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

Article


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. https://doi.org/10.1016/j.cma.2007.11.026
Article Title

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

ERA Journal ID4173
Article CategoryArticle
AuthorsRong, Jian Hua (Author) and Liang, Qing Quan (Author)
Journal TitleComputer Methods in Applied Mechanics and Engineering
Journal Citation197 (17-18), pp. 1447-1465
Number of Pages19
Year2008
Place of PublicationNetherlands
ISSN0045-7825
Digital Object Identifier (DOI)https://doi.org/10.1016/j.cma.2007.11.026
Web Address (URL)http://www.sciencedirect.com/science/journal/00457825
Abstract

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.

Keywordsstructural optimization; topology optimization; level set method; random mutation
ANZSRC Field of Research 2020400510. Structural engineering
490407. Mathematical logic, set theory, lattices and universal algebra
490412. Topology
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Byline AffiliationsChangsha University of Science and Technology, China
University of New South Wales
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