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.
Efficient Filtering in Topology Optimization via B-Splines1
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.
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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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