Smart material project number 1

Smart Material project number 1 :
MAtlabcode :
%matlab code of composite structure
%chapter four code
%michromechanics composite material
%calculation of material properties
%inputs: Em,Ef,Vm,Vf,Gm,Gf,alpha m, alpha f, neu f, neu m
%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);
%stiffines matrix:
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];
%_________
%chapter 6
%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));
A1690(i)=(Q16dash*alpha(i))+(Q16dash*beta(i))+(Q16dash*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)))
%
%
%
%
%
%
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
2)+Q(2,2)*(sind(theta))^4;
Q12dash =((Q(1,1)+Q(2,2)-
ta))^4));
Q22dash
2)+Q(2,2)*(cosd(theta))^4;
Q66dash =((Q(1,1)+Q(2,2)-2*Q(1,2)-
ta))^4));
ta))^2)+S(2,2)*(sind(theta))^4;
S12dash=((S(1,1)+S(2,2)-
))^4));
ta))^2)+S(2,2)*(cosd(theta))^4;
S66dash=((2*(2*S(1,1)+2*S(2,2)-4*S(1,2)-
a))^4));
S16dash S26dash S66dash];
%_________
%chapter 6
%Machrommechanics :
% t=1.5 %total thickness
% alpha=t1/t;
%beta=t2/t;
%gamma=t3/t;

%
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
2)+Q(2,2)*(sind(theta))^4;
Q12dash =((Q(1,1)+Q(2,2)-
ta))^4));
Q22dash
2)+Q(2,2)*(cosd(theta))^4;
Q66dash =((Q(1,1)+Q(2,2)-2*Q(1,2)-
ta))^4));
ta))^2)+S(2,2)*(sind(theta))^4;
S12dash=((S(1,1)+S(2,2)-
))^4));
ta))^2)+S(2,2)*(cosd(theta))^4;
S66dash=((2*(2*S(1,1)+2*S(2,2)-4*S(1,2)-
a))^4));
S16dash S26dash S66dash]
%_________
%chapter 6
%B1145=(Q11dash*alpha*(z1+z2))+(Q11dash*beta*(z3+z4+z5))+(Q11dash*gamma*(z6+z
7))
7))
7))
7))
7))

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
)))
)))
)))
)))
)))
)))
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
___________________________________________________________________________
Results :
Empty graph and I don’t know why is it empty
Note :
There is no error in the code and here is some of the results in workspace of
the matlab :
Sdash =
0.1005 -0.0510 -0.0311
-0.0510 0.1005 -0.0311
-0.0311 -0.0311 0.1307
Qdash =
18.6791 12.0791 7.3077
12.0791 18.6791 7.3077
7.3077 7.3077 11.6538

K =
195.3714 155.7714 43.8462
155.7714 136.9099 43.8462
43.8462 43.8462 76.5231
K is the matrix of the total coefficient of the eight layer of the lamina
4 layer at theta= 45
2 layer at theta=90
2 layer at theta =0
E2 =
11.3000
neu12 =
0.3000
S =
0.0264 -0.0079 0
0.0079 0.0885 0
0 0 0.3030
delta =
0.9100
Q =
41.6484 3.7253 0
3.7253 12.4176 0
0 0 3.3000
Qdash =
12.4176 3.7253 0
3.7253 41.6484 0
0 0 3.3000

Smart material project number 1

Smart material project number 1

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Smart material project number 1