Keywords: 
• 无网格法 /
• 复变量移动最小二乘法 /
• 无网格局部Petrov-Galerkin法 /
• 弹性力学问题

Abstract: 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.