why this not works? there is a error "??? Error using ==> times Matrix dimensions must agree." in Sx line. how can i fix and plot the graphic?

K = 300;

theta = 0:pi/10:pi/2;

x = 0.02:0.01:0.2;

y = 0.02:0.01:0.2;

[X,Y]=meshgrid(x,y);

r=(sqrt(X.^2+Y.^2));

Sx = (K./(sqrt(2.*pi.*r)).*(cos(theta./2)).*(1-(sin(theta./2).*sin((3.*theta)./2))));

mesh(x,y,Sx) grid on

i try plot the stresses graphic. 0<theta<90 0.02<r<0.2 K=300. x and y horizontal plane ,and the stresses in the vertical plane.and Sx formula i writed the above.

Answer 1

[Guillaume]

The basic problem is that you're trying to multiply

f1(x, y) =  K / sqrt(2*pi*r), with r = sqrt(x.^2+y.^2)

with

f2(theta) = cos(theta/2) .* ...

The former is a 19x19 matrix, the latter a 1x6 vector. So, of course, the matrix dimensions don't agree.

What are you trying to plot, though? Is it Sx(r, theta) or Sx(x, y, theta)?

The first one would be:

r = linspace(0.02, 0.2, 20); %20 values between 0.02 and 0.2
theta = linspace(0, pi/2, 6); %6 values between 0 and pi/2
[r, theta] = meshgrid(r, theta);
Sx = (K./(sqrt(2.*pi.*r)).*(cos(theta./2)).*(1-(sin(theta./2).*sin((3.*theta)./2))));

The second one would be a 3D matrix, you would have to change your meshgrid to ndgrid

[X, Y, theta] = ndgrid(x, y, theta);

[Bugra]

i try to plot the stresses graphic. mesh(x,y,Sx) Sx=stresses and 0<theta<90 and 0.02<r<0.2 and i have Sx formula but i cant that. i have plot the graphic but something is wrong.

[Guillaume]

Restating the same thing won't make anything clearer.

You say you want to plot

mesh(x, y, Sx)

So Sx is a variable of x and y

But then you say, it is a variable of theta and r. Which is it?

[Bugra]

i try to plot the coordinates x and y horizontal plane and the stresses in the vertical direction. but i have theta and r values. in formula there are r and theta. already theta=tan(y/x) and r=sqrt(x^2+y^2).i writed this code but not the same graphic i have example for K=300 graphic;

clc, clear all

K=300;

x = linspace(0.02, 0.2, 20)

y = linspace( 0.02,0.2,20)

[x,y]=meshgrid(x,y);

 r = sqrt(x.^2+y.^2)

 theta=tan(y/x)

r = linspace(0.02, 0.2, 20); %20 values between 0.02 and 0.2

theta = linspace(0, pi/2, 20); %20 values between 0 and pi/2

[r, theta] = meshgrid(r, theta);

Sx = (K./(sqrt(2.*pi.*r)).*(cos(theta./2)).*(1-(sin(theta./2).*sin((3.*theta)./2))));

Sy = (K./(sqrt(2.*pi.*r)).*(cos(theta./2)).*(1+(sin(theta./2).*sin((3.*theta)./2))));

Sxy = (K./(sqrt(2.*pi.*r)).*cos(theta./2).*sin(theta./2).*cos((3.*theta)./2));

mesh(x,y,Sx)

[Guillaume]

Ok, I understand now. You want to plot Sx(x,y) but the formula for Sx is based on polar coordinates, so:

K = 300;
[x, y] = meshgrid(linspace(0.02, 0.2, 20));
[r, theta] = cart2pol(x, y);
Sx = (K./(sqrt(2.*pi.*r)).*(cos(theta./2)).*(1-(sin(theta./2).*sin((3.*theta)./2))));
mesh(x, y, Sx)