This paper presents a B-spline based approach for topology optimization of three-dimensional (3D) problems where the density representation is based on B-splines. Compared with the usual density filter in topology optimization, the new B-spline based density representation approach is advantageous in both memory usage and central processing unit (CPU) time. This is achieved through the use of tensor-product form of B-splines. As such, the storage of the filtered density variables is linear with respect to the effective filter size instead of the cubic order as in the usual density filter. Numerical examples of 3D topology optimization of minimal compliance and heat conduction problems are demonstrated. We further reveal that our B-spline based density representation resolves the bottleneck challenge in multiple density per element optimization scheme where the storage of filtering weights had been prohibitively expensive.
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March 2015
Research-Article
Efficient Filtering in Topology Optimization via B-Splines1
Mingming Wang,
Mingming Wang
Mechanical, Materials and Aerospace
Engineering Department,
e-mail: mwang11@hawk.iit.edu
Engineering Department,
Illinois Institute of Technology
,Chicago, IL 60616
e-mail: mwang11@hawk.iit.edu
Search for other works by this author on:
Xiaoping Qian
Xiaoping Qian
2
Department of Mechanical Engineering,
e-mail: qian@engr.wisc.edu
University of Wisconsin
,Madison, WI 53706
e-mail: qian@engr.wisc.edu
2Corresponding author.
Search for other works by this author on:
Mingming Wang
Mechanical, Materials and Aerospace
Engineering Department,
e-mail: mwang11@hawk.iit.edu
Engineering Department,
Illinois Institute of Technology
,Chicago, IL 60616
e-mail: mwang11@hawk.iit.edu
Xiaoping Qian
Department of Mechanical Engineering,
e-mail: qian@engr.wisc.edu
University of Wisconsin
,Madison, WI 53706
e-mail: qian@engr.wisc.edu
2Corresponding author.
Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 9, 2014; final manuscript received December 3, 2014; published online January 9, 2015. Assoc. Editor: Shinji Nishiwaki.
J. Mech. Des. Mar 2015, 137(3): 031402 (10 pages)
Published Online: March 1, 2015
Article history
Received:
April 9, 2014
Revision Received:
December 3, 2014
Online:
January 9, 2015
Citation
Wang, M., and Qian, X. (March 1, 2015). "Efficient Filtering in Topology Optimization via B-Splines." ASME. J. Mech. Des. March 2015; 137(3): 031402. https://doi.org/10.1115/1.4029373
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