Elastic-plastic bending of plates with a central hole in a three-dimensional setting

This article presents a mathematical model and algorithm for analyzing the stress–strain state (SSS) of elastic-plastic plates with a central circular hole in a three-dimensional setting. The developed algorithm can be applied to any boundary conditions, dependencies, and materials for which experimental stress–strain diagrams are available. The model is based on the deformation theory of plasticity and was implemented using a combination of the finite element method (FEM) and the method of I.A. Birger’s variable elasticity parameters. To obtain reliable results, the type finite elements (FE) and their number in a three-dimensional setting were investigated, along with the convergence of the solutions on a mesh of tetrahedral and hexahedral FE for a plate with and without a hole in the center. The hexahedral FE was found to be the most optimal. Computational examples for a rectangular plate clamped along the contour and subjected to a constant load were provided. The plate material considered is pure aluminum described by the stress–strain diagram developed by Y. Ohashi and S. Murakami.