A NURBS-based Multi-Material Interpolation (N-MMI) for isogeometric topology optimization of structures

Gao, J; Luo, Z; Xiao, M; Gao, L; Li, P

A NURBS-based Multi-Material Interpolation (N-MMI) for isogeometric topology optimization of structures

Gao, J

Luo, Z

Xiao, M

Gao, L

Li, P

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Publication Type:: Journal Article
Citation:: Applied Mathematical Modelling, 2020, 81 pp. 818 - 843
Issue Date:: 2020-05-01

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Field	Value	Language
dc.contributor.author	Gao, J https://orcid.org/0000-0002-4760-2768	en_US
dc.contributor.author	Luo, Z https://orcid.org/0000-0002-6953-3986	en_US
dc.contributor.author	Xiao, M https://orcid.org/0000-0002-5544-9935	en_US
dc.contributor.author	Gao, L https://orcid.org/0000-0002-1485-0722	en_US
dc.contributor.author	Li, P	en_US
dc.date.issued	2020-05-01	en_US
dc.identifier.citation	Applied Mathematical Modelling, 2020, 81 pp. 818 - 843	en_US
dc.identifier.issn	0307-904X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/138095
dc.description.abstract	© 2020 In this paper, the main intention is to propose a new Multi-material Isogeometric Topology Optimization (M-ITO) method for the optimization of multiple materials distribution, where an improved Multi-Material Interpolation model is developed using Non-Uniform Rational B-splines (NURBS), namely the “NURBS-based Multi-Material Interpolation (N-MMI)”. In the N-MMI model, three key components are involved: (1) multiple Fields of Design Variables (DVFs): NURBS basis functions with control design variables are applied to construct DVFs with the sufficient smoothness and continuity; (2) multiple Fields of Topology Variables (TVFs): each TVF is expressed by a combination of all DVFs to present the layout of a distinct material in the design domain; (3) Multi-material interpolation: the material property at each point is equal to the summation of all TVFs interpolated with constitutive elastic properties. DVFs and TVFs are in the decoupled expression and optimized in a serial evolving mechanism. This feature can ensure the constraint functions are separate and linear with respect to TVFs, which can be beneficial to lower the complexity of numerical computations and eliminate numerical troubles in the multi-material optimization. Two kinds of multi-material topology optimization problems are discussed, i.e., one with multiple volume constraints and the other with the total mass constraint. Finally, several numerical examples in 2D and 3D are provided to demonstrate the effectiveness of the M-ITO method.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP160102491
dc.relation.ispartof	Applied Mathematical Modelling	en_US
dc.relation.isbasedon	10.1016/j.apm.2020.01.006	en_US
dc.rights	info:eu-repo/semantics/embargoedAccess
dc.subject.classification	Mechanical Engineering & Transports	en_US
dc.title	A NURBS-based Multi-Material Interpolation (N-MMI) for isogeometric topology optimization of structures	en_US
dc.type	Journal Article
utslib.citation.volume	81	en_US
utslib.for	091307 Numerical Modelling and Mechanical Characterisation	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0103 Numerical and Computational Mathematics	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	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
pubs.organisational-group	/University of Technology Sydney/Students
utslib.copyright.status	open_access	*
utslib.copyright.embargo	2022-01-16T00:00:00+1100
pubs.publication-status	Accepted	en_US
pubs.volume	81	en_US

Abstract:

© 2020 In this paper, the main intention is to propose a new Multi-material Isogeometric Topology Optimization (M-ITO) method for the optimization of multiple materials distribution, where an improved Multi-Material Interpolation model is developed using Non-Uniform Rational B-splines (NURBS), namely the “NURBS-based Multi-Material Interpolation (N-MMI)”. In the N-MMI model, three key components are involved: (1) multiple Fields of Design Variables (DVFs): NURBS basis functions with control design variables are applied to construct DVFs with the sufficient smoothness and continuity; (2) multiple Fields of Topology Variables (TVFs): each TVF is expressed by a combination of all DVFs to present the layout of a distinct material in the design domain; (3) Multi-material interpolation: the material property at each point is equal to the summation of all TVFs interpolated with constitutive elastic properties. DVFs and TVFs are in the decoupled expression and optimized in a serial evolving mechanism. This feature can ensure the constraint functions are separate and linear with respect to TVFs, which can be beneficial to lower the complexity of numerical computations and eliminate numerical troubles in the multi-material optimization. Two kinds of multi-material topology optimization problems are discussed, i.e., one with multiple volume constraints and the other with the total mass constraint. Finally, several numerical examples in 2D and 3D are provided to demonstrate the effectiveness of the M-ITO method.

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http://hdl.handle.net/10453/138095