Why am I getting the error: "Error using + Matrix dimensions must agree."?

Hello,

I am trying to create a 21x21 global stiffness matrix that look like this:

K = [1 -1  0  0  0...;
    -1  2 -1  0  0...;
     0 -1  2 -1  0...;
     0  0 -1  2 -1...
     ...]

This is my code so far:

 % Define number of nodes
 N = 21;

 k1 = [1 -1; -1 1];

 % Define global stiffness matrix with zeros
 K = zeros(N);

 % Populate diagonal of matrix, making sparse matrix
 for i = 1:(N-1)
    for j = 2:N
        K(i:j,i:j) = K(i:j,i:j) + k1
    end
 end

However, I am getting error:

 Error using  + 
 Matrix dimensions must agree.

 Error in Untitled2 (line 16)
        K(i:j,i:j) = K(i:j,i:j) + k1

The dimensions of the matrices that are being added are both 2x2 in every iteration so I do not understand why the loop stops after the first iteration. Any suggestions?

I have written the code for each iteration manually just to double check and the I end up with the correct solution. However, I want to know why the for loop solution is not working. Here is the code for the manual iterations:

 K(1:2,1:2) = K(1:2,1:2) +k1
 K(2:3,2:3) = K(2:3,2:3) +k1
 K(3:4,3:4) = K(3:4,3:4) +k1
 K(4:5,4:5) = K(4:5,4:5) +k1
 K(5:6,5:6) = K(5:6,5:6) +k1
 ....

I appreciate the help in advance.

[Stephen23]

The MATLAB approach using TOEPLITZ:

N = 21;
M = toeplitz([2,-1,zeros(1,N-2)]);
M([1,end]) = 1

M = 21×21

1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0

[Steven Lord]

Another approach is to use the technique shown in the "Create Tridiagonal Matrix" example on the spdiags documentation page and adjust the first and last elements.

Answer 1

[Abin Abraham]

I realized that I misunderstood the the nested for loop for a little while. I ended up figuring it out with a single for loop. For those that are curious and need help with a similar problem, this is my code. I'm sure this is a very inefficient way to solve the problem but its simple enough for me to understand as I am a beginner.

 % Define number of nodes
 N = 21;

 % Define global stiffness matrix with zeros
 K = zeros(N);

 % Define local stiffness matrix
 k1 = [1 -1; -1 1];

 % Populate diagonal of global stiffness matrix
 for i = 1:N-1
    K(i:i+1,i:i+1) = K(i:i+1,i:i+1) + k1;
 end

Answer 2

[KSSV]

This line:

K(i:j,i:j) = K(i:j,i:j) + k1 ;

when i = 1 and j = 3 ;K becomes 3X3..i.e. K(1:3,1:3) and to this 3x3 matrix you are adding 2x2 matrix. How you expect them to get added? So the error matrix dimensions do not agree. So your code runs for i = 1, and j = 1,2 and after this throws error.

[KSSV]

I guess this is FEM related. To make global stiffness matrix, you shall have nodal connectivity matrix. You must extract the matrix based on nodal connectivity.