Dear Milan,
I understand that your intent is to construct the global stiffness matrix for a structure comprising of three interconnected elements, aiming to obtain the stiffness matrix for the entire structure by implementing a function.
I attempted to execute the provided code on my system, but encountered an error that states:
```
Error using vertcat
Dimensions of arrays being concatenated are not consistent.
Error in MLAnswers6_w3 (line 80)
connect = {[1 2], [2,3]; [3,4]};
```
However, to assemble the global stiffness matrix for the structure with three interconnected elements, the following steps can be followed:
1. Initialize the global stiffness matrix, denoted as “K_global”, as a matrix of zeros with dimensions “(ndof*nele) x (ndof*nele)”.
2. For each element, compute its global stiffness matrix, denoted as “K_element_global”, by utilizing the transformation matrix gamma and the element stiffness matrix “Ke_local”.
3. Transpose the gamma matrix and multiply it with “Ke_local”.
4. Multiply the resulting matrix with “gamma”.
5. Assemble the local stiffness matrices into the global stiffness matrix.
6. For each element, determine the corresponding degrees of freedom (DOFs) in the global stiffness matrix.
7. Add the local stiffness matrix to the appropriate locations within the global stiffness matrix.
Example code to achieve the described steps:
function K_global = assembleGlobalStiffnessMatrix(nele, ndof, Ke_local, gamma)
K_global = zeros(ndof*nele);
for element = 1:nele
% Calculate the global stiffness matrix for the current element
Ke_element_global = gamma' * Ke_local * gamma;
% Identify the corresponding DOFs in the global stiffness matrix
dofs = (element-1)*ndof + 1 : element*ndof;
% Assemble the local stiffness matrix into the global stiffness matrix
K_global(dofs, dofs) = K_global(dofs, dofs) + Ke_element_global;
end
end
% Call the function to assemble the global stiffness matrix
K_global = assembleGlobalStiffnessMatrix(nele, ndof, Ke_1_local, gamma_1);
% Add the stiffness matrices of the remaining elements
K_global = K_global + K_2_global + K_3_global;
Hope this helps!
