Finite Element Analysis for Fixed Ended Beam with a Point Load example: I am getting this error: Error using * Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the se

Fixed Ended Beam with Point Load Example

%Data
E = 2.1E5; % N/mm^2
L = 6000; % length in mm
I = 78E6; % mm^4

Elemental Stiffness Matrix

Const = (E*I)/(L^3);
%Since we only have one element this is the overall
%stiffness matrix
KE1 = [12 6*L -12 6*L;
       6*L 4*L^2 -6*L 2*L^2;
       -12 -6*L 12 -6*L;
       6*L 2*L^2 -6*L 4*L^2];
KE1 = Const*KE1;
Solution
K = KE1;
KT = K;
KT(:,1) = 0;
KT(1,:) = 0;
KT(1,1) = 1;

KT(:,2) = 0;
KT(2,:) = 0;
KT(2,2) = 1;

KT(:,4) = 0;
KT(4,:) = 0;
KT(4,4) = 1;

KT(:,5) = 0;
KT(5,:) = 0;
KT(5,5) = 1;

KT(:,6) = 0;
KT(6,:) = 0;
KT(6,6) = 1;

KT
FT = [0;0; -50;0; 0;0];

d = inv(KT)*FT

F = K*d

Answer 1

[Divyajyoti Nayak]

Hi @Hamza Aboumaray,

The error in your code is caused because the dimensions of the matrices ‘K’ (4X4) and ‘d’ (6X1) are not suitable for matrix multiplication. The dimensions of these vectors are visible in the Workspace.

It is mentioned that only one element is considered so there should be 2 nodes with 2 degrees of freedom in the finite element analysis. But the stiffness matrix used ‘KT’ and the nodal displacements ‘d’ have 6 rows which imply 3 nodes, so that is likely the cause of the miscalculation.