MATLAB: Basic matrix equation Ax=B with restrictions

MATLABmatrix solve restrictions

Hi! Im modeling a truss using FEM and im trying to solve a very basic equation A*x=b where a is the stiffness matrix , x and b are the displacements and forces vectors. So A and b are known and i want to find x, the displacements. I know i could type x=b/A in matlab, the thing is i know some of the entries of the x vector due to boundary conditions, and typing a=b/A it works as if all x entries where unknowns. Is there a function to do this in MATLAB ?

Thanks a lot!!

Pd: Sorry for my poor english!

Best Answer

x = [ x1 ; x2 ]% x2 known

A = [ A1 A2 ]% A1 & A2 known

A*x = A1*x1 + A2*x2 % last term known

A1*x1 = b - A2*x2

Voila!

Hope this helps.

Greg

P.S. Ain't Linear Systems grand?

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x_min= 0;
x_max = 1;
N = 10; 
L = x_max-x_min; 
h = L/N; 
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uexact= @(x) 4*(x-x.^2);
f = @(x) 8*15*ones(1,N-1); % Source term 
u_exact = uexact(x); 
ua = uexact(x_min); 
ub = uexact(x_max);
u = zeros(N-1,1); 
A = zeros(N-1,N-1); 
b = f(x(2:N)); %
b(1) = b(1) + ua/h^2; 
for i=2:N-1
    b(i) = b(i) + ub/h^2;
end
dA = diag( 2*ones(1,N-1) ); 
dAp1 = diag( -1*ones(1,N-2), 1 ); 
dAm1 = diag( -1*ones(1,N-2), -1 ); 
A = (dA + dAp1 + dAm1);
A = 15*A/h^2;
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g = [ua; u; ub]; 
plot(x,u_exact,'b',x,g,'ro-');
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MATLAB: Am I getting the error of “Array indices must be positive integers or logical values.” in the f(x) line

Why on Earth do you need a loop?

x = -1.612 : 0.01 : -1.322 ;
f = 8 * x.^3 - 2 * x.^2 - 15 * x + 11 ;
g = -10 * x.^3 + 10 * x - 13 ;
figure(1)
plot(x, f, x, g)

Best Answer

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MATLAB: 1-D Heat equation

MATLAB: Am I getting the error of “Array indices must be positive integers or logical values.” in the f(x) line

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