General-purpose finite element solver - pyfe3d

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About pyfe3d

The pyfe3d module is a general-purpose finite element solver for structural analysis and optimization based on Python and Cython. The main principles guiding the development of pyfe3d are: simplicity, efficiency and compatibility. The aimed level of compatibility allows one to run this solver in any platform, including the Google Colab environment.

Citing this library

Saullo G. P. Castro. (2026). General-purpose finite element solver based on Python and Cython (Version 0.10.0). Zenodo. DOI: https://doi.org/10.5281/zenodo.6573489.

Documentation

The documentation is available on: https://saullocastro.github.io/pyfe3d.

Important features of this library

• efficient and simple for linear and nonlinear analyses
• importable and cimportable code
• 6 degrees-of-freedom per node

Available finite elements

• 'Quad4' - 4-node plate with linear interpolation, equivalent to Nastran's CQUAD4. The recommended quadrilateral plate element.

• 'Quad4R' - 4-node plate with linear interpolation, equivalent to Abaqus' S4R. It has a not very robust hourglass control.

• 'Tria3DSG' - 3-node plate with linear interpolation and a discrete shear gap transverse shear field, after Bletzinger, Bischoff and Ramm (2000). The recommended triangular plate element: it is free of shear locking by construction and needs no tuning parameter.

• 'Tria3R' - 3-node plate with linear interpolation, equivalent to Abaqus' S3R or Nastran's CTRIA3. Its transverse shear is taken at the centroid and locks, and it relies on the alpha_shear_locking stabilisation to unlock. No single value of that parameter serves every problem class, so it has to be verified per problem, see the element documentation. Prefer Tria3DSG for new work.

• 'BeamC' - 2-node Timoshenko beam element with consistent shape functions and analytical integration. The recommended beam element.

• 'BeamLR' - 2-node Timoshenko beam element with linear interpolation and reduced integration.

• 'Spring' - 2-node spring element with 6 stiffenesses defined in the element coordinate system.

• 'Truss' - 2-node truss element with only axial and torsion stiffness. I recommend using the BeamLR instead, which is physically more consistent.

Development history

See CHANGELOG.md for the details of each version.

Installing pyfe3d

First, you should try to install from the distributed binaries by simply doing:

python -m pip install pyfe3d

If a distribution could not be found, you can try to install from the source code using:

python -m pip install .

Another alternative is the following:

python -m pip install -r requirements.txt
python setup.py install

If none of the above alternatives worked for you, this link shares some information on how to set up a C compiler on different operating systems:

https://cython2.readthedocs.io/en/latest/src/quickstart/install.html

License

Distrubuted under the 3-Clause BSD license (https://raw.github.com/saullocastro/pyfe3d/main/LICENSE):

Copyright (c) 2021-2026, Saullo G. P. Castro (S.G.P.Castro@tudelft.nl)
All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Contacts:

• Saullo G. P. Castro, S.G.P.Castro@tudelft.nl