摘要
随着计算机技术的进步,数值计算方法在工程领域得到了广泛的应用。有限单元法(FEM)作为其中的典型代表,已发展为成熟的商业软件。然而,现有的有限元方法在无限域动力响应问题、应力集中问题和网格自动化剖分等方面仍存在一定的局限性。此外,日新月异的建模技术引入了大量新型几何模型格式,例如电子扫描图像、3D打印模型、点云模型等,都对数值模拟带来了新的挑战。比例边界有限元法(SBFEM)作为一种新型的半解析数值方法,融合了有限元方法(FEM)和边界元方法(BEM)的优势,只在单元表面进行离散化,而在单元内部进行解析求解,可将问题的维度降低一维,在处理无限域动力问题和带有奇异性的应力集中问题时具有独特的优势。SBFEM单元仅需满足可见性要求,提高了单元形状的灵活性,可以构造包含任意数量节点的多边形和多面体单元,结合八叉树等高效自动化网格剖分算法,可以实现与多种几何模型的无缝对接,适合大规模并行计算。近年来,SBFEM已经发展成为一种可满足现代工程计算需求的通用高效计算工具,在无限域动力问题、断裂力学、非线性问题、接触、自适应分析、反演问题、多场耦合、高性能计算等方面显示出了巨大的应用前景。本研究重点对SBFEM的发展历程和近期研究热点进行系统地综述,并展望未来发展趋势,为相关领域的研究人员和工程技术人员提供参考。
With the rapid development of modern computers,the numerical method has been widely used in engineering.The finite element method(FEM),one of the most popular methods,has been successfully integrated into many commercial software packages.However,there are still some limitations in the current FEM,including the modeling of dynamic response of unbounded domain,the representation of stress singularities,and the automatic mesh generation.Additional challenges are posed by the emerging data formats used in modern geometric modeling techniques,such as digital image,stereolithography(STL)models,and point cloud models.The scaled boundary finite element method(SBFEM)is a novel semi-analytical method combining some of the advantages of FEM and boundary element method(BEM).It only discretizes the boundary of the element,while the radial direction is solved analytically,reducing the spatial dimension by one.As a result,the SBFEM is perfectly suitable for the modelling of dynamic stiffness of unbounded domain and representing stress singularities.Furthermore,it is capable of modeling polyhedrons with an arbitrary number of faces and nodes,which greatly reduces the difficulty associated with mesh generation when combining with efficient octree algorithm.Over the years,it has been developed as a general-purpose numerical method,and a large number of researchers have endeavored to apply the SBFEM in fields such as dynamic response of unbounded domain,fracture mechanics,nonlinear analysis,contact problem,adaptive analysis,inverse problem,and high performance computing.In this article,the history and latest progress in SBFEM research are systematically reviewed.
作者
张俊奇
余波
宋崇民
ZHANG Junqi;YU Bo;SONG Chongmin(Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education,Beijing University of Technology,100124;Beijing,China,2.Institute of Applied Mechanics,School of Civil Engineering,Hefei University of Technology,230009;Hefei,China,3.School of Civil and Environmental Engineering,University of New South Wales,NSW 2052 Sydney,Australia)
出处
《应用力学学报》
CAS
CSCD
北大核心
2022年第6期1038-1054,共17页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金资助项目(No.11872166)。
关键词
比例边界有限元法
无限域
应力强度因子
多面体单元
八叉树网格
高性能计算
scaled boundary finite element method
unbounded domain
stress intensity factor
polyhedral element
octree mesh
high performance computing
