In collaboration with
Dr. Sangsoon Cho, Korea Atomic Energy Research Institute, Daejeon, Republic of Korea.
Prof. José González, Escuela Téchica Superior de Ingeniería, Universidad de Sevilla, Spain
Dr. Radek Kolman, Dr. Ján Kopačka, Institute of Thermomechanics, CAS, Prague, CZ
Dr. Jingyun Kim, Kyung Hee University, Seoul, Korea
In recent years, there have been several notable advances both in wave propagation and explicit transient structural dynamic analysis procedures. These include: (1) accurate wavefront tracking algorithms that can handle material heterogeneities; (2) accurate explicit algorithm employing improved non-diagonal inverse mass matrices; (3) large-step explicit integration of low and medium-frequency response analysis by filtering out mesh frequencies, among others. These advances offer structural dynamicists several options in wave propagation and transient analysis for capturing the predominant physics of the problems at hand, with drastically increased computational efficiency and robustness. In this talk, we will go over some salient features of these advances, and offer potential topics for further research.
This work was motivated by the author's six-month stay in the Aerospace Mechanics Research Center of the University of Colorado Boulder. The author joined the Multi-Physics Design Optimization group focusing on the level-set eXtended Finite Element Method (XFEM) topology optimization. The main aim was to revise existing interface formulations and come up with a new one that would be robust and stable enough to be used with the level-set XFEM. The mesh tying is an important issue encountered in the finite element analysis of complex structures. It enables to join the adjacent dissimilarly meshed parts or their regions. This problem is even more pronounced in the case of isogeometric analysis that is a modern spatial discretization technique which instead of Lagrange shape functions utilizes NURBS basis functions. Conventional mesh tying methods are based on the master-slave concept that leads to a biased algorithm. Consequently, results are influenced by the selection of the master and the slave interface. Inspired by the two-pass dual formulations, we come up with a new formulation which inherits all appealing properties of the mortar method. Namely, it preserves optimal convergence rates and is variationally consistent. At the same time, the newly proposed mesh tying formulation is unbiased, i.e. the formulation is independent on the selection of the master and slave side. As a result, it substantially simplifies the definition of mesh tying interface and has a great potential for the solution of the self-contact problems.
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