无网格法中幂权函数影响半径的优化

借鉴四次样条权函数最优影响半径的选取方法，对工程中常用的幂权函数建立了最优影响半径的计算模型。针对二维情形下的一次基、二次基求解了该模型。通过解二维弹性力学问题实例，分析了不同影响半径下数值解与解析解的误差，表明不同的幂权函数影响半径对数值解的影响是不可忽视的，同时也确认了本文给出的影响半径是可靠的、有效的、综合最优的。

Optimal Radius of Power Weight Function in Meshless Methods

Using the theory and implementation in moving least squares approximation, the optimal technology of the optimal radius of the 4 th order spline function influence radius of weight function for power weight function in the linear basis and the quadratic basis cases are developed. After solving the elastic mechanics problems in 2- dimension and analyzing the error between the numerical solutions and exact solutions, and the influence of the different radius of weight function is important to the numerical solutions. In addition, It is concluded the radius of the weight function proposeds here is reliable, efficient and optimal.