周立明^*， 孟广伟， 李峰， 赵云亮

（  吉林大学机械科学与工程学院；  ）

摘要： 通过对无网格法中基函数正交性的研究，得出使用多项式基函数与正交基函数的无网格法的形函数相一致的结论，二者一阶、二阶导数也是一致的。正交基函数对无网格法解的精度不产生影响，使矩阵成为对角矩阵，矩阵求逆变得简单，缩短了计算时间，使得无网格法具有更好的实用价值，并通过算例证明了本文结论。
关键词： 无网格法;移动最小二乘;正交基函数;权函数

Zhou Liming^*， Meng Guangwei， Li Feng， ZHAO Yunliang

（  College of the Mechanical Science and Engineering, Jilin University；  ）

Abstract： Through a study on the orthogonality of the basis function in the element-free method, the shape functions, obtained by using the orthogonal basis function, have been proved to be identical to that of using the polynomial basis function, and their first and second order derivatives also have the same property. The orthogonality of the basis function does not affect the precision of the solution of the element-free method, however, it can change a matrix into a triangular matrix, which makes it easier to solve the inverse matrix, and it can reduce the computing time, and make the element-free method more practical. Computational examples were used to illustrate the conclusion.

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