Stitching together matrices/ indexing matrices

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Kyle McLaughlin
Kyle McLaughlin on 15 Oct 2020
Commented: Kyle McLaughlin on 19 Oct 2020
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
  2 Comments
Kyle McLaughlin
Kyle McLaughlin on 15 Oct 2020
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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Answers (1)

Asad (Mehrzad)  Khoddam
Asad (Mehrzad) Khoddam on 15 Oct 2020
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
  6 Comments
Kyle McLaughlin
Kyle McLaughlin on 19 Oct 2020
Thank you, this worked to assemble the K matrix and added the values I needed. Much appreciated!!!

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