17_Direct Methods examples

 

I solve an example problem using the direct method explained in previous post. The problem as follows.

 

 

Each element stiffness matrix as follows

 

 

To expand each element stiffness matrix to the size of the global stiffness matrix, simply add rows and columns of zeros for displacements not related to that element.

Assembled in to the global stiffness matrix, as follows.

 

 

Organized in the form K=KU

 

 

Given that ${u_1} = 0$ and ${u_2} = 0$, the equation can be simplified as follows.

 

 

Therefore, with four unknowns ans four equations derived, it is possible to calculate each of the forces.