弹性力学的复变量无网格局部Petrov-Galerkin法

摘要

复变量移动最小二乘法构造形函数,其优点是采用一维基函数建立二维问题的试函数,使得试函数中所含的待定系数减少,从而有效提高计算效率.文章基于复变量移动最小二乘法和局部Petrov-Galerkin弱形式,采用罚函数法施加边界条件,推导相应的离散方程,提出弹性力学的复变量无网格局部Petrov-Galerkin法.数值算例验证了该方法的有效性.%In this paper, the shape functions are obtained by the moving least-squares method with complex variable （MLSCV）. The advantages of MLSCV are that the approximation function of a two-dimensional （2D） problem is formed with one-dimensional （ID） basis function, and the number of the undetermined coefficients is reduced, so it effectively improves the computational efficiency. Based on the MLSCV and meshless local Petrov-Galerkin method, the essential boundary conditions are imposed by the penalty method and the corresponding discrete equations are derived, then a meshless local Petrov-Galerkin method with complex variables is presented for 2D elasticity problems. Some examples given in this paper demonstrate the effictiveness of the present method.