无网格法中多项式基函数的正交性研究及应用
首发时间:2010-01-05
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。
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Research and Application on Orthogonality of the Polynomial Basis Function in Element-free Method
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.
Keywords: Element-free method Moving Least-Square Orthogonal basis function Weight function
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