PyFEMP 0.0.2

A python FEM solver for educational purposes.

PyFEMP Python Finite Element Program

PyFEMP (Python Finite Element Program) is a simple Finite Element program written in python. Its focus is on simplicity not on performance.

It should be easy to use, to understand and as portable as possible to be used in teaching. We aim to void overhead w.r.t. environmental setup (compiler, libraries, e.t.c. ...) or dealing with complex structures, to focus on the essense of the FEM.

Therefore PyFEMP is written completely in python with the only required modules are numpy and matplotlib. Furthermore the program provides lsess than 30 commands, including postprocessing and meshing. Python code is really easy to read and write. This holds especially when performance is not critical. In PyFEMP we emprace python loops (easy to read/write but weak in performance), leading to acceptable runtime (<20s) up to ~2000 Elements.

What it can do:

• static/dynamic FE analysis
• 1D, 2D analysis (3D is techniqually possible but visualisation is not supported via matplotlib)
• implementing user specific elements
• arbitrary number of nodal degrees of freedom e.g. for coupled FEM
• nonlinear analysisi via implemented Newton-Raphson
• visualsiation of element specific postprocessing fields
• access to all variables e.g. element matrices during the simulation or the linear equation system
• generation of simple regular meshes in 1D/2D using triangl- and quadrilateral elements (external meshes can be used)

Install

Requirements

Using PyFEMP requires a python (3.x) installation with numpy and matplotlib.

We recomend installing Anaconda. Its a free python distribution that comes with poth numpy and matplotlib installed by default and is available for all major computing platforms. This should result in the works out of the box experience:

https://www.anaconda.com/products/individual

Installation

Once downloaded this project you just need to execute the setup script and should be ready to run:

python setup.py

Remark: For updating PyFEMP just download the new project and run the setup script again. It always overwrites!

More information will follow in the documentation.

Usage

Once succesfully installed you can start by surveying and running the examples, e.g.

python cook.py

Function Reference

• functions of PyFEMP:

  • PyFEMP.FEM_Simulation(ELEMENT) Used to start a FEM Simlation by returnig the simulation object. The input is an element, providing the nessercary functions.

  • PyFEMP.msh_line(X0, X1, N, type='U1') -> XI, ELEM Used to generate a regular mesh in 1D. Returns a list of nodal coordinatex and a matrix of element connectivity.

  • PyFEMP.msh_rec(X0, X1, N, type='Q1') -> XI, ELEM Used to generate a regular mesh in 2D for a rectangle, specified by the lower left corner X0 and upper right X1. Returns a list of nodal coordinatex and a matrix of element connectivity.

  • PyFEMP.msh_conv_quad(X1, X2, X3, X4, N, type='Q1') -> XI, ELEM Same as msh_rec but for an arbitrary convex quadrilateral, specified by vertices X1, X2, X3, X4.

The PyFEMP.FEM_Simulation object

The PyFEMP.FEM_Simulation object represents your FEM Simulation. It provides the methods to e.g. introduce the mesh and boundary conditions i.e the discretized boundary value problem, but also to perform solution procedures on it.

properties