A level set-based parameterization method for structural shape and topology optimization

Luo, Z; Wang, MY; Wang, S; Wei, P

A level set-based parameterization method for structural shape and topology optimization

Luo, Z

Wang, MY Wang, S Wei, P

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Publication Type:: Journal Article
Citation:: International Journal for Numerical Methods in Engineering, 2008, 76 (1), pp. 1 - 26
Issue Date:: 2008-10-01

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Field	Value	Language
dc.contributor.author	Luo, Z https://orcid.org/0000-0002-6953-3986	en_US
dc.contributor.author	Wang, MY	en_US
dc.contributor.author	Wang, S	en_US
dc.contributor.author	Wei, P	en_US
dc.date.issued	2008-10-01	en_US
dc.identifier.citation	International Journal for Numerical Methods in Engineering, 2008, 76 (1), pp. 1 - 26	en_US
dc.identifier.issn	0029-5981	en_US
dc.identifier.uri	http://hdl.handle.net/10453/15400
dc.description.abstract	This paper presents an effective parametric approach by extending the conventional level set method to structural shape and topology optimization using the compactly supported radial basis functions (RBFs) and the optimality criteria (OC) method. The structural design boundary is first represented implicitly by embedding into a higher-dimensional level set function as its zero level set, and the RBFs of a favorable smoothness are then applied to interpolate the level set function. The original initial value problem is thus converted to a parametric optimization, with the expansion coefficients of the interplant posed as the design variables. The OC method is then applied to advance the structure boundary in terms of the velocity field derived from the parametric optimization. Hence, the structural shape and topology optimization is now transformed into a process of iteratively finding coefficients to update the level set function to achieve an optimal configuration. The numerical considerations of the conventional level set method, including upwind schemes, velocity extension, and reinitialization, are eliminated. The proposed scheme is capable of addressing structural shape fidelity and topology change simultaneously and of keeping the boundary smooth during the optimization process. Furthermore, numerical convergence is expected to be improved. A widely investigated example, in the framework of structural stiffness designs, is applied to demonstrate the efficiency and accuracy of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.	en_US
dc.relation.ispartof	International Journal for Numerical Methods in Engineering	en_US
dc.relation.isbasedon	10.1002/nme.2092	en_US
dc.subject.classification	Applied Mathematics	en_US
dc.title	A level set-based parameterization method for structural shape and topology optimization	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	76	en_US
utslib.for	0913 Mechanical Engineering	en_US
utslib.for	09 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	76	en_US

Abstract:

This paper presents an effective parametric approach by extending the conventional level set method to structural shape and topology optimization using the compactly supported radial basis functions (RBFs) and the optimality criteria (OC) method. The structural design boundary is first represented implicitly by embedding into a higher-dimensional level set function as its zero level set, and the RBFs of a favorable smoothness are then applied to interpolate the level set function. The original initial value problem is thus converted to a parametric optimization, with the expansion coefficients of the interplant posed as the design variables. The OC method is then applied to advance the structure boundary in terms of the velocity field derived from the parametric optimization. Hence, the structural shape and topology optimization is now transformed into a process of iteratively finding coefficients to update the level set function to achieve an optimal configuration. The numerical considerations of the conventional level set method, including upwind schemes, velocity extension, and reinitialization, are eliminated. The proposed scheme is capable of addressing structural shape fidelity and topology change simultaneously and of keeping the boundary smooth during the optimization process. Furthermore, numerical convergence is expected to be improved. A widely investigated example, in the framework of structural stiffness designs, is applied to demonstrate the efficiency and accuracy of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.

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http://hdl.handle.net/10453/15400