First FEM + Lagrange multipliers program in Grasshopper

Good, good…summer is about to finish and here I am, back in Ljubljana!

The last post was created two months ago and a shift in the researching techinques was announced: from C++ under Code:Blocks, Visual Studio or any other IDE (never found the one that fitted my needs), to Visual Basic under Grasshopper…

What a change! It really has boosted productivity…debugging is now as easy as dragging a panel and linking it to a component, results of the changes in the program can be viewed on real time and also with a bit of tweaking its consequences in a CAD model can be represented…wow..absolutely good…

In concrete means, during the summer I have been able to produce the whole Grasshopper definition shown below:

The initial part simply parses data from three files that I chose to be in .txt format, but anyone else could have chosen any other way (i.e. Excel or OpenOffice): Constraints.txt, Nodes.txt and ExternalForces.txt.
The heavy programming components are FEM, LM and LUPD, and I provide their contents here:

FEM Component:
LM Component:
LUPD Component:

Consistently with the hipothesis that numerical methods for structural can be classifed into Time integrators, Matter Integrators, and Constraint Integrators, I have so far distinguished between LM (Lagrange Multipliers) and FEM (Finite Element Method), remaining for a near future the implemementation of a Newmark-Beta component.
The code provided above simply serves to calculate statics of structures, as the time is yet to be integrated.

I have made the convenient comparisons with a SAP2000 model to verify the exactness of the implementation, with very satisfactory results.

Well…more to come in future editions!