Bending analysis of thin plates with variable stiffness resting on elastic foundation via a two-network strategy physics-informed neural network method

Abstract

A physics-informed neural network method based on a two-network strategy is introduced to address the bending problem of thin plates with variable stiffness resting on an elastic foundation. This problem is governed by a fourth-order partial differential equation (PDE), and the use of a one-network strategy to solve the PDE directly may lead to convergence issues due to singular points. Following the principles of Kirchhoff plate theory, the governing PDE is equivalently transformed into four second-order PDEs. A two-network strategy is employed for solution. We present numerical examples under various load conditions, plate geometries, foundation types, thicknesses, and material properties. The obtained results are validated against finite element method (FEM) solutions and literature. Discussions on alternative network strategies were conducted, and this study reveals that the presented two-network strategy have proven to be effective and robust. It also facilitates easier imposition of boundary conditions.