how would I add several matrices into one? (assembling global stiffness matrix for FEA)

I want to add several 4X4 matrices into one large one (see attached image for my general goal). This is to assemble a global stiffness matrix of several bar elements. I will have 205 matrices to add into 1 large one, but I figure it would be easiest to get an understanding by attempting to assemble the matrices in the image I atttached.

here is how I presume you'd start:

A = [1 1; 1 1];

B = [1 1; 1 1];

K = zeros(3,3); %empty matrix to add A & B to

How would I continue?

Answer 1

[Stephen23]

This is easy when you store all of the matrices in one cell array, then you just need a simple for loop:

>> C = {[1,1;1,1],[1,1;1,1]}; % <- all matrices
>> N = numel(C);
>> M = zeros(1+N,1+N);
>> for k = 1:N, M(k:k+1,k:k+1) = M(k:k+1,k:k+1)+C{k}; end
>> M
M =
   1   1   0
   1   2   1
   0   1   1

A more illustrative example:

>> C = {[1,1;1,1],[1,1;1,1],[2,3;4,5],[6,7;8,9]};
>> N = numel(C);
>> M = zeros(1+N,1+N);
>> for k = 1:N, M(k:k+1,k:k+1) = M(k:k+1,k:k+1)+C{k}; end
>> M
M =
    1    1    0    0    0
    1    2    1    0    0
    0    1    3    3    0
    0    0    4   11    7
    0    0    0    8    9

Here are some other answers on this topic:

https://www.mathworks.com/matlabcentral/answers/178214-combining-individual-matrices-diagonally-into-bigger-matrix-with-overlapping-elements-added

https://www.mathworks.com/matlabcentral/answers/423601-assemble-global-stiffness-matrix

https://www.mathworks.com/matlabcentral/answers/146736-help-creating-global-stiffness-matrix

Answer 2

[Peng Li]

To achieve your example, it's easy. You just need to think a bit about matrix multiplication. see below

>> A = [1 1; 1 1];
>> B = [1 1; 1 1];
>> 
>> helperA = [1 0; 0 1; 0 0];
>> helperB = [0 0; 1 0; 0 1];
>> helperA*A*helperA' + helperB*B*helperB'

ans =

     1     1     0
     1     2     1
     0     1     1

Not quite sure about your actual case. It might be easy to generalize this math to fit your goal. Hope this helps.