Fenics-arclength Documentation#

fenics-arclength is a Python implementation of the arclength solver built on top of FEniCS. The Arc Length Method, sometimes referred to as the Riks Method, is a method used to solve solid mechanics problems with geometric nonlinearity with complex equilibrium paths. The library aims to keep the usage as similar to FEniCS (version 2019.1.0) to allow for off-the-shelf implementation and integration with other FEniCS workflows.

Link to Github Repository

_images/fenics_project.png

Usage#

Dependencies#

This package solely depends on FEniCS 2019.1.0. It is not tested on other packages. Instructions to install FEniCS (legacy) can be found here. Our GitHub repository also contains more detailed installation instructions. For conda installations (available only on Mac and Linux), we also provide an environment.yml file in our GitHub repository.

Package Installation#

To use the arc-length solver, you can install it using pip or by downloading and adding the repository to your Python path.

Install directly using pip#

The recommended way to install the arc-length solver is to use pip. To do this, run the following command in your terminal:

pip install git+https://github.com/pprachas/fenics_arclength.git@master

This will install the latest version of the arc-length solver from the master branch of the repository.

Install by cloning the GitHub Repository#

If you prefer to download and install the arc-length solver and run the notebook examples/validation scripts, you can do so by following these steps:

  1. Clone the repository to your local machine:

    git clone https://github.com/pprachas/fenics_arclength.git

  2. Change directory to the fenics_arclength directory:

    cd fenics_arclength

  3. Install the arc-length solver:

    pip install .

This will install the arc-length solver from the source code in the fenics_arclength directory.

In the case of developer’s version, the last step can be replaced as pip install -e .

Once the arc-length solver is installed, you can import it into your Python scripts and use it to solve arc-length problems.

Google Colab#

Our notebooks in the examples directory can be run on Google Colab! Simply navigate to the notebook in the GitHub repository and change the domain from github.com to githubtocolab.com and run the notebook!

Theory#

The general concepts behind non-linear finite element analysis (FEA) are introduced here for both educational purposes and completeness. In addition, we briefly describe the implementation of both arclength solvers in our package. We also provide an example on modifying the arc-length predictor scheme for geometrically exact beams. The links below contain significant additional detail.

Arc-Length solvers in this package#

Notebook Examples#

To execute the Jupyter Notebooks in this repository, please download the repository and use the notebooks in the examples folder. Note that downloading the notebook directly from ReadTheDocs will not guarantee that the examples will run since the files will be missing other components (i.e. meshes, other scripts).