弹性地基圆板受集中力的快速无单元解法  

A Fast Computational Algorithm for the Element-free Galerkin Method for a Circular Plate on Elastic Foundation Subjected to Concentrated Load

作　　者：肖勇刚 冯迪 Yonggang Xiao;Di Feng(School of Civil Engineering,Changsha University of Science and Technology,Changsha,410000)

机构地区：[1]长沙理工大学土木工程学院

出　　处：《固体力学学报》2018年第5期522-529,共8页Chinese Journal of Solid Mechanics

摘　　要：论文基于无单元伽辽金法（EFGM）分析了集中载荷作用下弹性地基圆板的弯曲问题.针对问题特征提出了新的节点分布方案和点积分形式,并在此基础上对权函数参数的选取和集中载荷的处理方式作了相关研究.通过算例对比分析,论文方法正确,求解精度满足要求,且与传统无单元法相比计算速度更快.When solving the problem of an arbitrary thin plate on elastic foundation using the elementfree Galerkin method（EFGM）,it＇s important to promote computational efficiency and set a uniform standard to evaluate the quality of node refinement when necessary.In order to solve this problem,this article proposes a fast computational algorithm for a circular plate on elastic foundation subjected to concentrated load.In this algorithm,a new kind of point integral form is put forward to simplify the pre-processing and to reduce computational burden.At the same time,parameter L is proposed to remove the low-contribution nodes in the domain of influence.The parametric study of weight function is carried out to determine the proper value ranges,and the method of adaptive radium is applied to evaluate the quality of node refinement.By comparing the results of the algorithm with the finite element results and the analytical solutions,it is found that the method proposed in this paper has achieved good accuracy;and the computational efficiency is also found to be greatly improved by comparing the calculation time of the fast algorithm with the traditional EFGM algorithm.This method is equally applicable when dealing with other problems with irregular boundaries or node refinement,and its fast calculation speed can offset the disadvantages caused by the large number of matrix inversions.

关 键 词：弹性地基 无单元法 节点分布方案 点积分形式 求解效率 

分 类 号：O241.82[理学—计算数学] O342[理学—数学]