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摘要
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. ? 2022 Xi'an Jiaotong University.
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