报告主题：The Scaled Boundary Finite Element Method for Elastoplastic and Fracture Analysis

报告人：Chongmin Song 教授（澳大利亚新南威尔士大学）

报告时间：2025年11月5日（周三）10：00

报告地点：91麻豆 （江宁校区）乐学楼709

主办单位：91麻豆 动力学与控制研究所

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报告简介：

In this talk, the development and application of the scaled boundary finite element method for elastoplastic and fracture analysis are presented. Arbitrary polytope elements are constructed. The shape functions are obtained from the solution of the scaled boundary finite element equation for a linear problem. The conditions of partition of unity and linear completeness are satisfied. The material constitutive matrix and internal stresses are approximated spatially by polynomials inside a polytope element. The (tangential) stiffness matrix and internal nodal force vector are integrated semi-analytically. Both an integral-type nonlocal formulation and the phase-field models are incorporated in the scaled boundary finite element method to perform fracture analysis. An effective strategy for adaptive mesh refinement around the failure zone is devised using the quadtree/octree algorithm. Furthermore, the combination of the scaled boundary finite element method and octree mesh significantly reduces the computer time and memory requirement. After the introduction to the fundamental theory, numerical examples will be presented. The ongoing development of Abaqus UELs using the scaled boundary finite element method is also introduced.

报告人简介：

Prof. Chongmin Song(宋崇民)，澳大利亚新南威尔士大学土木与环境工程学院教授，基础结构安全中心主任。Song教授主要从事比例边界有限元、断裂力学、波动传播、地震工程与结构动力学等方面的研究。1996年他与瑞士联邦理工学院的Wolf J.P.教授共同创立了比例边界有限元法（Scaled Boundary Finite Element Method, SBFEM）。这种新型数值方法兼具了有限元法与边界元法的优点同时又避免了其缺点，其主要特点包括精度高、计算量节省，并且在处理无限域问题和应力奇异性方面具有突出优点。近年来在Computer Methods in Applied Mechanics and Engineering、Computers & Structures、Computational Mechanics、International Journal of Solids and Structures、Earthquake Engineering and Structural Dynamics等国际著名期刊上发表论文200余篇，独著《The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation》（2018，Song Ch.）、合著《Finite-Element Modelling of Unbounded Media》（Wolf J. P. and Song Ch., 1996）、《The semi-analytical fundamental-solution-less scaled boundary finite element method to model unbounded soil》（Wolf J. P. and Song Ch., 2003）两部。至今主持澳大利亚自然基金等项目20余项。