Numerical Simulation of Forging Process Using the Hybrid PCM/FEM

In this paper, for analyses of metal forming problems, a point collocation method (PCM) with a boundary layer of finite element is developed. PCMs have some advantages such as no mesh, no integration. While, the robustness of the PCMs is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important when using the PCMs. For boundary points, however, the positivity conditions cannot be satisfied, so that it is possible to get large numerical errors from the boundary points when using the PCMs. Specifically, the errors could arise in point collocation analyses with complicated boundary conditions. In this paper, by introducing a boundary layer of finite element in boundary domain of workpiece, unsatisfactory issue of the positivity conditions of boundary points can be avoided, and the complicated boundary conditions can be easily imposed with the boundary layer of finite element. A forging process is analyzed by using the hybrid PCM/FEM. Key-Words: Meshless method, Point collocation method, Positivity conditions, FEM, Hybrid method, Forging