A METHOD OF LAPLACE-BELTRAMI EQUATIONS FOR THE INITIAL GUESS SOLUTION OF INTERMEDIATE CONFIGURATIONS IN FEM

The one-step finite element method (FEM) has been applied widely in metal forming simulation because it can obtain solutions quickly. However, the problem of poor accuracy for stress may rise in this approach. By means of adding several intermediate configurations, a multi-step FEM is proposed to overcome this disadvantage. The intermediate configurations can be acquired by an iterative algorithm from an initial guess, and a desired initial guess of the intermediate configuration is very important for the multi-step FEM. In light of the decoupled method, an intermediate configuration is composed of two independent deformations, that is, the bending deformation and stretching deformation. The bending deformation is considered as the initial guess of the intermediate configuration so that the stability and convergence of the solution in the multi-step FEM are improved. According to the large displacement with small strain theory, the displacement constraints of nodes are established. The initial guess of the intermediate configurations is obtained accurately by the model of Laplace-Betrami equations for the first time. This method is easy to implement and has good stability. Numerical simulations of some standard stamping parts validate the effectiveness of the algorithm.