GLOBAL STIFFNESS MATRIX FOR ONE DIMENSIONAL BEAM ELEMENT WITH 2 DOF PER NODE 1

[miczad]

Hello Engineers,

This is MICZAD, a Structural Engineer. I love computer programming and at the moment, my interest is in programming the finite element method for one dimensional beam elements. I have got to the stage where I have keyed in the beam element stiffness matrices applicable to all the elements through an algorithm and I have to compile the global stiffness matrix. I am having problems in coming up with an algorithm involving loop programming to compile the global stiffness matrix. I would be extremely grateful if I could be provided the pseudocode for this. Thank you.

 

[XR250]

Are you talking about doing the Gaussian Elimination on the Matrix?

 

[Celt83]

Matrix Analysis of Structures by Kassimali, Link, provides full pseudocode for the global stiffness matrix assembly.

He uses a mapping array to store the order of the degrees of freedom which is then used to assign the element stiffness to the correct position so that the stiffness matrix is arranged with all of the unrestrained DOFs making it trivial index slicing to partition for the actual solution.