A Forging Simulation by Using the Point Collocation Method with a Boundary Layer of Finite Element

Abstract

Point collocation methods have no mesh, no integration. While, the robustness of the point collocation methods 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 point collocation methods. 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 point collocation methods. The author has proposed a point collocation method with a boundary layer of finite element. In this method, 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 point collocation method with a boundary layer of finite element.