Shell element formulation of multi-step inverse analysis for axisymmetric deep drawing process

Inverse analysis today is generally performed with membrane models in analysing sheet metal forming processes. Given the nal desired con guration, it usually estimates the deformation in a one-step calculation. However, for some practical problems where the bending e ect is signi cant and the strain history departs from a linear path, this calculation becomes not good enough to provide the optimal design values. In this paper, an axisymmetric shell element for the multi-step inverse analysis is developed for more accurate prediction of design variables such as the initial blank shape, strain distributions, and intermediate shapes, etc. The algorithm has been applied to deep drawing processes for both thin and relatively thick sheet metal. Numerical examples demonstrate that the proposed combination of shell element and multi-step inverse analysis can provide more precise results than the previous algorithms used in inverse analysis