Finite element correction matrices in metal forming analysis (with application to hydrostatic bulging of a circular sheet)

This paper presents a condensed review of finite element applications in metal forming processes. Difficulties in large strain-elastoplastic analysis of these processes are identified. Correction techniques for potential sources of errors, such as lack of nodal equilibrium, violation of yield conditions, overstiff performance of finite elements, and improper formulation of configuration-dependent problems, are discussed. A main feature of the paper is the account of mixed boundary data in the updated Lagrangian formulation variational procedure. The code developed is applied to the process of the hydrostatic bulging of a circular sheet clamped at its periphery. This is based on a convenient explicit form of the hydrostatic-pressure load correction stiffness matrix for isoparametric and allied types of elements.