Structural Health Monitoring using Smart Material and Smart System
Smart material project number 1
8
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;
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Transcript of Smart material project number 1
Smart materialMAtlabcode :
%chapter 4 micromechanics
Vf=0.5;Vm=0.6;
E1=37.9;E2=11.3G12=3.3;neu12=0.3
%___________________________________________________________
%chapter 5 ply mechanics :%__________________%compincematrix :%inputs :sigma1 , sigma2, sigma6%outputs: e1,e2,gamma6 e: strainsigma1=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(theta))^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(theta))^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(theta))^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(theta))^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(theta))^4));Sdash=[S11dash S12dash S16dash ; S12dash S22dash S26dash ; S16dash S26dash S66dash];%Machrommechanics :
for t3=0:0.1:1for i=1:length(t3)
t1=0.3 ;%thickness of 0 layert2=0.8 ;%thickness of 45 layer%t3=0.4 %thickness of 90 layer% t=1.5 %total thicknesst(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)))% 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)*(z3^2+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)*(z3^2+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)*(z3^2+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)*(z3^2+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)*(z3^2+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)*(z3^2+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(theta))^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(theta))^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(theta))^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(theta))^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(theta))^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))% 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(theta))^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(theta))^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(theta))^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(theta))^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(theta))^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+z7))%B1245=(Q12dash*alpha*(z1+z2))+(Q12dash*beta*(z3+z4+z5))+(Q12dash*gamma*(z6+z7))%B2245=(Q22dash*alpha*(z1+z2))+(Q22dash*beta*(z3+z4+z5))+(Q22dash*gamma*(z6+z7))%B1645=(Q16dash*alpha*(z1+z2))+(Q16dash*beta*(z3+z4+z5))+(Q16dash*gamma*(z6+z7))%B2645=(Q26dash*alpha*(z1+z2))+(Q26dash*beta*(z3+z4+z5))+(Q26dash*gamma*(z6+z7))%B6645=(Q66dash*alpha*(z1+z2))+(Q66dash*beta*(z3+z4+z5))+(Q66dash*gamma*(z6+z7))
%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)))
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
endend
