How to prepare a matrix with variables that contain a range of values?

This is my first time writing matlab code and I am struggling. I am trying to write a transformation matrix for compliance and stiffness tensors matrices. The tranformation matrix is supposed to be Tsigma=[c^2 s^2 2cs; s^2 c^2 -2cs; -cs cs c*2-s^2] where c=cos(x) and s=sin(x) and x=-pi/2:pi/16:pi/2. This is what I had typed in which I know is completely wrong but I do not know where to begin. I keep getting a complicated matrix that says I cannot take the inverse of it, even though I need to. I need a series of 3x3 matrices with the different values of x put in but cannot seem to get it.

S is the compliance matrix and was defined as: S=[1/E1 -v12/E1 0; -v12/E1 1/E2 0; 0 0 1/G12] where E1=155; E2=12; v12=0.25; G12=5

The end goal is to determine Sbar=inv(Tsigma)*S*Tepsilon and Qbar=inv(Sbar). Tepsilon=[c^2 s^2 cs; s^2 c^2 -cs; -2sc 2sc c^2-s^2]. I had trouble getting this matrix to work out as well.

Any help or direction to get started would be very much appreciated!

Answer 1

[Stephan]

syms c s x

% Tsigma
Tsigma = [c^2 s^2 2*c*s; s^2 c^2 -2*c*s; -c*s c*s c*2-s^2];
Tsigma = subs(Tsigma,[s, c],[sin(x), cos(x)])

Tsigma = 

% Tepsilon
Tepsilon = [c^2 s^2 c*s; s^2 c^2 -c*s; -2*s*c 2*s*c c^2-s^2];
Tepsilon = subs(Tepsilon,[s, c],[sin(x), cos(x)])

Tepsilon = 

% S
E1 = sym(155);
E2 = sym(12);
v12 = sym(0.25);
G12 = sym(5);
S = [1/E1 -v12/E1 0; -v12/E1 1/E2 0; 0 0 1/G12]

S = 

% Sbar symbolic function
Sbar(x) = inv(Tsigma)*S*Tepsilon

Sbar(x) = 

% Qbar symbolic function
Qbar(x) = inv(Sbar)

Qbar(x) = 

% Symbolic values of pi for the x values
pi_const = sym(pi);
xvals = -pi_const/2:pi_const/16:pi_const/2;

% preallocate
SbarVals = sym('sbar', [3,3,numel(xvals)]);
QbarVals = sym('qbar', [3,3,numel(xvals)]);

% calculate the resulting matrices
for k = 1:numel(xvals)
    SbarVals(:,:,k) = Sbar(xvals(k));
    QbarVals(:,:,k) = Qbar(xvals(k));
end

% Show values
SbarVals(:,:,1)

ans = 

QbarVals(:,:,2)

ans =