弹性力学的复变量无网格方法

在移动最小二乘法的基础上，提出了复变量移动最小二乘法.复变量移动最小二乘法的优点是采用一维基函数建立二维问题的逼近函数，所形成的无网格方法计算量小.然后，将复变量移动最小二乘法应用于弹性力学的无网格方法，提出了复变量无网格方法，推导了复变量无网格方法的公式.与传统的无网格方法相比，复变量无网格方法具有计算量小、精度高的优点.最后给出了数值算例. 关键词： 移动最小二乘法 复变量移动最小二乘法 无网格方法 弹性力学 复变量无网格方法

A meshless method with complex variables for elasticity

The moving least-square approximation with complex variables (MLSCV) is developed on the basis of moving least-square approximation. The advantages of MLSCV are that the approximation function of a 2-D problem is formed with 1-D basis function, and the meshless method obtained has greater computational efficiency. A meshless method with complex variables for 2-D elasticity is then presented using MLSCV, and the formulae of the meshless method with complex variables are obtained. Compared with the conventional meshless method, the meshless method with complex variables introduced in this paper has greater precision and computational efficiency. Some examples are given.