一种改进的无单元方法  

An improved element free method

作　　者：张湘伟[1] 蔡永昌[1] 等 

机构地区：[1]广东工业大学机电学院，广东广州510090

出　　处：《计算力学学报》2002年第1期26-30,共5页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金资助项目 ( 5 9975 0 5 7)

摘　　要：使用 1阶或 1阶以上最小滑动二乘法 ( MLS)形函数的无网格伽辽金法 ( EFGM) ,它们的主要缺点是形函数构造复杂、计算费用十分昂贵。本文提出了一种改进的无单元方法 ( IEFM) ,它通过采用 Shepard形函数 ( 0阶 MLS形函数 )对结点的覆盖位移函数加权求和来简化整体近似位移函数的构造 ,且能够避免 EFGM里求解结点形函数时矩阵的求逆及相乘计算。文中的数值算例表明 ,这种改进的 IEFM法收敛快、精度高 。The major shortcoming of the Element free Galerkin method (EFGM), which are based on the use of one or more order moving least square (MLS) approximation, has been that the complexity of the shape functions and the high cost of computational time. An improved formulation of the IEFM is presented in this paper. The proposed IEFM can simplify the construction of approximations by multiplying the Shepard shape functions with the polynomial cover displacement functions and avoid the inverse and multiply of matrix when calculation the shape functions. Numerical examples indicate that high rates of convergence are achieved in the present IEFM, and the computational time are also reduced markedly comparing with the standard EFGM.

关 键 词：无网格 权函数 最小滑动二乘法 IEFM 无单元方法 Shepavd形函数 

分 类 号：O343[理学—固体力学] O241.82[理学—力学]