A consistent Eulerian formulation of large deformation problems in statics and dynamics

Abstract

A concise survey of formulation methods of geometric and material non-linearity problems is given. The survey is concerned mainly with the differences between updated Lagrangian and Eulerian formulations, and with the specific nature and basic characteristics of each. The underlying mechanics and the spatial discretisation for an Eulerian formulation are discussed. An Eulerian formulation with the final equilibrium equations suitable for static and/or dynamic structural analysis is presented. Explicit forms for stiffness matrices and load vectors are given. Differences between the present formulation, the existing Lagrangian formulation, the updated Langrangian formulation and other attempted Eulerian formulations are discussed within the framework of a consistent classification of formulation methods.