A comparison between the rigid–plastic finite-boundary element method and the penalty rigid–plastic finite element method

The rigid–plastic finite-boundary element method (FBEM) is formulated with mixed-type. Therefore, this method can meet the need for compatibility of not only the nodal velocity but also the deritives of the nodal velocity. Then nodal velocities and derivatives of the nodal velocity can be calculated with the same precision for the rigid–plastic FBEM. Whilst the penalty rigid–plastic finite element method (FEM) is formulated with single-type like the other conventional rigid–plastic FEMs, the penalty rigid–plastic FEM cannot meet the need for compatibility of the derivitive of nodal velocity. On the other hand, the rigid–plastic FBEM is a kind of solution in open form, so that this method possesses another merit in that it does not need repetitive calculations, and there is not any possibility of divergence with the repetitive calculations. However, the penalty rigid–plastic FEM is a kind of solution in closed form like the other conventional rigid–plastic FEMs, so that there are some divergence possibilities with the repetitive calculations for the penalty rigid–plastic FEM. This paper makes analyses of an axisymmetric forging process by the two methods. It is found that the outline of the workpiece calculated by the rigid–plastic FBEM is smoother than that calculated by the penalty rigid–plastic FEM from the calculated results of this paper.