first time user, need help with matrix variables?

Hello,

I am looking for help on writing code for this problem. I am not looking for the answer so much as I am looking for some direction. So far, what I have done is the following: E1=155; E2=12; v12=0.25; G12=5; S=[1/E1 -v12/E1 0; -v12/E1 1/E2 0; 0 0 1/G12] and C=inv(S). As can be seen on the attached formula sheet, in order to get Sbar, I need Tsigma matrix and Tepsilon matrix. I set x=linspace(-pi/2, pi/2); s=sin(x); c=cos(x) as per the instructions. But, I am having difficulties moving on from there. I do not know how to get the Tsigma matrix as shown on the formula sheet and also do not know how I would plot it properly. I need to plot the following six positions in the Sbar matrix from x=-pi/2 to pi/2: S(1,1), S(1,2), S(1,3), S(2,2), S(2,3), and S(3,3).

Any help would be greatly appreciate as I am very confused!

Answer 1

[Steven Lord]

If your x vector were:

x = linspace(-pi, pi, 9)

x = 1×9

-3.1416 -2.3562 -1.5708 -0.7854 0 0.7854 1.5708 2.3562 3.1416

As written this would give you a 3-by-27 matrix.

c = cos(x);
s = sin(x);
T = [c.^2, s.^2, 2*c.*s;
    s.^2, c.^2, -2*c.*s;
    -c.*s, c.*s, c.^2-s.^2];
size(T)

ans = 1×2

3 27

If you wanted a series of T matrices, one for each element of x, you could create T as a 3-dimensional array and take each page of that array in turn:

x2 = reshape(x, 1, 1, []);
c2 = cos(x2);
s2 = sin(x2);
T2 = [ c2.^2,  s2.^2,  2*c2.*s2;
       s2.^2,  c2.^2, -2*c2.*s2;
     -c2.*s2, c2.*s2, c2.^2-s2.^2];
size(T2)

ans = 1×3

3 3 9

Let's look at one of the pages, the one for x(2) which is essentially -3*pi/4.

format longg
T2(:, :, 2)

ans = 3×3

0.5 0.5 1 0.5 0.5 -1 -0.5 0.5 -2.22044604925031e-16

Or if you don't want to create the whole 3-dimensional array at once, you could write a function:

Tfun = @(x) [cos(x).^2, sin(x).^2, 2*cos(x).*sin(x);
             sin(x).^2, cos(x).^2, -2*cos(x).*sin(x);
             -cos(x).*sin(x), cos(x).*sin(x), cos(x).^2-sin(x).^2];
Tfun(x(2))

ans = 3×3

0.5 0.5 1 0.5 0.5 -1 -0.5 0.5 -2.22044604925031e-16