Abstract: Since the radical basis functions satisfy the kronecker  property, the velocity boundary condition can be employed directly. The polynomial functions can be accurately reproduced through the coupling of the polynomial functions into the radical basis function approximation. The meshless Galerkin method is introduced into the metal forming simulations. A meshless Galerkin method based on the consistent radical basis function approximation is developed under the hypothesis of the rigid plastic theory. The volume strain rate projection method is used to deal with the incompressibility constraint. An arctangent frictional model is used to impose the frictional boundary condition under the local coordinate system. In this way, the meshless simulation of the metal forming processes with arbitrarily shaped die is realized. Several typical metal forming processes are analyzed by using the method developed. The effectiveness of the method is demonstrated through the comparisons of the simulation results with those obtained by using rigid plastic FEM method and experiments data.

Key words: Consistent radical basis function, Meshless method, Metal forming, Rigid plastic