A new four-node shell element with enhanced bending performance for springback analysis with explicit FEM

摘要

Springback is a sort of shape distortion of sheet metal when removed from the die after forming,and remains as a major problem in stamping sheet metal products.Springback is comprised of forming stage and springback stage.Explicit FEM is generally preferred to implicit FEM for forming stage due to fastre computational speed and more reliable performance.Implicit FEM is preferred for springback stage since the workpiece undergoes undamped free vibration during springback,which requires excessively long computational time in explicit FEM.Since springback angle is determined by the residual stress,calculation of stress distribution in forming stage is critical to the accuracy of springback simulation.In a typical forming process,the workpiece undergoes bending and unbending over small die corners.Due to the rapidly changing boundary condition in this area,linear shell elements show poor results unless very fine mesh is used.Higher order elements generally have better bending performance,thus preferred under such a boundary condition,but higher order elements are computationally too expensive in explicit FEM.A new four-node shell element presented in this paper.The present element is designed to have enhanced bending performance by using quadratic incompatible shape functions,and to be applicable to both explicit FEM and implicit FEM.Due to the enhanced bending performance of the present element,it showed faster convergence rate than the linear shell element in the U-bending benchmark problem of NUMISHEET93.