Analyses of plane-strain upsetting by the rigid–plastic domain-boundary element method

Abstract

In this paper, the rigid–plastic domain-boundary element method is formulated. This method does not need iterative calculations in any computing step. Therefore, the rigid–plastic domain-boundary element method possesses a merit in that there is no possibility of divergence of the iterative calculations and the computing costs are less than those of the rigid–plastic finite element methods which are a kind of iterative solution. On the other hand, the rigid–plastic domain-boundary element method is formulated with mixed variables which are nodal velocities and derivatives of nodal velocity. Therefore, nodal velocities and derivatives of nodal velocity can be calculated with the same precision, whilst the rigid–plastic finite element methods are formulated with single variables which are nodal velocities. Therefore, the rigid–plastic finite element methods cannot meet the need for compatibility of the nodal velocity’s derivative, and nodal velocities and derivatives of nodal velocity cannot be calculated with the same precision for these methods. In this paper a plane-strain metal forming (cold upsetting) problem is analyzed by the rigid–plastic domain-boundary element method. Contours of effective strain rate, effective strain and shear stress, etc. are obtained successfully.