报告人:  Chongmin Song （宋崇民）教授 （澳大利亚新南威尔士大学）
地   点：河海大学江宁校区乐学楼1116室
主办单位:  国际合作处 力学与材料学院动力学与控制研究所

报告题目 1: The Scaled Boundary Finite-Element Method for Dynamic Analysis
时   间 ：2020年12月12日（周六）13:00-14:00

报告内容简介：
The scaled boundary finite element has been developed into a general-purpose numerical method. In this method, an element is generated by scaling its boundary and the element solution is obtained semi-analytically. In comparison with standard finite element technology, this approach allows the construction of elements of more complex shapes such as polygons and polyhedrons. The semi-analytical formulation provides an accurate and efficient way for the modelling of problems involving unbounded media and singularities.
This presentation will focus on the theory and application of the scaled boundary finite element method for dynamic analysis of bounded and unbounded domains. When applied to fracture mechanics problems, the stress intensity factors and the T-stress are extracted directly from their definitions without requiring an asymptotic expansion and local mesh refinement.  When applied to an unbounded domain, a high-order transmitting boundary is constructed with frequency-independent high-order static stiffness and damping matrices. Standard methods in classical structural dynamics can be applied to evaluate the response in the frequency and time domains.

报告题目 2: A massively parallel explicit dynamic solver using the scaled boundary
           finite element method with octree meshes
时   间 ：2020年12月13日（周日）13:00-14:00
报告内容简介：
The applications of transient dynamic analyses include impact, crash test, and wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and time stepping schemes are required. To this end, a parallel explicit solver exploiting the advantages of balanced octree meshes is introduced. To avoid the hanging nodes problem encountered in standard finite element analysis (FEA), the scaled boundary finite element method (SBFEM) is deployed as a spatial discretization scheme. Consequently, arbitrarily shaped star-convex polyhedral elements are straightforwardly generated. Considering the scaling and transformation of octree cells, the stiffness and mass matrices of a limited number of unique cell patterns are pre-computed. A mass lumping technique yields a well-conditioned diagonal mass matrix. This enables us to leverage the advantages of explicit time integrator, i.e., it is possible to efficiently compute the nodal displacements without the need for solving a system of linear equations. We implement the proposed scheme together with a central difference method (CDM) in a distributed computing environment. The performance of our parallel explicit solver is evaluated by means of several numerical benchmark examples, including complex geometries and various practical applications. A significant speedup is observed for these examples with up to 1 billion of degrees of freedom and running on up to 16,384 computing cores.

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。Prof. Song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、International Journal for Numerical Methods in 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130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。近期主持澳大利亚自然基金等项目20余项。