Analysis of three-dimensional deep drawing by the energy method

Abstract

A systematic approach of the energy method is proposed for analysis of three-dimensional sheet metal forming of noncircular cups with complicated shape. In the proposed method, the whole deforming region is divided into several zones by considering the geometric characteristics and contact boundary condition. The geometric shape is expressed by sweeping the section curves defined on the boundary of each zone. Velocity fields are expressed in a similar manner by sweeping the boundary velocity functions. The solution is found through optimization of the total energy dissipation with respect to some parameters assumed in the kinematically admissible velocity field defined over each zone. In order to-check the effectiveness of the present method, three-dimensional deep drawing by the elliptic punch and the clover-type punch are analysed and compared with the corresponding experiments. In analysing the deep drawing process by the elliptic and clover-type punches, the total deforming region has been divided into five zones. The computed results are shown to be in good agreement with the experiment in punch load, deformed edge contour and distribution of thickness strain.