https://github.com/zolabar/fem

FEM 1D example with Python
https://github.com/zolabar/fem

displacement fem fvm jupyter-notebook numerics numpy python strain

Last synced: about 1 month ago
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FEM 1D example with Python

• Host: GitHub
• URL: https://github.com/zolabar/fem
• Owner: zolabar
• License: mit
• Created: 2021-09-30T20:20:04.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2022-11-16T12:05:11.000Z (over 2 years ago)
• Last Synced: 2023-03-08T22:06:11.454Z (about 2 years ago)
• Topics: displacement, fem, fvm, jupyter-notebook, numerics, numpy, python, strain
• Language: Jupyter Notebook
• Homepage: https://zolabar.github.io/FEM/
• Size: 3.22 MB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE
  • Citation: citation.cff

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README

        
[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/zolabar/FEM/HEAD)

# FEM: Finite Element Method 

## not only for solid mechanics :)

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

[![GitHub](https://img.shields.io/badge/github-%23121011.svg?style=for-the-badge&logo=github&logoColor=white)](https://github.com/zolabar)

[![LinkedIn](https://img.shields.io/badge/linkedin-%230077B5.svg?style=for-the-badge&logo=linkedin&logoColor=white)](https://www.linkedin.com/in/zoufine-lauer-bare-14677a77)

[![Google Scholar](https://img.shields.io/badge/google%20scholar-4285F4?style=for-the-badge&logo=google%20assistant&logoColor=white)](https://scholar.google.com/citations?user=Gsm7ZzUAAAAJ&hl=en&oi=sra)

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



![meshing](/FEM/assets/diskretisierung.PNG)

### Assemble system: Shape Functions



![shape functions](/FEM/assets/formfunktionen.PNG)

### Solution: Numerical FEM approximation exact at the nodes!



![solution](/FEM/assets/verschiebung.PNG)

### Usage

Click on the binder button [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/zolabar/FEM/HEAD) for using the Python Code in Cloud

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

### FEM vs. FVM: Find the difference!



![fem vs fvm](/FEM/assets/fem_vs_fvm.PNG)

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

### Visualization of analytical plate deformation in 3D!



![fem vs fvm](/FEM/assets/plate_analytical_uz_scaled.PNG)