A physically meaningful level set method for topology optimization of structures

Luo, Z; Zhang, N; Wang, Y

A physically meaningful level set method for topology optimization of structures

Luo, Z

Zhang, N

Wang, Y

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Publication Type:: Journal Article
Citation:: CMES - Computer Modeling in Engineering and Sciences, 2012, 83 (1), pp. 73 - 96
Issue Date:: 2012-04-02

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Field	Value	Language
dc.contributor.author	Luo, Z https://orcid.org/0000-0002-6953-3986	en_US
dc.contributor.author	Zhang, N https://orcid.org/0000-0001-6408-0044	en_US
dc.contributor.author	Wang, Y	en_US
dc.date.issued	2012-04-02	en_US
dc.identifier.citation	CMES - Computer Modeling in Engineering and Sciences, 2012, 83 (1), pp. 73 - 96	en_US
dc.identifier.issn	1526-1492	en_US
dc.identifier.uri	http://hdl.handle.net/10453/18376
dc.description.abstract	This paper aims to present a physically meaningful level set method for shape and topology optimization of structures. Compared to the conventional level set method which represents the design boundary as the zero level set, in this study the boundary is embedded into non-zero constant level sets of the level set function, to implicitly implement shape fidelity and topology changes in time via the propagation of the discrete level set function. A point-wise nodal density field, non-negative and value-bounded, is used to parameterize the level set function via the compactly supported radial basis functions (CSRBFs) at a uniformly defined set of knots. The set of densities are used to interpolate practical material properties in finite element approximation via the standard Lagrangian shape function. CSRBFs knots are supposed to be consistent with finite element nodes only for the sake of numerical simplicity. By doing so, the discrete values of the level set function are assigned with practical material properties via the physically meaningful interpolation. The original more difficult shape and topology optimization of the Hamilton-Jacobi partial differential equations (PDEs) is transformed to a relatively easier size optimization of the nodal densities, to which more efficient optimization algorithms can be directly applied. In this way, the dynamic motion of the design boundary is just a question of transporting the discrete level set function until the optimal criteria of the structure is satisfied. Two widely studied examples are applied to demonstrate the effectiveness of the proposed method. Copyright © 2012 Tech Science Press.	en_US
dc.relation.ispartof	CMES - Computer Modeling in Engineering and Sciences	en_US
dc.subject.classification	Applied Mathematics	en_US
dc.title	A physically meaningful level set method for topology optimization of structures	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	83	en_US
utslib.for	0902 Automotive Engineering	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0103 Numerical and Computational Mathematics	en_US
utslib.for	0915 Interdisciplinary Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	83	en_US

Abstract:

This paper aims to present a physically meaningful level set method for shape and topology optimization of structures. Compared to the conventional level set method which represents the design boundary as the zero level set, in this study the boundary is embedded into non-zero constant level sets of the level set function, to implicitly implement shape fidelity and topology changes in time via the propagation of the discrete level set function. A point-wise nodal density field, non-negative and value-bounded, is used to parameterize the level set function via the compactly supported radial basis functions (CSRBFs) at a uniformly defined set of knots. The set of densities are used to interpolate practical material properties in finite element approximation via the standard Lagrangian shape function. CSRBFs knots are supposed to be consistent with finite element nodes only for the sake of numerical simplicity. By doing so, the discrete values of the level set function are assigned with practical material properties via the physically meaningful interpolation. The original more difficult shape and topology optimization of the Hamilton-Jacobi partial differential equations (PDEs) is transformed to a relatively easier size optimization of the nodal densities, to which more efficient optimization algorithms can be directly applied. In this way, the dynamic motion of the design boundary is just a question of transporting the discrete level set function until the optimal criteria of the structure is satisfied. Two widely studied examples are applied to demonstrate the effectiveness of the proposed method. Copyright © 2012 Tech Science Press.

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http://hdl.handle.net/10453/18376