How can I generate the global stiffness matrix from the various stiffness member matrices using the structural matrix method?

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I'm trying to solve a problem involving a planar roof truss using the structural matrix method. I have gotten the various stiffness member matrices but I can't figure out how to combine these to get the global matrix. Efficiency isn't a priority I really just need to understand how to call and sum the appropriate elements of the individual matrices. If anyone has any advice or segments of code that would be helpful I would be greatly appreciative. This is what I have coded so far to get the member matrices.
lambda = [0.8944 0.8944 0.8944 0.8944 0.8944 0.8944 1 1 1 1 1 1 0 -0.8944 0 -0.7071 0 0.7071 0 0.8944 0];
mu = [0.4473 0.4473 0.4473 -0.4473 -0.4473 -0.4473 0 0 0 0 0 0 1 0.4473 1 0.7071 1 0.7071 1 0.4473 1];
i = 1;
k = cell(21,1);
for i = 1:length(lambda)
c2 = lambda(i)^2;
s2 = mu(i)^2;
cs = lambda(i)*mu(i);
k{i} = [c2, cs, -c2, -cs; cs, s2, -cs, -s2;-c2, -cs, c2, cs;-cs, -s2, cs, s2];
end
Note: I calculated mu and lambda by hand because I can't figure out how to include cross braces. As in for instance if one node can be considered the far end node for several members rather than just a single member.
  1 comentario
James Murphy
James Murphy el 11 de Abr. de 2016
I've since refined my code to calculate lambda and mu
nodes = [0,0;1,.5;2,1;3,1.5;4,1;5,.5;6,0;5,0;4,0;3,0;2,0;1,0]; nodes = nodes'; linksN = [1 2 3 4 5 6 8 9 10 11 12 1 12 11 11 10 10 10 9 9 8]; linksF = [2 3 4 5 6 7 7 8 9 10 11 12 2 2 3 3 4 5 5 6 6]; connect = [linksN; linksF];
k = cell(21,1);
for i = 1:length(linksF)
v = connect(:,i);
C = nodes(:,v(2))-nodes(:,v(1));
lmem = sqrt(sum((nodes(:,v(2))-nodes(:,v(1))).^2));
T = C/lmem;
c2 = (T(1)^2)/lmem;
cs = (T(1)*T(2))/lmem;
s2 = (T(2)^2)/lmem;
k{i} = [c2 cs -c2 -cs;cs s2 -cs -s2;-c2 -cs c2 cs;-cs -s2 cs s2];
end
Im still unsure as to how to combine these matrices into the global structural matrix

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