MATLAB Answers

plotting is giving me multiple lines

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Eddy Ramirez
Eddy Ramirez on 19 Apr 2021 at 5:11
Answered: Alan Stevens on 19 Apr 2021 at 7:42
Greetings,
I made some modifications to my code and I am trying to plot this, but it is giving me different lines. My intent is to plot the first row of "stress1f(:,k)" for the x axis and y axis z_1=[z(k) z(k+1)]; I tried to do it inside and outside the for loop, but matlab seems to graph the same points multiple times when i do it inside the for loop and outside it seems the same. any suggestions would be greatly appreciated it
My graph should look as the three graphs on the right when I graph the first, second, and third row against z_1=[z(k) z(k+1)];
close all
clear all
clc
%%%FIBER
Ef=220e9;%[N/m] GPA to Newton/square meter
Vf=.63; %fiber volume fraction
vf=.33;%fiber poissions ratio
%%MATRIX
Em=10e9;%[N/m] GPA to Newton/square meter
Vm=1-Vf; %%matrix volume fraction
vm=.33;%%matrix poissons ratio
Em2=Em/(1-vm^2); %equation 3.31
%%Lamina's Thickness
h=1e-3;%[N/m] mm to Newton/square meter
%%Shear modulus
Gf=Ef/(2*(1+vf));
Gm=Em/(2*(1+vm));
%%Lamina Properties
E1=(Vf*Ef)+(Vm*Em);
E2=(Ef*Em)/(Vf*Gm+Vm*Gf);
E_2=Ef*Em2/(Vf*Em2+Vm*Ef); %equation 3.32
v12=(Vf*vf)+(Vm*vm);
v21=(E2/E1)*v12;
G12=(Gf*Gm)/((Vf*Gm)+(Vm*Gf));
% Reduced local in plane stiffness Q
Q11=E1/(1-v12*v21);
Q12=(v21*E1)/(1-v12*v21);
Q22=E2/(1-v12*v21);
Q66=G12;
Q=[Q11,Q12,0;
Q12,Q22,0;
0,0,Q66];
%%Laminate rotations in degrees
theta=[0,45,-45,90,30,60,-30,-60,-60,-30,60,30,90,-45,45,0];
%%Z-Values
z=(-length(theta)/2+(0:length(theta)))'*h;
% Global Q matrix:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:length(theta)
m=cosd(theta(i));
n=sind(theta(i));
T=[m.^2,n.^2,2.*m.*n;
n.^2,m.^2,-2.*m.*n;
-m.*n,m.*n,m.^2-n.^2];
% Global transformed reduced stiffness coefficients Q_bar
Q_bar{i}=inv(T).*Q.*T;
end
Aij=0;
Bij=0;
Dij=0;
for j=1:length(theta)
A_j=Q_bar{j}*(z(j+1)-z(j));
Aj{j}=A_j;
Aij=Aij+Aj{j};
B_j=Q_bar{j}*((z(j+1))^2-(z(j))^2);
Bj{j}=B_j;
Bij=Bij+Bj{j};
D_j=Q_bar{j}*((z(j+1))^3-(z(j))^3);
Dj{j}=D_j;
Dij=Dij+Dj{j};
end
A=Aij;
B=(1/2)*Bij;
D=(1/3)*Dij;
%%Forces
Nx=2e6;
Ny=4.6e6;
Ns=0;
N=[Nx;Ny;Ns];
%%Moments
Mx=3e3;
My=0;
Ms=-1e-3;
M=[Mx;My;Ms];
%%Shear
e_x=sym('Epsilonx');
e_y=sym('Epsilony');
gamma_xy=sym('Gammaxy');
shear=[e_x;e_y; gamma_xy];
%%Bending Twist
k_x=sym('Kx');
k_y=sym('Ky');
k_xy=sym('Kxy');
bending=[k_x;k_y;k_xy];
%%Shear Extension Coupling
SEC=N==A*shear;
SEC_F=solve(SEC);
e_xf=vpa(SEC_F.Epsilonx);
e_yf=vpa(SEC_F.Epsilony);
gamma_xyf=(SEC_F.Gammaxy);
shearf=[e_xf;e_yf; gamma_xyf];
%%Bending
BEC=M==D*bending;
BEC_F=solve(BEC);
k_xf=vpa(BEC_F.Kx);
k_yf=vpa(BEC_F.Ky);
k_xyf=vpa(BEC_F.Kxy);
bendingf=[k_xf;k_yf;k_xyf];
for k=1:length(theta)
stress1=Q_bar{k}*shearf+z(k)*Q_bar{k}*bendingf;%%BOTTOM LAYER
stress2=Q_bar{k}*shearf+z(k+1)*Q_bar{k}*bendingf;%%TOP LAYER
stress1f(:,k)=stress1; %Bottom
stress2f(:,k)=stress2; %Top
b=stress1f(1,:)';
t=stress2f(1,:)';
tt=[b t];
z_1=[z(k) z(k+1)];
% figure(1)
% stressx=[stress1f(1,k) stress2f(1,k)];
% z_1=[z(k) z(k+1)];
% plot(stressx,z_1)
% xline(0)
% hold on
% figure(2)
% stressy=[stress1f(2,k) stress2f(2,k)];
% z_2=[z(k) z(k+1)];
% plot(stressy,z_2)
% xline(0)
% figure(3)
% stressxy=[stress1f(3,k) stress2f(3,k)];
% z_3=[z(k) z(k+1)];
% plot(stressxy,z_3)
% xline(0)
% hold on
end
figure(1)
plot(tt,z_1)

Answers (1)

Alan Stevens
Alan Stevens on 19 Apr 2021 at 7:42
A little more like this perhaps:
%%%FIBER
Ef=220e9;%[N/m] GPA to Newton/square meter
Vf=.63; %fiber volume fraction
vf=.33;%fiber poissions ratio
%%MATRIX
Em=10e9;%[N/m] GPA to Newton/square meter
Vm=1-Vf; %%matrix volume fraction
vm=.33;%%matrix poissons ratio
Em2=Em/(1-vm^2); %equation 3.31
%%Lamina's Thickness
h=1e-3;%[N/m] mm to Newton/square meter
%%Shear modulus
Gf=Ef/(2*(1+vf));
Gm=Em/(2*(1+vm));
%%Lamina Properties
E1=(Vf*Ef)+(Vm*Em);
E2=(Ef*Em)/(Vf*Gm+Vm*Gf);
E_2=Ef*Em2/(Vf*Em2+Vm*Ef); %equation 3.32
v12=(Vf*vf)+(Vm*vm);
v21=(E2/E1)*v12;
G12=(Gf*Gm)/((Vf*Gm)+(Vm*Gf));
% Reduced local in plane stiffness Q
Q11=E1/(1-v12*v21);
Q12=(v21*E1)/(1-v12*v21);
Q22=E2/(1-v12*v21);
Q66=G12;
Q=[Q11,Q12,0;
Q12,Q22,0;
0,0,Q66];
%%Laminate rotations in degrees
theta=[0,45,-45,90,30,60,-30,-60,-60,-30,60,30,90,-45,45,0];
%%Z-Values
z=(-length(theta)/2+(0:length(theta)))'*h;
% Global Q matrix:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:length(theta)
m=cosd(theta(i));
n=sind(theta(i));
T=[m.^2,n.^2,2.*m.*n;
n.^2,m.^2,-2.*m.*n;
-m.*n,m.*n,m.^2-n.^2];
% Global transformed reduced stiffness coefficients Q_bar
Q_bar{i}=inv(T).*Q.*T;
end
Aij=0;
Bij=0;
Dij=0;
for j=1:length(theta)
A_j=Q_bar{j}*(z(j+1)-z(j));
Aj{j}=A_j;
Aij=Aij+Aj{j};
B_j=Q_bar{j}*((z(j+1))^2-(z(j))^2);
Bj{j}=B_j;
Bij=Bij+Bj{j};
D_j=Q_bar{j}*((z(j+1))^3-(z(j))^3);
Dj{j}=D_j;
Dij=Dij+Dj{j};
end
A=Aij;
B=(1/2)*Bij;
D=(1/3)*Dij;
%%Forces
Nx=2e6;
Ny=4.6e6;
Ns=0;
N=[Nx;Ny;Ns];
%%Moments
Mx=3e3;
My=0;
Ms=-1e-3;
M=[Mx;My;Ms];
%%Shear Extension Coupling
shearf = A\N;
e_xf = shearf(1); e_yf = shearf(2); gamma_xyf = shearf(3);
%%Bending
bendingf = D\M;
k_xf = bendingf(1); k_yf = bendingf(2); k_xyf = bendingf(3);
for k=1:length(theta)
stress1=Q_bar{k}*shearf+z(k)*Q_bar{k}*bendingf;%%BOTTOM LAYER
stress2=Q_bar{k}*shearf+z(k+1)*Q_bar{k}*bendingf;%%TOP LAYER
stress1f(:,k)=stress1; %Bottom
stress2f(:,k)=stress2; %Top
b=stress1f(1,:)';
t=stress2f(1,:)';
tt=[b t];
z_1(k,:)=[z(k) z(k+1)];
end
z_1 = z_1';
z_1 = z_1(:);
figure(1)
stressx=[stress1f(1,:)' stress2f(1,:)']';
stressx = stressx(:);
plot(stressx,z_1)
xline(0);
figure(2)
stressy=[stress1f(2,:)' stress2f(2,:)']';
stressy = stressy(:);
plot(stressy,z_1)
xline(0);
figure(3)
stressxy=[stress1f(3,:)' stress2f(3,:)']';
stressxy = stressxy(:);
plot(stressxy,z_1)
xline(0);

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