An Efficient One-Step Inverse Approach Based on Nodal Tangent Plane

An efficient One-Step inverse approach (IA) based on nodal tangent plane (NTP) is proposed to predict the optimum blank shapes and sizes and reasonable estimation of forming severity (i.e., thickness, strain distributions) from desired final workpieces. According to the deformation theory of plasticity, Hill’s planar isotropic yield criteria and the principle of virtual work (PVW), the non-linear elasto-plastic finite element equilibrium equations are obtained, in which the simplified boundary force conditions are also implemented to simulate the effects of punch, die, blank-holder and draw-bead. For solving the non-linear problem, Newton-Raphson method is used. However, in traditional One-Step IA, the local element stiffness matrix is assembled in the global coordinate system where bad convergence is always a severe problem, especially when vertical or quasi-vertical walls happen. Fortunately, the NTP method provides a smart solution to enhance the convergence, where the ill-conditioned matrix is avoided by assembling the local element stiffness matrix to the tangent plane and to the normal of node. The developed algorithm is integrated into independently developed KMAS (KingMesh Analysis System) for sheet metal forming. To validate its efficiency and feasibility, it is applied to square cup deep drawing of Numisheet’93 and front fender forming of Numisheet’2002 by comparing with DynaForm based on incremental algorithm and traditional One-Step IA.