Solving Matrix Equations with Multiple Variable Vectors

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nick12391 2020-10-30

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https://ww2.mathworks.cn/matlabcentral/answers/631829-solving-matrix-equations-with-multiple-variable-vectors

评论： Stephan 2020-10-31

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I have an equation: S = QE

where Q is a 3x3 matrix with known constants,

S and E are both 3 element vectors. S has a single variable and E has 2 variables.

I want to solve for the 3 variables. This is what I tried:

E1 = 140e9;    % [Pa]
E2 = 10e9;     % [Pa]
G12 = 7e9;     % [Pa]
V12 = 0.3;
V21 = V12;
syms tau Exx Eyy
S = [tau + 5e6;...  % S11
    -tau + 5e6;...  % S22
       -5e6];       % S12
Q = [E1/(1-V12*V21) V12*E2/(1-V12*V21) 0;... % All known values
  V12*E2/(1-V12*V21)  E2/(1-V12*V21)   0;...
         0                 0           0];
E = [Exx/2 + Eyy/2;...
     Exx/2 + Eyy/2;...
       Exx - Eyy];
solve(S == Q*E);

But it comes up empty. I've done this same process with a set of equations, but never in matrix form. I could, of course, expand this out by hand and input the seperate equations, but I'd rather not have to do that because I'd like to be able to turn this into a function. I'm pretty sure linsolve() won't work since the variable are not spread between 2 vectors. Not sure what else to try.

Any suggestions are appreciated, thanks.