FlightBEND 1.0.0

A Python package for flexible body dynamics simulation of airframes

🌀 fb.beamSection

A Saint-Venant Torsion Module for the FlightBEND Finite Element Framework

Overview

This repository contains the Saint-Venant Torsion Module, developed for the FlightBEND Finite Element Framework, a Python-based environment for numerical simulation in solid and structural mechanics, which is an ongoing development project.

The name FlightBEND is a tribute to Bernoulli, Euler, Saint-Venant, and Santos Dumont. The project was originally conceived as a computational platform for the numerical analysis of aerospace structures. Over time, it has evolved into a general-purpose finite element framework designed for research, education, and engineering applications.

This project has been carried out at the Numerical Analysis Laboratory (LANum) of the Federal University of Santa Maria - UFSM, involving graduate students from the Mechanical Engineering Program - PGMec and faculty members from the Departments of Mechanical Engineering and Mathematics.

Features

• Implements the classical Saint-Venant torsion theory.
• Computes shear stress distribution, torsional stiffness, and warping functions.
• Fully written in Python, using an object-oriented and modular design.
• Integrates with FlightBEND’s components for mesh generation, boundary conditions, and post-processing.
• Supports structured and unstructured meshes.
• Ready for extension to nonlinear torsion, coupled problems, and aeroelastic analyses.

Implementation Notes

The finite element formulation adopted in this module follows the standard weak form of Saint-Venant’s torsion problem.
The resulting linear system is assembled using FlightBEND’s internal FEM infrastructure, ensuring compatibility with other FlightBEND modules.

Requirements

• Python ≥ 3.10
• NumPy
• SciPy
• Matplotlib

Usage

See the multicell profile example.

Or

# Clone the repository
git clone https://github.com/tiagoburiol/fb.beamSection.git
cd fb.beamSection


# Example: open the multicell profile example using jupyter
jupyter-notebook notebooks/multicell_profile_example.ipynb

Other examples of usage can be found in fb.beamSection/examples. The figure below is from the wing_torsion_box.ipynb example.

Verification

The .inp files for the ABAQUS 3D exemples from the paper may be found at the verification_files folder in a compacted .7z format.

Mesh generation

For all examples we used the mesh generation from the GiD pre-processing software. If you wish to create .py files like the ones from our examples you'll also need to install the MATFem plugin and download our customized .bas file. The plugin allows for element material assigment and the .bas file exports the mesh as a python dictionary saved in the variable mesh_data containing the keys 'materials', 'coordinates' and 'elements'. Check our tutorial on how to use GiD for this application on the notebooks folder.

Citation

If you use this module in your research, please cite it as:

Pedro F. M. Pires, Pedro F. M., Buriol, Tiago M. e Santos, Tiago dos (2025). Saint-Venant Torsion Module for the FlightBEND Finite Element Framework. GitHub repository.
https://github.com/tiagoburiol/fb.beamSection

License

This project is distributed under the MIT License — see the LICENSE file for details.

Future Work

• Nonlinear torsion formulation
• Coupling with elasticity and thermal modules
• Validation with analytical and experimental results
• GUI integration for torsion analysis setup