PyFEMP 0.0.3

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

The package is available to be installed via pip:

pip install --upgrade PyFEMP

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.

        self.NoElementMaterial = len(self.ElementMaterialNames)
        self.NoNodeDofs = len(self.ElementDofNames)

        # general program variables
        self.verbose = verbose
        self.verbose_system = True
        self.state = 0

        # general discretization variables
        self.time = 0.0                     # current time
        self.dt = 1.0                       # time increment gone frome last time
        self.step = 0                       # current step
        self.lambda_load = 0                # global load multiplier
        self.NoElements = 0                 # number of elements
        self.NoNodes = 0                    # number of nodes
        self.NoDofs = 0                     # number of degrees of freedom
        self.XI = 0                         # nodal coordinates
        self.ELEM = 0                       # element connectivity
        self.h_n = 0                        # previous history field
        self.h_t = 0                        # current history field

        # initialize fields for boundary conditions
        self.NBC = []                       # python list to collect natural boundary conditions before analysis
        self.NBC_Indexes = 0                # vector of indexes to the external load vector where a nbc is present
        self.NBC_Values = 0                 # vector of values to be placed in the external load vector for each nbc index
        self.EBC = []                       # python list to collect essential boundary conditions before analysis
        self.EBC_Indexes = 0                # vector of indexes of constrained degrees of freedom
        self.EBC_Values = 0                 # vector of values for each constrained degree of freedom
        self.NoEquations = 0                # number of all unconstrained dofs

        # element discretization parameter
        self.ElementMaterial = []           # list of material parameter
        self.h_n = 0                        # vector of element history field of t=t   (previous)
        self.h_t = 0                        # vector of element history field of t=t+1 (current)
        self.DI = 0                         # vector of degrees of freedom
        self.R_ext = 0                      # vector of external forces

properties