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  

A New Radial Basis Function Differential Quadrature Method with Fictitious Points and Its Application in Thin Plate Bending

作　　者：赵宇翔 林继[1] Yuxiang Zhao;Ji Lin(College of Mechanics and Materials,Hohai University,Nanjing,211100)

机构地区：[1]河海大学力学与材料学院,南京211100

出　　处：《固体力学学报》2021年第6期623-632,共10页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(12072103);中央高校基本科研业务费(B200202126);江苏省自然科学基金项目(BK20190073)资助。

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

关 键 词：微分求积法 径向基函数 无网格 薄板弯曲 虚点 

分 类 号：O34[理学—固体力学] O241[理学—力学]