Massively effective filter for topology optimization based on the splitting of tensor product structure

Recently, a research group lead by Prof. Shuting Wang from topology optimization of Huazhong University of Science and Technology has put forward a massively efficient filter utilizing the splitting of the tensor product structure. This study can be found in the journal Frontiers of Mechanical Engineering on 10 January, 2023.

With the aid of spitting technique, the traditional weight matrices of both B-splines and non-uniform rational B-splines implicit filters are equivalently decomposed into two or three submatrices, by which the sensitivity analysis is reformulated for the nodal design variables without altering the optimization process.

“Afterwards, we establish an explicit sensitivity filter in terms of the tensor product of the axial distances between adjacent elements centroids, which is decomposed by the splitting pipeline as that applied to implicit filter, and the corresponding sensitivity analysis is derived for elemental design variables.” said by Dr. Aodi Yang, the author of this study.

According to the numerical results, compared to the traditional filter, the average updating time for design variables is accelerated by two orders of magnitude for the decomposed filter. Besides, both memory burden and computing time of weight matrix are decreased by six and three orders of magnitude for the decomposed filter.

The research team of Prof. Shuting Wang is one of the outstanding teams in topology optimization in China. This team has been devoted to topology optimization research for more than ten years and has achieved plenty of academic achievements.

“In the future, the combination of the proposed decomposed filter with the geometric reconstruction-based IGA method will extend the IGA-based topology optimization method into the design problems with complex CAD models,” said Dr. Xie.

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Reference:  Aodi YANG, Shuting WANG, Nianmeng LUO, Tifan XIONG, Xianda XIE. Massively efficient filter for topology optimization based on the splitting of tensor product structure. Front. Mech. Eng., 2022, 17(4): 54 https://doi.org/10.1007/s11465-022-0710-6

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About Frontiers of Mechanical Engineering

Frontiers of Mechanical Engineering is an international peer-reviewed academic journal sponsored by the Ministry of Education of China. The journal seeks to provide a forum for a broad blend of high-quality academic papers in order to promote rapid communication and exchange between researchers, scientists, and engineers in the field of mechanical engineering. The journal publishes original research articles, review articles and feature articles. The journal covers all major branches of mechanical engineering including (not limited to): machines and mechanisms, gears and transmissions, mechanical system dynamics, mechanical structures and stress analysis, tribology and surface technology, mechanical design and bionics, machining processes and technologies, manufacturing automation, precision engineering, mechatronics and embedded systems, micro/nano manufacturing and systems, robotics, sensing, MEMS, and green manufacturing.

The Editors-in-Chief are Academician Zheng You from Huazhong University of Science and Technology, China, Academician Dongming Guo from Dalian University of Technology, China. The journal has been indexed by SCI, SCOPUS, INSPEC, Astrophysics Data System (ADS), Google Scholar, CSA, Academic OneFile, Chinese Science Citation Database, Expanded Academic, Gale, OCLC, Summon by ProQuest, etc.