徑向基函數無網格伽遼金法求解彈性地基板的彎曲

An EFGM Method Based on Radial Basis Function Interpolation for Solving the Bending of Plates on the Elastic Foundation

趙敏(Min Zhao) ； 陳文(Wen Chen)

《中國土木水利工程學刊》 21卷4期 (2009/12) Pp. 445-451

https://doi.org/10.6652/JoCICHE.200912_21(4).0006

摘要

徑向基函數插值是一種新型的無網格插值方法，它具有形式簡單、空間維數無關、各向同性等優點。通過該插值方法構造的形函數具有δ函數的性質，易於滿足本質邊界條件，且形函數導數求解過程比通常的移動最小二乘法（MLS）簡單，精度也比較高。本文的徑向基函數無網格法就是通過徑向基函數插值構造形函數，結合伽遼金弱格式離散控制方程，並將之運用于求解彈性地基上板的彎曲問題。作者將這種方法與其他方法進行比較，給出了數值算例。數值算例結果表明該方法能夠取得不錯的效果，在工程上有一定的應用前景。

關鍵字

徑向基函數 ； 無網格伽遼金法 ； 彈性地基板

並列摘要

RBF interpolation is a recent meshless interpolation method. It has a very easy form, no correlation with the space dimensions, and is also isotropy. The shape function obtained by RBF has δ function property, so can easily satisfy the essential boundary condition, and their derivatives of the shape function are much easier to obtain compared to that of the moving least square shape function. RBF interpolation accuracy is also found very high. In the EFGM method based on RBF of this paper, the shape function is constructed using the RBF interpolation, and the system equation is discretized by Galerkin weak form. This method is used to solve the bending of plates on the elastic foundation. Some results of numerical examples were given to demonstrate that the proposed method is more effective by comparing with other methods. It is a promising method in engineering.

並列關鍵字

RBF ； EFGM ； plates on elastic foundation