Hybrid BEM-PINNs framework for thin-walled elasticity problems

This paper introduces a hybrid computational framework that integrates the boundary element method (BEM) with physics-informed neural networks (PINNs) to address inhomogeneous elasticity problems in thin-walled structures. In the proposed framework, PINNs are employed to approximate the particular solution corresponding to the inhomogeneous terms, and the original inhomogeneous problem is reformulated into an equivalent homogeneous problem, thereby retaining the boundary-only discretization advantage and avoiding the need for costly domain meshing. Furthermore, a nonlinear sinh transformation is incorporated to regularize nearly singular integrals by mapping them into a transformed coordinate system, thereby effectively smoothing the integrand. The synergy of BEM, PINNs, and the sinh transformation results in an efficient and highly accurate computational framework for analyzing elasticity in thin-walled structures.