FEM: Finite Element Method

not only for solid mechanics :)

FEM 1D example with Python created by Zoufiné Lauer-Baré

5 Node example for 1D PDE with constant right hand side and prescribed Dirichlet boundary conditions. Example could be a rod displacement or plane gap flow.

Meshing: Nodes and Elements

<img src=FIGURES/diskretisierung.PNG height=’200’>

Assemble system: Shape Functions

<img src=FIGURES/formfunktionen.PNG height=’200’>

Solution: Numerical FEM approximation exact at the nodes!

<img src=FIGURES/verschiebung.PNG height=’200’>

Usage

Click on the binder button for using the Python Code in Cloud

or install Python, Jupyter etc… and download or clone this repository.

FEM vs. FVM: Find the difference!

<img src=FIGURES/fem_vs_fvm.PNG height=’500’>

-> FEM exact on nodes and FVM exact at gradients between nodes

Visualization of analytical plate deformation in 3D!

<img src=FIGURES/plate_analytical_uz_scaled.PNG height=’500’>