Using 3x3 matrix to create 21x21 matrix

I have built a 3x3 matrix using the code below

EA = 1; 
h = 1; 

F = @(xi)(xi-0.5).*(xi-0.5)  
k(1,1) =EA/h* 2*quad(F, -1, 1)

F = @(xi)(xi-0.5).*(-2*xi)
k(1,2) = EA/h* 2*quad(F, -1, 1)

F = @(xi)(xi-0.5).*(xi+0.5)
k(1,3) = EA/h* 2*quad(F, -1, 1)

F = @(xi)(-2*xi).*(-2*xi)
k(2,2) =EA/h* 2*quad(F, -1, 1)

F = @(xi)(xi+0.5).*(-2*xi)
k(2,3) = EA/h*2*quad(F, -1, 1)

F = @(xi)(xi+0.5).*(xi+0.5)
k(3,3) = EA/h*2*quad(F, -1, 1)

k(2,1) = k(1,2)
k(3,1) = k(1,3)
k(3,2) = k(2,3)

I want to use the 3x3 matrix above to create a 21x21 matrix following the pattern below

the overlapped elements should be added together, the numbers not in the 3x3 matrix are zero in the bigger matrix...k(4,1)=0 etc..

10 3x3 matrices should be used

I want to use a for loop unless there's another method

[Walter Roberson]

This was recently discussed in https://www.mathworks.com/matlabcentral/answers/489626-adding-matrices-to-make-bigger-matrix

It is a lot easier and clearer to loop building up the matrix, at least in the case where the different matrices on the diagonal are different.

Answer 1

[Erivelton Gualter]

It is not clear the overlap values. I assumed the following:

1. k33+k11
2. k33+k12
3. K33+k13
4. K33+k23
5. ..., Until the last is k33+k33

The other values is just copy from the given location. Then, you might use only for loop for this. Check in the following:

k19 = reshape(k(1:3,1:3),1,9); % Reshape for [k11 k12 k12 k21 k22 k23 k31 k32 k33]

j = 1;
for i=4:2:21
    k(i,i-1) = k(2,1);
    k(i-1,i) = k(2,1);
    
    k(i+1,i-1) = k(3,1);
    k(i-1,i+1) = k(3,1);
    
    k(i+1,i) = k(3,2);
    k(i,i+1) = k(3,2);
    
    k(i,i) = k(2,2);
    k(i+1,i+1) = k(3,3) + k19(j);  % Overlap goes here
    j = j + 1;
end

[Maria Galle]

the last value k(21,21) should equal k(3,3)

[Erivelton Gualter]

Can you rephrase what is the values for k(3,3), k(5,5), k(7,7), ...

[Maria Galle]

k(3,3)=k(3,3)+k(1,1)

EA = 1; 
h = 1; 

F = @(xi)(xi+0.5).*(xi+0.5)
k(3,3) = EA/h*2*quad(F, -1, 1)

F = @(xi)(xi-0.5).*(xi-0.5)  
k(1,1) =EA/h* 2*quad(F, -1, 1)

this equals k(5,5) and k(7,7)...