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Energy-based methods for solving forward and inverse linear elasticity problems in 2D structures
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DOI：10.1016/j.compstruc.2025.107899.png)
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Abstract
En 中文
Physics Informed Neural Networks (PINNs) and the Deep Energy Method (DEM) are two recently developed approaches for solving partial differential equations (PDEs) using deep neural networks. While PINNs aim to minimize the residual of the strong form of PDEs, DEM solvers work by minimizing the total potential energy. However, these methods have limitations in capturing the complex characteristics of displacement and stress fields. To overcome these limitations, we propose two new extensions of DEM: the deep energy method with traction-free boundary loss term (t-DEM) and the energy minimization method (EMM) with finite element method (FEM) basis. The t-DEM includes an additional loss term to enforce traction-free boundary conditions, and the EMM combines the FEM basis with the DEM to efficiently minimize the total potential energy of the system.
Keywords:
Physics Informed Neural Networks
Deep Energy Method
Partial Differential Equations
Traction-Free Boundary Conditions
Finite Element Method
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