A Solution to Rigid-Plastic Deformation Problems using the Hybrid Element Method

摘要

In this paper, a metal forming problem is analyzed by using the rigid-plastic hybrid element method. The rigid-plastic hybrid element method is a mixed approach of the rigid-plastic domain-BEM and the rigid-plastic FEM, in which the boundary conditions of friction and free surface can be imposed easily. In the rigid-plastic hybrid element method, the division of the domain for the rigid-plastic domain-BEM is the same as that of the element for the rigid-plastic FEM, and the equations of the two methods are simultaneously used, so that the compatibilities of both velocity and velocity's derivative between the adjoining boundary elements and finite elements can be met, the velocity and the velocity's derivative can be calculated with the same precision for the rigid-plastic hybrid element method. While, for the conventional rigid-plastic FEMs, the velocity and the derivative of the velocity cannot be calculated with the same precision. On the other hand, coefficient matrices of the domain-boundary integral equations in the domain-BEM are sparse ones, while the coefficient matrices of equations in ordinary BEMs are not sparse ones. A plane strain forging problem is analyzed by the rigid-plastic hybrid element method and the conventional rigid-plastic FEM. Comparisons between the calculated results of the two methods are made.