Welcome

Numerical Tours of Computational Mechanics with FEniCSx

Jeremy Bleyer

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Welcome#

What is it about ?#

These numerical tours will introduce you to a wide variety of topics in computational continuum and structural mechanics using the finite element software FEniCSx, http://fenicsproject.org.

Important

These tours comply with dolfinx v.0.8.0.

The book is organized in the following different parts:

Introduction#

This part contains a set of short demos to get introduced to FEniCSx via basic examples:

Introductory demos

Linear elasticity

Nonlinear elasticity

Multi-field plate problem

Tours#

This part is the main body of the book. These numerical tours are intended to complement the existing FEniCSx tutorials in the official documentation by focusing on specific applications within the field of computational solid and structural mechanics. The purpose of these tours is to offer users with a background in mechanics a starting point for utilizing FEniCSx, using examples familiar to them.

While many of the covered topics are standard and relatively easy to implement, others, such as structural elements (beams, plates, and shells) or nonlinear constitutive models, present more complexity. Other topics will also be more advanced and exploratory and will reflect currently investigated research topics, illustrating the versatility of FEniCSx for handling advanced models. The difficulty of each tour will be indicated by the star symbols: = easy, = difficult.

Numerical tours

Linear problems

Dynamics problems

Nonlinear problems

Eigenvalue problems

Homogenization

Beams

Plates

Shells

Tips & Tricks#

This part provides code snippets for various small tasks frequently encountered in computational mechanics with FEniCSx.

Citing#

If you find these demos useful for your research work, please consider citing them using the following Zenodo DOI:

@software{bleyer2024comet,
  author       = {Bleyer, Jeremy},
  title        = {{Numerical tours of Computational Mechanics with 
                   FEniCSx}},
  month        = jan,
  year         = 2024,
  publisher    = {Zenodo},
  version      = {v0.1},
  doi          = {10.5281/zenodo.10470942},
  url          = {https://doi.org/10.5281/zenodo.10470942}
}

All this work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License license .

About the author#

Jeremy Bleyer is a researcher in Solid and Structural Mechanics at Laboratoire Navier, a joint research (UMR 8205) of Ecole Nationale des Ponts et Chaussées, Université Gustave Eiffel and CNRS.

jeremy.bleyer@enpc.fr

jeremy-bleyer

0000-0001-8212-9921