How to take double integral of a function matrix?

Hello!

I have a matrix that consist of 2 variables (x,y) functions and i have to take double integral of it.

clear

clc

syms x y

a=1; b=1; t=1;

E=100/72; v=0.2;

x1=0; x2=b; x3=b; x4=0;

y1=0; y2=0; y3=a; y4=a;

B1 = [y-y4;0;x-x2];

B2 = [0;x-x2;y-y4];

B3 = [y3-y;0;x1-x];

B4 = [0;x1-x;y3-y];

B5 = [y-y2;0;x-x4];

B6 = [0;x-x4;y-y2];

B7 = [y1-y;0;x3-x];

B8 = [0;x3-x;y1-y];

B = [B1 B2 B3 B4 B5 B6 B7 B8];

D = (E/((1+v)*(1-2*v)))*[1-v v 0;v 1-v 0;0 0 0.5-v];

A = B.'*D*B

g = matlabFunction(A)

integral2(g,0,1,0,1)

I got this error.

Error using reshape

To RESHAPE the number of elements must not change.

Is there any possible way to convert symbolic function matrix to function handle in form of matrix? and how can i take integral of that matrix? otherwise i have to write every 64 equation seperately to take integral of them

[Rik]

Regarding your flag ("It is my homework so and i don't think it will be helpful to answer common problems. I request it to be deleted. Best regards."): If you didn't want this question to be public you should not have posted. Now you have received an answer. It would be unkind to Catalytic to delete this thread. That is also why you no longer see delete button on your thread. Just in case you decide to edit away your question, I will make a copy here so it can be easily restored.

How to take double integral of a function matrix?

Hello!

I have a matrix that consist of 2 variables (x,y) functions and i have to take double integral of it.

clear

clc

syms x y

a=1; b=1; t=1;

E=100/72; v=0.2;

x1=0; x2=b; x3=b; x4=0;

y1=0; y2=0; y3=a; y4=a;

B1 = [y-y4;0;x-x2];

B2 = [0;x-x2;y-y4];

B3 = [y3-y;0;x1-x];

B4 = [0;x1-x;y3-y];

B5 = [y-y2;0;x-x4];

B6 = [0;x-x4;y-y2];

B7 = [y1-y;0;x3-x];

B8 = [0;x3-x;y1-y];

B = [B1 B2 B3 B4 B5 B6 B7 B8];

D = (E/((1+v)*(1-2*v)))*[1-v v 0;v 1-v 0;0 0 0.5-v];

A = B.'*D*B

g = matlabFunction(A)

integral2(g,0,1,0,1)

I got this error.

Error using reshape

To RESHAPE the number of elements must not change.

Is there any possible way to convert symbolic function matrix to function handle in form of matrix? and how can i take integral of that matrix? otherwise i have to write every 64 equation seperately to take integral of them

Answer 1

[Catalytic]

syms x y
a=1; b=1; t=1;
E=100/72; v=0.2;
x1=0; x2=b; x3=b; x4=0;
y1=0; y2=0; y3=a; y4=a;
B1 = [y-y4;0;x-x2];
B2 = [0;x-x2;y-y4];
B3 = [y3-y;0;x1-x];
B4 = [0;x1-x;y3-y];
B5 = [y-y2;0;x-x4];
B6 = [0;x-x4;y-y2];
B7 = [y1-y;0;x3-x];
B8 = [0;x3-x;y1-y];
B = [B1 B2 B3 B4 B5 B6 B7 B8];
D = (E/((1+v)*(1-2*v)))*[1-v v 0;v 1-v 0;0 0 0.5-v];
A = B.'*D*B;
g = matlabFunction(A);

in1=@(fun) integral(fun,0,1,'ArrayValued',1);

out=in1( @(x) in1( @(y)g(x,y) ) )

out = 8×8

0.7073 0.2411 -0.4180 -0.0482 -0.3537 -0.2411 0.0643 0.0482 0.2411 0.7073 0.0482 0.0643 -0.2411 -0.3537 -0.0482 -0.4180 -0.4180 0.0482 0.7073 -0.2411 0.0643 -0.0482 -0.3537 0.2411 -0.0482 0.0643 -0.2411 0.7073 0.0482 -0.4180 0.2411 -0.3537 -0.3537 -0.2411 0.0643 0.0482 0.7073 0.2411 -0.4180 -0.0482 -0.2411 -0.3537 -0.0482 -0.4180 0.2411 0.7073 0.0482 0.0643 0.0643 -0.0482 -0.3537 0.2411 -0.4180 0.0482 0.7073 -0.2411 0.0482 -0.4180 0.2411 -0.3537 -0.0482 0.0643 -0.2411 0.7073