Hourglass Control in Rigid-Plastic Finite Element Analysis

강소성 유한요소해석에서 Hourglass Control

  • Gang, Jeong-Jin (Department of Mechanical Design & Production Engineering Graduate School of Seoul National University) ;
  • O, Su-Ik (Dept.of Mechanical Engineering, Seoul National University)
  • 강정진 (서울대학교 대학원 기계설계학과) ;
  • 오수익 (서울대학교 기계설계학과)
  • Published : 1996.04.01


The finite element method, based on rigid-plastic formulation, is widely used to simulate metal forming processes. In order to improve the computational efficiency of the rigid-plastic FEM, one-point integration is used to evaluate the stiffness matrix with four-node rectangular elements and eight-node brick elements. In order to control the hourglass modes, hourglass strain rate components were introduced and included in the effective strain rate definition, Numerical tests have shown that the proposed one-point integration scheme reduces the stiffness matrix evaluation time without deteriorating the convergence behavior of Newton-Raphson method. Simulations of a ring compression, a plane-strain closed-die forging and the three-dimensional spike forging processes were carried out by using the proposed integration method. The simulation results are compared to those obtained by applying the conventional integraiton method in terms of the solution accuracy and computational efficiency.


Rigid-Plastic FEM;One-Point Integration;Hourglass Modes