QF Solver, Open-Source Finite Element Solver

QF Solver is an open-source finite element solver developed in Python for structural mechanics, numerical simulation, vibration analysis and rotating machinery.

The project aims to make finite element analysis more transparent, accessible and reproducible, providing researchers, engineers and students with tools to explore numerical methods and understand how simulation results are obtained.

Unlike purely black-box approaches, QF Solver emphasizes documented mathematical formulations, numerical verification, explicit solver diagnostics and traceable computational results.

Main Capabilities

QF Solver covers several areas of computational mechanics:

• Linear static analysis: Structural deformation, stresses and mechanical equilibrium using finite element formulations.
• Modal analysis: Natural frequencies, eigenmodes, mass and stiffness orthogonality, modal projection and reduced-order modelling.
• Harmonic vibration analysis: Frequency-domain response to harmonic excitation, including modal superposition and reduced-order harmonic analysis.
• Structural dynamics: Time-domain integration, transient vibration response, Newmark integration and reduced-order dynamic analysis.
• Nonlinear mechanics: Selected geometric and material nonlinear formulations, including elastoplasticity.
• Contact mechanics: Numerical contact formulations with documented limitations and validation status.
• Rotating machinery and rotordynamics: Experimental capabilities including gyroscopic effects, rotating modal analysis, Campbell diagrams and the investigation of speed-dependent vibration behaviour.

The software includes different finite element families and numerical methods, with capabilities, numerical assumptions and maturity levels documented individually.

Scientific Verification and Reproducibility

A central objective of QF Solver is to distinguish between a computation that successfully completes, a numerically verified result and a prediction validated against physical experiments.

The project incorporates:

• Automated unit, integration and regression testing.
• Numerical verification using analytical references and benchmark problems.
• Residual, orthogonality and numerical consistency diagnostics.
• Verification procedures for modal and dynamic analyses.
• Explicit reporting of solver limitations, experimental capabilities and inconclusive verification results.
• Reproducible simulation configurations, documented mathematical formulations and traceable numerical methods.

Not all implemented capabilities have the same validation maturity. Some formulations remain experimental or have restricted domains of demonstrated validity. These limitations are explicitly documented rather than hidden.

A successful numerical computation does not automatically imply that the underlying physical model has been experimentally validated.

Research and Development

QF Solver is independently developed as a long-term open-source scientific computing project.

Current research directions include:

• Numerical verification and experimentals validation of finite element models.
• Modal analysis, harmonic vibrations and structural dynamics.
• Reduced-order modelling and computational efficiency.
• Nonlinear finite element methods and contact mechanics.
• Rotordynamics and the vibration behaviour of rotating machinery.
• Reproducible scientific simulations and transparent numerical algorithms.

The project is intended to support research, education, numerical experimentation and the development of transparent engineering simulation workflows.

Availability

QF Solver is publicly available under the Apache-2.0 open-source license.

Installation

pip install qf-solver

Project resources

• Official website and documentation
• Source code on GitHub
• Python package on PyPI
• Software archive on Zenodo

The software is under active development. Users are encouraged to consult the documentation, numerical assumptions and version-specific verification reports before applying individual capabilities to engineering or research problems.