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 0.12.0). 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
• linear static analyses, also of unsupported structures with inertia relief, balancing the loads with the inertia forces of the rigid-body accelerations (pyfe3d.solver.apply_inertia_relief)
• linear buckling, natural frequency and damped (complex) frequency analyses, with verified eigenvalues
• geometrically non-linear static analyses with the Newton-Raphson method and the arc-length methods of Riks and Crisfield, configuration-dependent loads and prescribed displacements
• large rotations with the element-independent co-rotational formulation of pyfe3d.corotational, for every element
• cross-sectional analysis of composite beams with pyfe3d.vabs, whose 6x6 sectional stiffness matrix, with all its couplings, is taken by the beam elements

Available finite elements

• 'Quad4' - 4-node plate with linear interpolation, equivalent to Nastran's CQUAD4, with the MITC4 transverse shear of Dvorkin and Bathe (1984) by default. The recommended quadrilateral plate element.

• 'Quad4R' - 4-node plate with linear interpolation and one integration point, with the physical stabilisation of Belytschko and Leviathan (1994) for the bending and the transverse shear, and the hourglass control of Brockman (1987) for the membrane.

• 'Tria3DSG' - 3-node plate with linear interpolation and a discrete shear gap transverse shear field, after Bletzinger, Bischoff and Ramm (2000), free of shear locking by construction and without a tuning parameter, with a constant-strain membrane. The better choice on coarse meshes of doubly curved shells, where it is less stiff than Tria3R.

• 'Tria3R' - 3-node shell with linear interpolation, the recommended triangular element. Since 0.12.0 it takes the discrete shear gap transverse shear field of Tria3DSG by default, with the membrane enriched by the drilling rotations of Allman (1984), which makes it much better than Tria3DSG in in-plane bending. Its former transverse shear, sampled at the centroid and stabilised by alpha_shear_locking, remains available with shear_model = 0, but it does not converge on thin plates and shells, see the element documentation.

• 'BeamC' - 2-node Timoshenko beam element with consistent shape functions and analytical integration, exact under nodal loads for any sectional stiffness matrix. 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 -m pip install --no-build-isolation .

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