Simulation of sheet metal forming process using reproducing kernel particle method

Numerical simulation of sheet metal forming process using the meshless method called reproducing kernel particle method (RKPM) is studied in this paper. Owing to limitations of meshless approximation under parametric coordinate system, a constrained reproducing kernel (RK) approximation under Cartesian coordinate system is employed to describe the sheet metal deformation. Several technologies are used to solve the crucial problems involved in the numerical procedure. RKPM shape function is modified to impose essential boundary conditions; stabilized conforming nodal integration method is adopted to implement numerical integration of weak formulation; and an algorithm based on moment method is used to treat contact detection during sheet metal forming process. A program based on constrained RK approximation is developed to simulate two sheet metal forming examples: square-cup deep drawing and hemispherical part drawing. Numerical results are presented to demonstrate the effectiveness of the RKPM in numerical simulation of sheet metal forming. Copyright © 2009 John Wiley & Sons, Ltd.