A level set method for topology optimization of continuum structures with bounded design domain

Rong, Jian Hua and Liang, Qing Quan (2008) A level set method for topology optimization of continuum structures with bounded design domain. Computer Methods in Applied Mechanics and Engineering, 197 (17-18). pp. 1447-1465. ISSN 0045-7825


In practice, a continuum structure is usually designed to carry the traction applied to the boundary of the structure subject to prescribed displacements imposed on its boundary. The design domains of practical structures are often limited and significantly affect the final optimal design of the structures. Structural boundaries under traction and prescribed displacements should be treated as a zero level set in the level set methods. Firstly, to overcome the limitations of current level set methods and the stopping issue of structural boundary movements, this paper presents a set of new level set based optimization formulae for the optimal design of continuum structures with bounded design domains. A set of new normal velocities required by level set movements is given. A level set based optimization algorithm is developed and implemented with several robust and efficient numerical techniques, which include the level set regularization algorithm, gradient projection algorithm, nonlinear velocity mapping algorithm and return mapping algorithm. Secondly, in order to overcome the difficulty in nucleating holes in the design domain in the level set based optimization method, this paper introduces a new optimization strategy with a small possibility random topology mutations and crossovers. A mixed topology optimization algorithm is implemented and presented for the compliance minimization problems of continuum structures with material volume constraints. The validity and effectiveness of the proposed method are demonstrated with two examples.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Awaiting paper from author. Deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Agricultural, Civil and Environmental Engineering
Date Deposited: 02 Apr 2008 02:27
Last Modified: 29 Aug 2014 06:24
Uncontrolled Keywords: structural optimization; topology optimization; level set method; random mutation
Fields of Research : 09 Engineering > 0905 Civil Engineering > 090506 Structural Engineering
01 Mathematical Sciences > 0101 Pure Mathematics > 010107 Mathematical Logic, Set Theory, Lattices and Universal Algebra
01 Mathematical Sciences > 0101 Pure Mathematics > 010112 Topology
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: 10.1016/j.cma.2007.11.026
URI: http://eprints.usq.edu.au/id/eprint/4034

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