Commun. Comput. Phys., 13 (2013), pp. 1292-1308.

A Variational Binary Level Set Method for Structural Topology Optimization

Xiaoxia Dai 1, Peipei Tang 1*, Xiaoliang Cheng 2, Minghui Wu 1

1 School of Computing Science, Zhejiang University City College, Hangzhou, P.R. China.
2 Department of Mathematics, Zhejiang University, Hangzhou, P.R. China.

Received 16 September 2011; Accepted (in revised version) 11 May 2012
Available online 8 October 2012


This paper proposes a variational binary level set method for shape and topology optimization of structural. First, a topology optimization problem is presented based on the level set method and an algorithm based on binary level set method is proposed to solve such problem. Considering the difficulties of coordination between the various parameters and efficient implementation of the proposed method, we present a fast algorithm by reducing several parameters to only one parameter, which would substantially reduce the complexity of computation and make it easily and quickly to get the optimal solution. The algorithm we constructed does not need to re-initialize and can produce many new holes automatically. Furthermore, the fast algorithm allows us to avoid the update of Lagrange multiplier and easily deal with constraints, such as piecewise constant, volume and length of the interfaces. Finally, we show several optimum design examples to confirm the validity and efficiency of our method.

AMS subject classifications: 65K10, 74B05, 74S05

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Key words: Structural optimization, binary level set method, finite element method.

*Corresponding author.
Email: (X. Dai), (P. Tang), (X. Cheng), (M. Wu)

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