无网格Galerkin法在金属弹塑性大变形问题中的应用  

Application of Element-free Galerkin Method to Metal Elasto-plastic Large Deformation Problems

作　　者：彭建新[1] 谢桂兰[1] 刘新 张建卿[3] 

机构地区：[1]湘潭大学机械工程学院,湘潭411105 [2]湖南工业大学机械工程学院,株洲412008 [3]怀化职业技术学院机械与汽车工程系,怀化418000

出　　处：《机械科学与技术》2009年第9期1248-1251,共4页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金项目(50875223);湖南省优秀青年项目(06B096);湖南省教育厅重点项目(08A079)资助

摘　　要：用无网格伽辽金法研究了金属塑性成形过程模拟中的弹塑性大变形问题。采用修正的拉格朗日法建立金属大变形弹塑性无网格伽辽金方程,求解过程根据Newton-Raphson增量进行迭代,在增量刚度方程的计算中,引进修正的弹塑性应力应变矩阵,从而实现了金属塑性大变形问题的无网格模拟。应用FORTRAN语言对圆柱体压缩和反向平面挤压两个大变形弹塑性过程进行了编程模拟,验证了该方法的可行性。此法对网格没有依赖性,模拟大变形问题时不需要网格重构,计算简单。Element-free galerkin （EFG） method is applied to the elasto-plastic large deformation problem in simulating the metal plastic deformation process. The up-dated Lagrangian method is used to build the equation of metal elasto-plastic large deformation problem using the EFG method, and the Newton-Raphson iteration method is used for calculating the increment stiffness equation, the modified stress-strain matrix is introduced to realize the simulation of metal elasto-plastic large deformation by the EFG method. FORTRAN is applied to simulating the elastoplastic process of cylinder compression and reverse plane extrusion problems, and the result shows that this method is feasible. The main advantage of this method is not dependent on mesh, the reconstruction of grid for simulation of large deformation problems is avoided and the calculation is dramatically simplified.

关 键 词：无网格GALERKIN法 金属塑性成形 弹塑性大变形 牛顿-拉夫森迭代法 

分 类 号：TG3[金属学及工艺—金属压力加工]