Numerical Solutions of the von Karman Equations for a Thin Plate

TL;DR

This paper introduces a new iterative algorithm for solving the nonlinear von Karman equations in elasticity, effectively handling convergence issues and demonstrating its application to various boundary conditions in thin plate problems.

Contribution

The paper presents a novel successive reconditioning method that ensures convergence in solving nonlinear von Karman equations for thin plates.

Findings

The algorithm successfully solves complex plate deformation problems.

It avoids convergence issues at high nonlinear energy ratios.

Numerical results validate the method's effectiveness.

Abstract

In this paper, we present an algorithm for the solution of the von Karman equations of elasticity theory and related problems. Our method of successive reconditioning is able to avoid convergence problems at any ratio of the nonlinear streching and the pure bending energies. We illustrate the power of the method by numerical calculations of pinched or compressed plates subject to fixed boundaries.