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<p>This work presents a open-source finite element framework for analyzing Saint-Venant torsion in prismatic composite beams with arbitrary cross-sectional geometries. The model is grounded in the Principle of Virtual Work and employs the kinematic assumptions of Saint-Venant theory to derive a variational formulation of the torsion problem. This leads to two coupled variational equations: one governing the warping function within the cross-section and the other describing the torsional behavior along the beam’s length. Standard Lagrangian finite elements are used to solve for both the warping function and the angle of twist. Special emphasis is placed on the accurate modeling of the warping function using linear and quadratic triangular or quadrilateral elements, enabling the analysis of single- and multi-material beams with complex geometries. While the work does not introduce new theoretical or numerical advances in finite element technology, conceived as a tutorial contribution, it provides a well-structured and largely self-contained application of the classical finite element method to Saint-Venant torsion. This makes it particularly valuable for students, early-career researchers, and engineers seeking accessible and practical guidance on finite element modeling of torsional behavior. The framework computes key torsional parameters—including the warping function, torsional stiffness, shear stress distribution, and twist center location—and is verified through mesh convergence studies and comparison with high-fidelity 3D simulations using ABAQUS/Standard 2023. The results show excellent agreement in warping displacement and stress components, while achieving a reduction in computational cost of more than 99%. To demonstrate its versatility, the tool is applied to a range of beam cross-section configurations, including Single-material and heterogeneous solid sections, open and closed thin-walled sections, and a wing torsion box. The results highlight its potential for early-stage structural assessment in engineering applications. The corresponding code, documentation, and benchmark examples are available in an open-access repository, as described in the text.</p>

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An open-source finite element framework for Saint-Venant torsion of heterogeneous beams with arbitrary cross-sections

  • 期刊论文

  • 发表日期：

    2025年11月16日

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  • Pedro F. M. Pires,
  • Tiago M. Buriol,
  • Tiago dos Santos

摘要

This work presents a open-source finite element framework for analyzing Saint-Venant torsion in prismatic composite beams with arbitrary cross-sectional geometries. The model is grounded in the Principle of Virtual Work and employs the kinematic assumptions of Saint-Venant theory to derive a variational formulation of the torsion problem. This leads to two coupled variational equations: one governing the warping function within the cross-section and the other describing the torsional behavior along the beam’s length. Standard Lagrangian finite elements are used to solve for both the warping function and the angle of twist. Special emphasis is placed on the accurate modeling of the warping function using linear and quadratic triangular or quadrilateral elements, enabling the analysis of single- and multi-material beams with complex geometries. While the work does not introduce new theoretical or numerical advances in finite element technology, conceived as a tutorial contribution, it provides a well-structured and largely self-contained application of the classical finite element method to Saint-Venant torsion. This makes it particularly valuable for students, early-career researchers, and engineers seeking accessible and practical guidance on finite element modeling of torsional behavior. The framework computes key torsional parameters—including the warping function, torsional stiffness, shear stress distribution, and twist center location—and is verified through mesh convergence studies and comparison with high-fidelity 3D simulations using ABAQUS/Standard 2023. The results show excellent agreement in warping displacement and stress components, while achieving a reduction in computational cost of more than 99%. To demonstrate its versatility, the tool is applied to a range of beam cross-section configurations, including Single-material and heterogeneous solid sections, open and closed thin-walled sections, and a wing torsion box. The results highlight its potential for early-stage structural assessment in engineering applications. The corresponding code, documentation, and benchmark examples are available in an open-access repository, as described in the text.