无网格伽辽金法中两种基函数的性质

通过对无网格伽辽金法中基函数的研究,推导出了使用正交基函数后得到的形函数与形函数导数和使用多项式基函数所得到的形函数与形函数导数,得到了两者等价的结论。使用正交基函数使矩阵A成为对角矩阵,简化了对矩阵A求逆的过程,既节约了时间,还不影响计算精度,使得无网格伽辽金法具有更好的实用价值。在一维、二维中进行的验证结果,证明了本文结论,并进行了计算时间的比较。

Properties of two basis functions in element-free Galerkin method

The basis function of the Element Free Galerkin method was researched. It can be shown that the shape functions and their derivatives calculated with orthogonal basis function were equivalent to that calculated with polynomial basis function.The matrix was transformed to a diagonal matrix using orthogonal basis function, which made the computation of an inverse matrix much simpler and less computational time, and had no effect on the calculating accuracy. Two numerical examples were used to prove the validity of the proposed method and comparisons of CPU time were given.