Stitching together matrices/ indexing matrices

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Kyle McLaughlin 2020년 10월 15일
댓글: Kyle McLaughlin 2020년 10월 19일
Hi there any help would be appreciated...
I am a mech engineer working with rotor dynamics and am being asked to do FEA on matlab. I have the following formula for the stiffness matrix for each element: K = ( E * A / Le) * [1 -1; -1 1]. What I would like to is compute the values of these matricies for 4 elements, the soln should be 4 K matricies... and my question regarding this is how do I index these 2x2 K matricies to be K1, K2, K3, K4? When I try to do this using a For Loop, I code the following:
%noel is number of elements which is 4
for i = 1: noel
K{i} = ( E * A / Le) * [1 -1; -1 1];
end
-doing this I get an error saying theres an issue with usijng { }, I have tried [] and () and had no luck either.
(I understand it says ask one question per post but I want to include my second one for a little more context to the overall problem)
The next step I need to do is to stitch the matricies together diagonally. What I mean by this is if you consider the 2x2 to be [A B;C D] for each K value, I need to produce one final matrix consisting of adding the first and last elements of each K matrix together. EX: if K1 = [A B; C D] and K2 = [E F; G H] I want to merge them such as K_system = [A B 0; C (d+E) F; 0 G H]. I need to do this for K1-4.
Sorry for the multiple question post, do not feel obliged to answer both, I can post them separately. The dual question is for sake of context.
Thanks,
Kyle
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Kyle McLaughlin 2020년 10월 15일
Right, this question is about assembling them into the global matrix, the K matrix is the same for all elements as described above. The problem statement is specifically regarding modeling a free-free beam in axial vibration and that was the equation my prof gave in the slides for "pure axial vibration". I am unaware of how to index these individual K values for the purpose of assembly, in addition to the assembly process of the first and last elements. The logic I imagined to follow was to 1) index K values 2) add the last and first elements of adjacent arrays 3) assemble global matrix 4) repeat for mass matrix 5) perform eig()....

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답변(1개)

For each k, you should know the connectivity array, for example if the first element is connected to the following degrees of freedom:
cArray=[1, 2, 5, 6]
Then
K(cArray, cArray) = K(cArray, cArray) + k;
Where k is the local stiffness matrix
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Kyle McLaughlin 2020년 10월 19일
Thank you, this worked to assemble the K matrix and added the values I needed. Much appreciated!!!

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