基于四叉树算法的网格划分及其在比例边界有限元法中的应用  

Mesh Generation Based on Quadtree Algorithm and its Application in Scaled Boundary Finite Element Method

作　　者：刘翔宇 LIU Xiangyu(Beijing General Municipal Engineering Design&Research Institute Co.,Ltd,Beijing 100082)

机构地区：[1]北京市市政工程设计研究总院有限公司,北京100082

出　　处：《现代工程科技》2022年第9期5-8,32,共5页Modern Engineering Technology

摘　　要：基于四叉树算法的网格剖分遵循域的递归分解原理,可在不改变整个区域的前提下,对特定区域进行细化剖分。传统有限元在处理因相邻四叉树单元层级不匹配产生的悬挂节点时会遇到计算困难,比例边界有限元法恰好可解决这一难题。提出了基于四叉树算法的网格划分技术并与比例边界有限元法相结合,采用具有不同几何结构和边界条件的数值算例,对比了软件矩阵实验室(MATLAB)与商用有限元软件ANSYS的计算结果。分析结果表明,基于四叉树网格剖分技术的比例边界有限元法是一种通用、精确以及具有高计算效率的数值计算方法。Mesh generation based on quadtree algorithm follows the principle of recursive decomposition of a domain.It can only increase the resolution in certain area of interest without changing the whole domain.Additionally,the SBFEM can solve the problems caused by the presence of hanging nodes due to the level-mismatch between adjacent quadtree elements that lead to difficulties in the traditional Finite Element Analysis.This paper presents the mesh generation based on the quadtree algorithm and combines it with the SBFEM.Numerical examples of various geometries and boundary conditions are analyzed.Results from MATLAB program have been compared with solutions obtained from a commercial Finite Element Analysis package ANSYS,and positive agreements are observed.Those examples demonstrate that SBFEM based on the quadtree mesh generation is a versatile,accurate and computationally efficient numerical method.

关 键 词：比例边界有限元法 四叉树算法 网格划分 应力分析 数值方法 

分 类 号：TP302[自动化与计算机技术—计算机系统结构]