^2+z4^2+z5^2))+(beta^3/108)))+(Q22dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48))
)
%
D160=(Q16dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q16dash*(((beta/3)*(z3
^2+z4^2+z5^2))+(beta^3/108)))+(Q16dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48))
)
%
D260=(Q26dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q26dash*(((beta/3)*(z3
^2+z4^2+z5^2))+(beta^3/108)))+(Q26dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48))
)
%
D660=(Q66dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q66dash*(((beta/3)*(z3
^2+z4^2+z5^2))+(beta^3/108)))+(Q66dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48))
)
theta = 45;
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)-
2*Q(3,3))*(sind(theta))^2*(cosd(theta))^2)+(Q(3,3)*((sind(theta))^4+(cosd(the
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));](https://image.slidesharecdn.com/smartmaterialprojectnumber1-140520154234-phpapp02/85/Smart-material-project-number-1-5-320.jpg)
![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]
%_________
%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))
%B2245=(Q22dash*alpha*(z1+z2))+(Q22dash*beta*(z3+z4+z5))+(Q22dash*gamma*(z6+z
7))
%B1645=(Q16dash*alpha*(z1+z2))+(Q16dash*beta*(z3+z4+z5))+(Q16dash*gamma*(z6+z
7))
%B2645=(Q26dash*alpha*(z1+z2))+(Q26dash*beta*(z3+z4+z5))+(Q26dash*gamma*(z6+z
7))
%B6645=(Q66dash*alpha*(z1+z2))+(Q66dash*beta*(z3+z4+z5))+(Q66dash*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)*(
z3^2+z4^2+z5^2))+(beta^3/108)))+(Q12dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48
)))
%D2245=(Q22dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q22dash*(((beta/3)*(
z3^2+z4^2+z5^2))+(beta^3/108)))+(Q22dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48
)))
%D1645=(Q16dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q16dash*(((beta/3)*(
z3^2+z4^2+z5^2))+(beta^3/108)))+(Q16dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48
)))
%D2645=(Q26dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q26dash*(((beta/3)*(
z3^2+z4^2+z5^2))+(beta^3/108)))+(Q26dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48
)))
%D6645=(Q66dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q66dash*(((beta/3)*(
z3^2+z4^2+z5^2))+(beta^3/108)))+(Q66dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48
)))](https://image.slidesharecdn.com/smartmaterialprojectnumber1-140520154234-phpapp02/85/Smart-material-project-number-1-6-320.jpg)
![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](https://image.slidesharecdn.com/smartmaterialprojectnumber1-140520154234-phpapp02/85/Smart-material-project-number-1-7-320.jpg)
Smart material project number 1
- 1. Smart material 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));
- 2. 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)- 2*Q(3,3))*(sind(theta))^2*(cosd(theta))^2)+(Q(3,3)*((sind(theta))^4+(cosd(the 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)))
- 3. % B1290=(Q12dash*alpha(i)*(z1(i)+z2(i)))+(Q12dash*beta(i)*(z3(i)+z4(i)+z5(i)))+ (Q12dash*gamma(i)*(z6(i)+z7(i))) % B2290=(Q22dash*alpha(i)*(z1(i)+z2(i)))+(Q22dash*beta(i)*(z3(i)+z4(i)+z5(i)))+ (Q22dash*gamma(i)*(z6(i)+z7(i))) % B1690=(Q16dash*alpha(i)*(z1(i)+z2(i)))+(Q16dash*beta(i)*(z3(i)+z4(i)+z5(i)))+ (Q16dash*gamma(i)*(z6(i)+z7(i))) % B2690=(Q26dash*alpha(i)*(z1(i)+z2(i)))+(Q26dash*beta(i)*(z3(i)+z4(i)+z5(i)))+ (Q26dash*gamma(i)*(z6(i)+z7(i))) % B6690=(Q66dash*alpha(i)*(z1(i)+z2(i)))+(Q66dash*beta(i)*(z3(i)+z4(i)+z5(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) )) % D1290=(Q12dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q12dash*(((beta/3)*(z 3^2+z4^2+z5^2))+(beta^3/108)))+(Q12dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48) )) % D2290=(Q22dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q22dash*(((beta/3)*(z 3^2+z4^2+z5^2))+(beta^3/108)))+(Q22dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48) )) % D1690=(Q16dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q16dash*(((beta/3)*(z 3^2+z4^2+z5^2))+(beta^3/108)))+(Q16dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48) )) % D2690=(Q26dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q26dash*(((beta/3)*(z 3^2+z4^2+z5^2))+(beta^3/108)))+(Q26dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48) )) % D6690=(Q66dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q66dash*(((beta/3)*(z 3^2+z4^2+z5^2))+(beta^3/108)))+(Q66dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48) )) theta = 0; 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);
- 4. Q66dash =((Q(1,1)+Q(2,2)-2*Q(1,2)- 2*Q(3,3))*(sind(theta))^2*(cosd(theta))^2)+(Q(3,3)*((sind(theta))^4+(cosd(the 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]; %_________ %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) ) % B120=(Q12dash*alpha*(z1+z2))+(Q12dash*beta*(z3+z4+z5))+(Q12dash*gamma*(z6+z7) ) % B220=(Q22dash*alpha*(z1+z2))+(Q22dash*beta*(z3+z4+z5))+(Q22dash*gamma*(z6+z7) ) % B160=(Q16dash*alpha*(z1+z2))+(Q16dash*beta*(z3+z4+z5))+(Q16dash*gamma*(z6+z7) ) % B260=(Q26dash*alpha*(z1+z2))+(Q26dash*beta*(z3+z4+z5))+(Q26dash*gamma*(z6+z7) )
- 5. % B660=(Q66dash*alpha*(z1+z2))+(Q66dash*beta*(z3+z4+z5))+(Q66dash*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)) ) % D120=(Q12dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q12dash*(((beta/3)*(z3 ^2+z4^2+z5^2))+(beta^3/108)))+(Q12dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48)) ) % D220=(Q22dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q22dash*(((beta/3)*(z3 ^2+z4^2+z5^2))+(beta^3/108)))+(Q22dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48)) ) % D160=(Q16dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q16dash*(((beta/3)*(z3 ^2+z4^2+z5^2))+(beta^3/108)))+(Q16dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48)) ) % D260=(Q26dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q26dash*(((beta/3)*(z3 ^2+z4^2+z5^2))+(beta^3/108)))+(Q26dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48)) ) % D660=(Q66dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q66dash*(((beta/3)*(z3 ^2+z4^2+z5^2))+(beta^3/108)))+(Q66dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48)) ) theta = 45; 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)- 2*Q(3,3))*(sind(theta))^2*(cosd(theta))^2)+(Q(3,3)*((sind(theta))^4+(cosd(the 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));
- 6. 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] %_________ %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)) %B2245=(Q22dash*alpha*(z1+z2))+(Q22dash*beta*(z3+z4+z5))+(Q22dash*gamma*(z6+z 7)) %B1645=(Q16dash*alpha*(z1+z2))+(Q16dash*beta*(z3+z4+z5))+(Q16dash*gamma*(z6+z 7)) %B2645=(Q26dash*alpha*(z1+z2))+(Q26dash*beta*(z3+z4+z5))+(Q26dash*gamma*(z6+z 7)) %B6645=(Q66dash*alpha*(z1+z2))+(Q66dash*beta*(z3+z4+z5))+(Q66dash*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)*( z3^2+z4^2+z5^2))+(beta^3/108)))+(Q12dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48 ))) %D2245=(Q22dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q22dash*(((beta/3)*( z3^2+z4^2+z5^2))+(beta^3/108)))+(Q22dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48 ))) %D1645=(Q16dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q16dash*(((beta/3)*( z3^2+z4^2+z5^2))+(beta^3/108)))+(Q16dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48 ))) %D2645=(Q26dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q26dash*(((beta/3)*( z3^2+z4^2+z5^2))+(beta^3/108)))+(Q26dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48 ))) %D6645=(Q66dash*(((alpha/2)*(z1^2+z2^2))+(alpha^3/48)))+(Q66dash*(((beta/3)*( z3^2+z4^2+z5^2))+(beta^3/108)))+(Q66dash*(((gamma/2)*(z6^2+z7^2))+(gamma^3/48 )))
- 7. 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