function TEST_CODE2()R = 10 / 1000;H = 20 / 1000;%number of elements in z directionN_z=5;%number of elements in r directionN_r=10;%number of total elementsN_E=(N_z)*(N_r);%number of nodes in z directionNN_z=(N_z)+1;%number of nodes in r directionNN_r=(N_r)+1;% number of total nodesNN=NN_z*NN_r;%r = zeros(NN, 1);theta = zeros(NN, 1);z = zeros(NN, 1);IEN = zeros(N_E*4, 1);%a=(2*pi*R)/(N_r);b=H/(N_z);c=(2*pi)/(N_r);N_z_index = 1;z_value = 0;%r_value = 0;theta_value = 0;for i = 1:1:NN% r(i) = r_value;z(i) = z_value;theta(i) = theta_value;if N_z_index >= NN_zN_z_index = 1;z_value = 0;%r_value = r_value + a;theta_value = theta_value + c;elsez_value = z_value + b;N_z_index = N_z_index + 1;endendIEN_count = 1;IEN_index = 1;for i = 1:1:N_Etemp = 4*(i-1);IEN(4*(i-1) + 1) = IEN_index;IEN(4*(i-1) + 2) = IEN_index + NN_z;IEN(4*(i-1) + 3) = IEN_index + NN_z + 1;IEN(4*(i-1) + 4) = IEN_index + 1;if IEN_count == N_zIEN_index = IEN_index + 2;IEN_count = 1;elseIEN_index = IEN_index + 1;IEN_count = IEN_count + 1;endendh = zeros(N_E, 1);h_theta = zeros(N_E, 1);mu=1;c=2;e=3;for i = 1:1:N_EF1 = 0;k = 0;F2 = 0;F = 0;for xi=(-1/sqrt(3)):(2/sqrt(3)):(1/sqrt(3))for eta=(-1/sqrt(3)):(2/sqrt(3)):(1/sqrt(3))NodeNum1 = IEN(4*(i-1) + 1);NodeNum2 = IEN(4*(i-1) + 2);NodeNum3 = IEN(4*(i-1) + 3);NodeNum4 = IEN(4*(i-1) + 4);theta1 = theta(NodeNum1);theta2 = theta(NodeNum2);theta3 = theta(NodeNum3);theta4 = theta(NodeNum4);z1 = z(NodeNum1);z2 = z(NodeNum2);z3 = z(NodeNum3);z4 = z(NodeNum4);h1=c+e*cos(theta1);h2=c+e*cos(theta2);h3=c+e*cos(theta3);h4=c+e*cos(theta4);h = (h1+h2+h3+h4)/4;h1_theta = e*cos(theta1)-e*sin(theta1);h2_theta = e*cos(theta2)-e*sin(theta2);h3_theta = e*cos(theta3)-e*sin(theta3);h4_theta = e*cos(theta4)-e*sin(theta4);h_theta = (h1_theta+h2_theta+h3_theta+h4_theta)/4N1=0.25*(1-xi)*(1-eta);N2=0.25*(1+xi)*(1-eta);N3=0.25*(1+xi)*(1+eta);N4=0.25*(1-xi)*(1+eta);N=[N1,0,N2,0,N3,0,N4,0;0,N1,0,N2,0,N3,0,N4];dN1_xi=0.25*(-1+eta);dN1_eta=0.25*(-1+xi);dN2_xi=0.25*(1-eta);dN2_eta=0.25*(-1-xi);dN3_xi=0.25*(1+eta);dN3_eta=0.25*(1+xi);dN4_xi=0.25*(-1-eta);dN4_eta=0.25*(-1-xi);dN_xi = zeros(2,8);dN_xi(1,1) = dN1_xi;dN_xi(1,2) = 0.0;dN_xi(1,3) = dN2_xi;dN_xi(1,1) = 0.0;dN_xi(1,1) = dN3_xi;dN_xi(1,1) = 0.0;dN_xi(1,1) = dN4_xi;dN_xi(1,8) = 0.0;dN_xi(2,1) = 0.0;dN_xi(2,2) = dN1_xi;dN_xi(2,3) = 0.0;dN_xi(2,1) = dN2_xi;dN_xi(2,1) = 0.0;dN_xi(2,1) = dN3_xi;dN_xi(2,1) = 0.0;dN_xi(2,8) = dN4_xi;dN_eta = zeros(2,8);dN_eta(1,1) = dN1_eta;dN_eta(1,2) = 0.0;dN_eta(1,3) = dN2_eta;dN_eta(1,1) = 0.0;dN_eta(1,1) = dN3_eta;dN_eta(1,1) = 0.0;dN_eta(1,1) = dN4_eta;dN_eta(1,8) = 0.0;dN_eta(2,1) = 0.0;dN_eta(2,2) = dN1_eta;dN_eta(2,3) = 0.0;dN_eta(2,1) = dN2_eta;dN_eta(2,1) = 0.0;dN_eta(2,1) = dN3_eta;dN_eta(2,1) = 0.0;dN_eta(2,8) = dN4_eta;J11=-1*(1-eta)*theta1+(1-eta)*theta2+(1+eta)*theta3-(1+eta)*theta4;J12=-1*(1-eta)*z1+(1-eta)*z2+(1+eta)*z3-(1+eta)*z4;J21=-1*(1-xi)*theta1-(1+xi)*theta2+(1+xi)*theta3+(1-xi)*theta4;J22=-1*(1-xi)*z1-(1+xi)*z2+(1+xi)*z3+(1-xi)*z4;J = zeros(2,2);J = 0.25*[J11, J12;J21,J22];detJ=J11*J22-J21*J12;%invJ=[J22,-1*J12;% -1*J21,J11]/detJ;dN_theta=(J22*dN_xi-J12*dN_eta)/detJ;dN_z=(-1*J12*dN_xi+J11*dN_eta)/detJ;F1_xi_eta=(1/R)*(dN_theta)*(dN_theta);F2_xi_eta=(dN_z)*(dN_z);%h=c+e*cos(theta);% Gauss integral method% initializek = k + detJ*(h(i)^3)*(F1_xi_eta)*(F2_xi_eta)/(12*mu);V_theta1 = R*(theta1)/2;V_theta2 = R*(theta2)/2;V_theta3 = R*(theta3)/2;V_theta4 = R*(theta4)/2;V_theta = (V_theta1+V_theta2+V_theta3+V_theta4)/4V_z = (e)/2;F1 = F1+detJ*(h(i))*((F1_xi_eta)*(V_theta)+(F2_xi_eta)*(V_z));F2 = F2+detJ*(h_theta(i))*N;F = F1-F2;endP = F/k;endendy = StiffnessAssemble(K,k,NodeNum1,NodeNum2,NodeNum3,NodeNum4);end% change local to global%nodes i,j,m,nfunction y=StiffnessAssemble(K,k,i,j,m,n)K = zeros(NN*2,NN*2);K(2*i-1,2*i-1)= K(2*i-1,2*i-1) + k(1,1);K(2*i-1,2*1)=K(2*i-1,2*i)+k(1,2);K(2*i-1,2*j-1)=K(2*i-1,2*j-1)+k(1,3);K(2*i-1,2*j)=K(2*i-1,2*j)+k(1,4);K(2*i-1,2*m-1)=K(2*i-1,2*m-1)+k(1,5);K(2*i-1,2*m)=K(2*i-1,2*m)+k(1,6);K(2*i-1,2*n-1)=K(2*i-1,2*n-1)+k(1,7);K(2*i-1,2*n)=K(2*i-1,2*n)+k(1,8);K(2*i,2*i-1)=K(2*i,2*i-1)+k(2,1);K(2*i,2*i)=K(2*i,2*i)+k(2,2);K(2*i,2*j-1)=K(2*i,2*j-1)+k(2,3);K(2*i,2*j)=K(2*i,2*j)+k(2,4);K(2*i,2*m-1)=K(2*i,2*m-1)+k(2,5);K(2*i,2*m)=K(2*i,2*m)+k(2,6);K(2*i,2*n-1)=K(2*i,2*n-1)+k(2,7);K(2*i,2*n)=K(2*i,2*n)+k(2,8);K(2*j-1,2*i-1)=K(2*j-1,2*i-1)+k(3,1);K(2*j-1,2*i)=K(2*j-1,2*i)+k(3,2);K(2*j-1,2*j-1)=K(2*j-1,2*j-1)+k(3,3);K(2*j-1,2*j)=K(2*j-1,2*j)+k(3,4);K(2*j-1,2*m-1)=K(2*j-1,2*m-1)+k(3,5);K(2*j-1,2*m)=K(2*j-1,2*m)+k(3,6);K(2*j-1,2*n-1)=K(2*j-1,2*n-1)+k(3,7);K(2*j-1,2*n)=K(2*j-1,2*n)+k(3,8);K(2*j,2*i-1)=K(2*j,2*i-1)+k(4,1);K(2*j,2*i)=K(2*j,2*i)+k(4,2);K(2*j,2*j-1)=K(2*j,2*j-1)+k(4,3);K(2*j,2*j)=K(2*j,2*j)+k(4,4);K(2*j,2*m-1)=K(2*j,2*m-1)+k(4,5);K(2*j,2*m)=K(2*j,2*m)+k(4,6);K(2*j,2*n-1)=K(2*j,2*n-1)+k(4,7);K(2*j,2*n)=K(2*j,2*n)+k(4,8);K(2*m-1,2*i-1)=K(2*m-1,2*i-1)+k(5,1);K(2*m-1,2*i)=K(2*m-1,2*i)+k(5,2);K(2*m-1,2*j-1)=K(2*m-1,2*j-1)+k(5,3);K(2*m-1,2*j)=K(2*m-1,2*j)+k(5,4);K(2*m-1,2*m-1)=K(2*m-1,2*m-1)+k(5,5);K(2*m-1,2*m)=K(2*m-1,2*m)+k(5,6);K(2*m-1,2*n-1)=K(2*m-1,2*n-1)+k(5,7);K(2*m-1,2*n)=K(2*m-1,2*n)+k(5,8);K(2*m,2*i-1)=K(2*m,2*i-1)+k(6,1);K(2*m,2*i)=K(2*m,2*i)+k(6,2);K(2*m,2*j-1)=K(2*m,2*j-1)+k(6,3);K(2*m,2*j)=K(2*m,2*j)+k(6,4);K(2*m,2*m-1)=K(2*m,2*m-1)+k(6,5);K(2*m,2*m)=K(2*m,2*m)+k(6,6);K(2*m,2*n-1)=K(2*m,2*n-1)+k(6,7);K(2*m,2*n)=K(2*m,2*n)+k(6,8);K(2*n-1,2*i-1)=K(2*n-1,2*i-1)+k(7,1);K(2*n-1,2*i)=K(2*n-1,2*i)+k(7,2);K(2*n-1,2*j-1)=K(2*n-1,2*j-1)+k(7,3);K(2*n-1,2*j)=K(2*n-1,2*j)+k(7,4);K(2*n-1,2*m-1)=K(2*n-1,2*m-1)+k(7,5);K(2*n-1,2*m)=K(2*n-1,2*m)+k(7,6);K(2*n-1,2*n-1)=K(2*n-1,2*n-1)+k(7,7);K(2*n-1,2*n)=K(2*n-1,2*n)+k(7,8);K(2*n,2*i-1)=K(2*n,2*i-1)+k(8,1);K(2*n,2*i)=K(2*n,2*i)+k(8,2);K(2*n,2*j-1)=K(2*n,2*j-1)+k(8,3);K(2*n,2*j)=K(2*n,2*j)+k(8,4);K(2*n,2*m-1)=K(2*n,2*m-1)+k(8,5);K(2*n,2*m)=K(2*n,2*m)+k(8,6);K(2*n,2*n-1)=K(2*n,2*n-1)+k(8,7);K(2*n,2*n)=K(2*n,2*n)+k(8,8);y=K;end& 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