新型带虚点的径向基函数微分求积法及其在薄板弯曲中的应用

本文提出了新型带虚点的径向基函数微分求积法，并将其应用于模拟薄板弯曲问题。带虚点的径向基函数微分求积法是一种基于传统径向基函数微分求积法的新型无网格方法，传统方法只将中心点放在计算域内，而该方法扩展了中心点的区域，使其既位于计算域内又位于计算域外，在不增加计算量和存储量的基础上，显著提高计算精度。本文首次尝试将此方法应用于求解薄板弯曲问题，并与解析解和传统方法进行对比，验证了此方法的优越性

A new radial basis function differential quadrature method with fictitious points and its application in thin plate bending

In this paper, the radial basis function differential quadrature method with fictitious points (FRBF-DQ) is proposed and applied to simulate thin plate bending problems. The FRBF-DQ method is a new meshless method based on the traditional radial basis function differential quadrature method. While the traditional radial basis function differential quadrature method (RBF-DQ) method places the centers exclusively inside the solution domain, the proposed method expands the region for the centers allowing them to place both inside and outside the computational domain. The FRBF-DQ method applies radial basis functions and weight coefficients to solve differential equations approximately. Meanwhile, the solution accuracy has been significantly improved without the increasing of calculation cost and storage. The thin plate bending problems are controlled by the fourth order partial differential equation based on the Kirchhoff and the Winkler hypothesis. The examples reveal that the FRBF-DQ method works even for arbitrary distributed nodes with better computational convergence and higher computational accuracy than the traditional RBF-DQ method. The proposed method can be considered as a good alternative method for engineering problems.