Engineering application of physics-informed neural networks for Saint-Venant torsion

TL;DR

This paper introduces physics-informed neural networks (PINNs) as a novel, efficient approach for solving Saint-Venant torsion equations, offering accurate solutions for complex geometries without extensive computational costs.

Contribution

The study develops multiple PINN-based solvers for Saint-Venant torsion problems, including arbitrary geometries, sharp transitions, and parametric cases, advancing computational methods in structural analysis.

Findings

PINN solvers accurately match reference solutions

The methods handle complex geometries and transitions effectively

PINNs reduce computational costs compared to traditional methods

Abstract

The Saint-Venant torsion theory is a classical theory for analyzing the torsional behavior of structural components, and it remains critically important in modern computational design workflows. Conventional numerical methods, including the finite element method (FEM), typically rely on mesh-based approaches to obtain approximate solutions. However, these methods often require complex and computationally intensive techniques to overcome the limitations of approximation, leading to significant increases in computational cost. The objective of this study is to develop a series of novel numerical methods based on physics-informed neural networks (PINN) for solving the Saint-Venant torsion equations. Utilizing the expressive power and the automatic differentiation capability of neural networks, the PINN can solve partial differential equations (PDEs) along with boundary conditions without the need for intricate computational techniques. First, a PINN solver was developed to compute the torsional constant for bars with arbitrary cross-sectional geometries. This was followed by the development of a solver capable of handling cases with sharp geometric transitions; variable-scaling PINN (VS-PINN). Finally, a parametric PINN was constructed to address the limitations of conventional single-instance PINN. The results from all three solvers showed good agreement with reference solutions, demonstrating their accuracy and robustness. Each solver can be selectively utilized depending on the specific requirements of torsional behavior analysis.