A new method to get initial guess configuration for multi-step sheet metal forming simulations

This study aims to develop a universal, robust, and linear method to obtain an initial guess configuration for the multi-step finite element method (FEM) solver of sheet metal forming. Using the decoupling theory, the deformation at each step in the multi-step FEM solver of the sheet metal forming is decoupled into two independent deformation modes: bending-dominated deformation and stretching-dominated deformation. The configuration of the bending-dominated deformation constrained by the sliding constraint surface is considered as the initial guess configuration for the current step in multi-step FEM solver. To get an accurate initial configuration at each step, the method of Laplace-Beltrami operator (LBO) on a simplicial surface is employed to obtain the initial guess configuration effectively. Several numerical examples are provided for validation and verification of the proposed method through its applications for complicated sheet metal workpieces of finite element simulations. The results show that the proposed method on the simplicial surface for the initial guess configuration within a few iterations to be significantly effective.