An energy method for analysing deep drawing process by simulated annealing optimization algorithm

A systematic approach of the energy method has been used for analyzing of deep drawing process. The so called simulated annealing algorithm has been used for energy optimization. In this method, the whole deforming region has been divided into five zones. Then the geometry has been expressed by sweeping the section curves defined on the boundary of each zone. The velocity fields have been expressed in a similar manner by sweeping the boundary velocity functions. In every step, the solution has been found through optimization of the total energy dissipation with respect to some parameters assumed in kinematically admissible velocity field defined over each zone. The energy dissipated in the bending zone has been estimated and added to the total energy due to strain and friction energies. In order to check the effectiveness of the present method, deep drawing of circular and square punches have been analyzed and variation of punch load versus punch depth, flange contour and distribution of thickness strain have been obtained and compared with published experimental data. The results show good agreement with the experiment.