A nonlinear rigid-plastic analysis for metal forming problem using the rigid-plastic point collocation method
A rigid-plastic point collocation method is applied to the analysis of plane strain forging, which is a nonlinear rigid-plastic problem of bulk metal forming. In general, the bulk metal forming problems are nonlinear and large deformation problems, used to be analyzed with the conventional rigid-plastic finite element methods. While the conventional rigid-plastic finite element methods have some shortcomings such as necessities of mesh generation, remeshing and numerical integration for these methods. The rigid-plastic point collocation method not only is a kind of truly meshless method, but also is a kind of no integration and no fundamental solution method. In this paper, the first, a linear elastic cantilever beam problem is analyzed by using the point collocation method, into which the concepts of the considered nodes and the unconsidered nodes are introduced. The numerical solution of the problem is compared with the exact solution of it, and quite high accuracy of the numerical solution has been achieved. The second, a plane strain metal forming problem has been analyzed by using the rigid-plastic point collocation method. Because the considered nodes and the unconsidered nodes are used, no renoding is needed. The solution of the rigid-plastic problem is compared with a conventional rigid-plastic finite element solution, and reasonable results have been obtained.
rigid-plasticity metal forming point collocation method meshless method