关键词: 材料形函数, 无网格法, 稀疏“矩阵” 本征边界条件, 有限元法

Abstract: Meshfree method depends on only nodes with high order continuous and non-interpolant shape function. According to the numerical simulation of sheet metal forming, meshfree methods have more advantages over finite element methods. However, the contact between tools and sheet metal in meshfree numerical simulation of sheet metal forming is a very important problem. A sparse “matrix” is constructed to fasten search. In order to impose essential boundary conditions exactly, shape function is reconstructed to be interpolant and shape function is constructed under frame of material coordinates. Expression of contact force applying slave nodes is derived from computational model of contact force. Contact treatment is realized exactly by the presented methods. Numerical results show that the methods for treating contact are effective.

Key words: Essential boundary condition, Finite element method, Material shape function, Meshfree methods, Spare “matrix”