Construction of sliding constraint surfaces and initial guess shapes for intermediate steps in multi-step finite element inverse analysis

Multi-step inverse analysis has been developed for more accurate results while one-step analysis can affirm qualitative deformation behavior. An inverse finite element approach has more capability to design the optimum blank shape from the desired final shape with small amount of computation time and effort. In forming simulation with the inverse method, multi-step inverse analysis is difficult to apply because sliding constraint surfaces and initial guesses of intermediate steps described by complex die and punch set are hard to generate with present mapping schemes. In this paper, intermediate sliding constraint surfaces for multi-step finite element inverse analysis are automatically constructed from the die–punch set at each step with the given stroke. The initial guess of intermediate steps is constructed by a direct mesh mapping scheme that is suggested to generate an initial guess on the constructed sliding constraint surface. Construction of sliding constraint surfaces and initial guesses for intermediate steps is applied to a multi-step rectangular cup drawing process and an S-rail forming process. The numerical example of the multi-step rectangular cup drawing process demonstrates that the proposed mapping scheme is applicable to construct sliding constraint surfaces and initial guesses for analysis of a multi-step drawing process with large aspect ratio. The analysis result of the S-rail forming process is compared with that of a direct finite element analysis to evaluate the effectiveness of the mapping scheme proposed.