Simulation of Hydroforming of Metal Sheets with an Efficient FE‐Formulation Based on an Analytical Meshfree Description of a Compressible Fluid

Abstract

Hydroforming is very interesting for the automotive industry, as it offers a great variety to efficiently manufacture thin walled structures. In order to simulate such static large deformation processes under hydraulic or pneumatic pressure, an analytical meshfree description of a compressible heavy or weightless fluid is presented. Thus a fully nonlinear formulation of the fluid-structure-interaction only based on the surface of the wetted membrane structure and the constitutive equations for the fluid can be derived. Considering physically realistic boundary conditions this formulation finally leads for all combinations of fluids and gas to a symmetric tangential stiffness matrix including several dyadic rank updates, which can be cast into a very efficient solution procedure by sequential applications of the Sherman-Morrison formula. Furthermore other algorithms such as mesh refinements and structural contact can be restricted to the models for the work piece and the matrix.