%%%%%%%%%%%%%%%%%materials: AS4/PEEK-PEEK liner: (1)=PEEK; (2)=AS4/PEEK: E1(1)=3.64e9;E2(1)=3.64e9;E3(1)=3.64e9;v12(1)=0.4;v13(1)=0.4;v23(1)=0.4;G12(1)=1.3e9;G13(1)=1.3e9;G23(1)=1.3e9;v21(1)=v12(1)*E2(1)/E1(1);v31(1)=v13(1)*E3(1)/E1(1);v32(1)=v23(1)*E2(1)/E3(1); E1(2)=131e9;E2(2)=8.7e9;E3(2)=8.7e9;v12(2)=0.28;v13(2)=0.28;v23(2)=0.48;G12(2)=5e9;G13(2)=5e9;G23(2)=2.78e9;v21(2)=v12(2)*E2(2)/E1(2);v31(2)=v13(2)*E3(2)/E1(2);v32(2)=v23(2)*E2(2)/E3(2); AS4/Epoxy-steel liner: (1)=steel; (2)=AS4/epoxy: E1(1)=2.07e11;E2(1)=2.07e11;E3(1)=2.07e11;v12(1)=0.3;v13(1)=0.3;v23(1)=0.3;G12(1)=7.96154e10;G13(1)=7.96154e10;G23(1)=7.96154e10;v21(1)=v12(1)*E2(1)/E1(1);v31(1)=v13(1)*E3(1)/E1(1);v32(1)=v23(1)*E2(1)/E3(1); E1(2)=1.354e11;E2(2)=9.37e9;E3(2)=9.37e9;v12(2)=0.32;v13(2)=0.32;v23(2)=0.46;G12(2)=4.96e9;G13(2)=4.96e9;G23(2)=3.2e9;v21(2)=v12(2)*E2(2)/E1(2);v31(2)=v13(2)*E3(2)/E1(2);v32(2)=v23(2)*E2(2)/E3(2); AS4/Epoxy-Ti liner: (1)=Ti; (2)=AS4/epoxy: E1(1)=1.138e11;E2(1)=1.138e11;E3(1)=1.138e11;v12(1)=0.342;v13(1)=0.342;v23(1)=0.342;G12(1)=4.24e10;G13(1)=4.24e10;G23(1)=4.24e10;v21(1)=v12(1)*E2(1)/E1(1);v31(1)=v13(1)*E3(1)/E1(1);v32(1)=v23(1)*E2(1)/E3(1); E1(2)=1.354e11;E2(2)=9.37e9;E3(2)=9.37e9;v12(2)=0.32;v13(2)=0.32;v23(2)=0.46;G12(2)=4.96e9;G13(2)=4.96e9;G23(2)=3.2e9;v21(2)=v12(2)*E2(2)/E1(2);v31(2)=v13(2)*E3(2)/E1(2);v32(2)=v23(2)*E2(2)/E3(2); AS4/Epoxy-Al liner: (1)=Al; (2)=AS4/epoxy: E1(1)=7.1e10;E2(1)=7.1e10;E3(1)=7.1e10;v12(1)=0.3;v13(1)=0.3;v23(1)=0.3;G12(1)=2.731e10;G13(1)=2.731e10;G23(1)=2.731e10;v21(1)=v12(1)*E2(1)/E1(1);v31(1)=v13(1)*E3(1)/E1(1);v32(1)=v23(1)*E2(1)/E3(1); E1(2)=1.354e11;E2(2)=9.37e9;E3(2)=9.37e9;v12(2)=0.32;v13(2)=0.32;v23(2)=0.46;G12(2)=4.96e9;G13(2)=4.96e9;G23(2)=3.2e9;v21(2)=v12(2)*E2(2)/E1(2);v31(2)=v13(2)*E3(2)/E1(2);v32(2)=v23(2)*E2(2)/E3(2); E1(1)=1.38e11;E2(1)=8.96e9;E3(1)=8.96e9;v12(1)=0.3;v13(1)=0.3;v23(1)=0.3;G12(1)=7.1e9;G13(1)=7.1e9;G23(1)=7.1e9;v21(1)=v12(1)*E2(1)/E1(1);v31(1)=v13(1)*E3(1)/E1(1);v32(1)=v23(1)*E2(1)/E3(1); %%%%%%%%%%%%%%%%%only one material E1=input('E1=');E2=input('E2=');E3=input('E3=');v12=input('v12=');v13=input('v13=');v23=input('v23=');G12=input('G12=');G13=input('G13=');G23=input('G23='); E1(1)=16.5;E2(1)=1.4;E3(1)=1.4;v12(1)=0.33;v13(1)=0.33;v23(1)=0.54;G12(1)=0.87;G13(1)=0.87;G23(1)=0.45;v21(1)=v12(1)*E2(1)/E1(1);v31(1)=v13(1)*E3(1)/E1(1);v32(1)=v23(1)*E2(1)/E3(1); format long C_global_total=zeros(6,6); N=input('number of layers=');t_total=0; for m=1:1:N; t(m)=input('t='); angle(m)=input('angle='); t_total=t_total+t(m); end for k=1:1:N; V(k)=t(k)/t_total; end for m=1:1:N; s(m)=sin(angle(m)*pi/180); c(m)=cos(angle(m)*pi/180); end [S]=[1/E1 -v12/E1 -v13/E1 0 0 0 -v21/E2 1/E2 -v23/E2 0 0 0 -v31/E3 -v32/E3 1/E3 0 0 0 0 0 0 1/G23 0 0 0 0 0 0 1/G13 0 0 0 0 0 0 1/G12]; [C]=inv(S); for i=1:1:N; T_stress(:,:,i)=[(c(i))^2 (s(i))^2 0 0 0 2*c(i)*s(i) (s(i))^2 (c(i))^2 0 0 0 -2*c(i)*s(i) 0 0 1 0 0 0 0 0 0 c(i) -s(i) 0 0 0 0 s(i) c(i) 0 -c(i)*s(i) c(1)*s(i) 0 0 0 (c(i))^2-(s(i))^2]; T_strain(:,:,i)=[(c(i))^2 (s(i))^2 0 0 0 c(i)*s(i) (s(i))^2 (c(i))^2 0 0 0 -c(i)*s(i) 0 0 1 0 0 0 0 0 0 c(i) -s(i) 0 0 0 0 s(i) c(i) 0 -2*c(i)*s(i) 2*c(i)*s(i) 0 0 0 (c(i))^2-(s(i))^2]; end for i=1:1:N; C_global(:,:,i)=T_stress(:,:,i)*C*(T_strain(:,:,i))^(-1); end for i=[4 5]; for j=[4 5]; for k=1:N Sum_3=0; for q=1:N; for l=1:N; Sum_3=Sum_3+V(l)*(C_global(4,4,q)*C_global(5,5,l)-C_global(4,5,q)*C_global(5,4,l))/(C_global(4,4,l)*C_global(5,5,l)-C_global(4,5,l)*C_global(5,4,l)); end end C_global_total(i,j)=C_global_total(i,j)+(V(k)*C_global(i,j,k)/(C_global(4,4,k)*C_global(5,5,k)-C_global(4,5,k)*C_global(5,4,k)))/(V(k)/(C_global(4,4,k)*C_global(5,5,k)-C_global(4,5,k)*C_global(5,4,k))*Sum_3); end end end for i=[1 2 3 6]; for j=[1 2 3 6]; Sum_1=0; Sum_2=0; for k=1:N; for l=1:N Sum_1=Sum_1+V(l)*C_global(3,j,l)/C_global(3,3,l); Sum_2=Sum_2+V(l)/C_global(3,3,l); end C_global_total(i,j)=C_global_total(i,j)+V(k)*(C_global(i,j,k)-C_global(i,3,k)*C_global(3,j,k)/C_global(3,3,k)+(C_global(i,3,k)*Sum_1/C_global(3,3,k)/Sum_2)); end end end for i=[1 2 3 6]; for j=[4 5]; C_global_total(i,j)=0; C_global_total(j,i)=0; end end H=inv(C_global_total); Ex=1/H(1,1); Ey=1/H(2,2); Ez=1/H(3,3); v_yz=-H(2,3)/H(2,2); v_xz=-H(1,3)/H(1,1); v_xy=-H(1,2)/H(1,1); v_zy=-H(2,3)/H(3,3); v_zx=-H(1,3)/H(3,3); v_yx=-H(1,2)/H(2,2); Gyz=1/H(4,4); Gxz=1/H(5,5); Gxy=1/H(6,6); Ex Ey Ez v_yz v_xy v_xz %%%%%%%%%%%%%%%%% several materials E1_1=input('E1_1=');E2_1=input('E2_1=');E3_1=input('E3_1=');v12_1=input('v12_1=');v13_1=input('v13_1=');v23_1=input('v23_1=');G12_1=input('G12_1=');G13_1=input('G13_1=');G23_1=input('G23_1='); v21_1=v12_1*E2_1/E1_1;v31_1=v13_1*E3_1/E1_1;v32_1=v23_1*E2_1/E3_1; E1_2=input('E1_2=');E2_2=input('E2_2=');E3_2=input('E3_2=');v12_2=input('v12_2=');v13_2=input('v13_2=');v23_2=input('v23_2=');G12_2=input('G12_2=');G13_2=input('G13_2=');G23_2=input('G23_2='); v21_2=v12_2*E2_2/E1_2;v31_2=v13_2*E3_2/E1_2;v32_2=v23_2*E2_2/E3_2; E1(1)=3.64e9;E2(1)=3.64e9;E3(1)=3.64e9;v12(1)=0.4;v13(1)=0.4;v23(1)=0.4;G12(1)=1.3e9;G13(1)=1.3e9;G23(1)=1.3e9;v21(1)=v12(1)*E2(1)/E1(1);v31(1)=v13(1)*E3(1)/E1(1);v32(1)=v23(1)*E2(1)/E3(1); E1(2)=131e9;E2(2)=8.7e9;E3(2)=8.7e9;v12(2)=0.28;v13(2)=0.28;v23(2)=0.48;G12(2)=5e9;G13(2)=5e9;G23(2)=2.78e9;v21(2)=v12(2)*E2(2)/E1(2);v31(2)=v13(2)*E3(2)/E1(2);v32(2)=v23(2)*E2(2)/E3(2); format long C_global_total=zeros(6,6); %%%here the N=total layers including liner N=input('number of layers=');M=input('number of material=');t_total=0; for m=1:1:N; t(m)=input('t='); angle(m)=input('angle='); material(m)=input('material='); t_total=t_total+t(m); end for k=1:1:N; V(k)=t(k)/t_total; end for m=1:1:N; s(m)=sin(angle(m)*pi/180); c(m)=cos(angle(m)*pi/180); end for i=1:M S(:,:,i)=[1/E1(i) -v12(i)/E1(i) -v13(i)/E1(i) 0 0 0 -v21(i)/E2(i) 1/E2(i) -v23(i)/E2(i) 0 0 0 -v31(i)/E3(i) -v32(i)/E3(i) 1/E3(i) 0 0 0 0 0 0 1/G23(i) 0 0 0 0 0 0 1/G13(i) 0 0 0 0 0 0 1/G12(i)]; C(:,:,i)=inv(S(:,:,i)); end for i=1:1:N; T_stress(:,:,i)=[(c(i))^2 (s(i))^2 0 0 0 2*c(i)*s(i) (s(i))^2 (c(i))^2 0 0 0 -2*c(i)*s(i) 0 0 1 0 0 0 0 0 0 c(i) -s(i) 0 0 0 0 s(i) c(i) 0 -c(i)*s(i) c(1)*s(i) 0 0 0 (c(i))^2-(s(i))^2]; T_strain(:,:,i)=[(c(i))^2 (s(i))^2 0 0 0 c(i)*s(i) (s(i))^2 (c(i))^2 0 0 0 -c(i)*s(i) 0 0 1 0 0 0 0 0 0 c(i) -s(i) 0 0 0 0 s(i) c(i) 0 -2*c(i)*s(i) 2*c(i)*s(i) 0 0 0 (c(i))^2-(s(i))^2]; end for i=1:1:N; if material(i)==1 C_global(:,:,i)=T_stress(:,:,i)*C(:,:,1)*(T_strain(:,:,i))^(-1); %%%%%%%%%%%%%%%%%using if commond to add different materials,in this example 8 materials can be defined. end if material(i)==2 C_global(:,:,i)=T_stress(:,:,i)*C(:,:,2)*(T_strain(:,:,i))^(-1); end if material(i)==3 C_global(:,:,i)=T_stress(:,:,i)*C(:,:,3)*(T_strain(:,:,i))^(-1); end if material(i)==4 C_global(:,:,i)=T_stress(:,:,i)*C(:,:,4)*(T_strain(:,:,i))^(-1); end if material(i)==5 C_global(:,:,i)=T_stress(:,:,i)*C(:,:,5)*(T_strain(:,:,i))^(-1); end if material(i)==6 C_global(:,:,i)=T_stress(:,:,i)*C(:,:,6)*(T_strain(:,:,i))^(-1); end if material(i)==7 C_global(:,:,i)=T_stress(:,:,i)*C(:,:,7)*(T_strain(:,:,i))^(-1); end if material(i)==8 C_global(:,:,i)=T_stress(:,:,i)*C(:,:,8)*(T_strain(:,:,i))^(-1); end end for i=[4 5]; for j=[4 5]; for k=1:N Sum_3=0; for q=1:N; for l=1:N; Sum_3=Sum_3+V(l)*(C_global(4,4,q)*C_global(5,5,l)-C_global(4,5,q)*C_global(5,4,l))/(C_global(4,4,l)*C_global(5,5,l)-C_global(4,5,l)*C_global(5,4,l)); end end C_global_total(i,j)=C_global_total(i,j)+(V(k)*C_global(i,j,k)/(C_global(4,4,k)*C_global(5,5,k)-C_global(4,5,k)*C_global(5,4,k)))/(V(k)/(C_global(4,4,k)*C_global(5,5,k)-C_global(4,5,k)*C_global(5,4,k))*Sum_3); end end end for i=[1 2 3 6]; for j=[1 2 3 6]; Sum_1=0; Sum_2=0; for k=1:N; for l=1:N Sum_1=Sum_1+V(l)*C_global(3,j,l)/C_global(3,3,l); Sum_2=Sum_2+V(l)/C_global(3,3,l); end C_global_total(i,j)=C_global_total(i,j)+V(k)*(C_global(i,j,k)-C_global(i,3,k)*C_global(3,j,k)/C_global(3,3,k)+(C_global(i,3,k)*Sum_1/C_global(3,3,k)/Sum_2)); end end end for i=[1 2 3 6]; for j=[4 5]; C_global_total(i,j)=0; C_global_total(j,i)=0; end end H=inv(C_global_total); Ex=1/H(1,1); Ey=1/H(2,2); Ez=1/H(3,3); v_yz=-H(2,3)/H(2,2); v_xz=-H(1,3)/H(1,1); v_xy=-H(1,2)/H(1,1); v_zy=-H(2,3)/H(3,3); v_zx=-H(1,3)/H(3,3); v_yx=-H(1,2)/H(2,2); Gyz=1/H(4,4); Gxz=1/H(5,5); Gxy=1/H(6,6); Ex Ey Ez v_yz v_xz v_xy Gyz Gxz Gxy