A simple statics FEM program

Well...this summer I have been busy with my thesis research (which I keep updated in www.stochasticandlagrangian.blogspot.com), and some results that might of the interest of Grasshopper community have been made.

I wanted to share here but I will briefly explain what this is about without entering into much detail.

FEM (Finite Element Method) is a quite popular engineering tool that for some reason results quite obscure to grasp but still everyone utilizes in common engineering practice.

As it plays some important part in my Phd thesis, I am interested in making it more accessible to anyone (included myself), and as surely by trying to explain I will gain much more hindsight..well...let's see...:)

What I have developed here with VB for Grasshopper is an elementary Finite Element component (for simple 3d beams) that provides a global rigidity matrix. This matrix is afterwards processed and "expanded" by means of a Lagrange Multipliers expansion that can later be introduced in a LUPD linear algebra solver (LU Decomposition with Pivoting...yes, I know the initials don't match, but ask the literature about it..)

The real advantage of explaining all this methodology by means of Grasshopper's visual interface is that the whole system can be seen at a glance. For research and didactic purposes this is unvaluable in my opinion.

Here is the attached file with the definition and some sample structure: GH-FEM.zip

This can perfectly be utilized as an initial toy program to understand and see the "mechanics" of the whole FEM.

I invite anyone interested into further developing functionalities like selecting the data from the drawing instead of hardtyping in a .txt file, applying the displacement results into a a different set of lines, etc.

Well, have fun!