Finite Element Method of Analysis of the Hydrostatic Bulging of a Sheet Metal (Part 1)

Abstract

An incremental finite element method of the large elastic-plasic deformation of non-axisymmetric metal diaphragms which are edge-clamped and bulged by hydrostatic pressure has been formulated. The diaphragm is divided into a number of flat triangular elements and the behavior of a typical element is described in terms of the displacements of its nodes. The authors derive stiffness matrices, taking account of effects of shape change on the equilibrium equations, from a total differential of the equivalent nodal forces. In order to check the theory, numerical calculations were carried out for the bulging of a circular diaphragm under hydrostatic pressure. Theoretical results were in reasonable agreement with experiments for aluminium sheet and also with numerical solutions by means of a finite difference method.