Design of compliant mechanisms using meshless level set methods

Luo, Z; Zhang, N; Wu, T

Design of compliant mechanisms using meshless level set methods

Luo, Z

Zhang, N

Wu, T

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Publication Type:: Journal Article
Citation:: CMES - Computer Modeling in Engineering and Sciences, 2012, 85 (4), pp. 299 - 328
Issue Date:: 2012-10-24

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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	Wu, T	en_US
dc.date.issued	2012-10-24	en_US
dc.identifier.citation	CMES - Computer Modeling in Engineering and Sciences, 2012, 85 (4), pp. 299 - 328	en_US
dc.identifier.issn	1526-1492	en_US
dc.identifier.uri	http://hdl.handle.net/10453/22021
dc.description.abstract	This paper presents a meshless Galerkin level-set method (MGLSM) for shape and topology optimization of compliant mechanisms of geometrically nonlinear structures. The design boundary of the mechanism is implicitly described as the zero level set of a Lipschitz continuous level set function of higher dimension. The moving least square (MLS) approximation is used to construct the meshless shape functions with the global Galerkin weak-form in terms of a set of arbitrarily distributed nodes. The MLS shape function is first employed to parameterize the level set function via the surface fitting rather than interpolation, and then used to implement the meshless approximations of the discrete state equations. Since the MLS shape function lacks of Kronecker delta function property, a constrained Galerkin global weak-form using the penalty method is applied to enforce the essential boundary conditions. In this way, the shape and topology optimization of the design boundary is just a question of advancing the discrete level set function in time by updating the unknown parameters for the parameterized size optimization. Compared to most conventional level set methods, the proposed MGLSM is able to (1) propagate the discrete level set function and solve the state equations at the same time with one unified set of meshes, (2) avoid numerical difficulties in solving the complicate Hamilton-Jacobi partial differential equations (PDEs), and (3) describe the implicit moving boundaries without remeshing for discontinuities. A benchmark numerical example is used 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	Design of compliant mechanisms using meshless level set methods	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	85	en_US
utslib.for	091306 Microelectromechanical Systems (MEMS)	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	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	85	en_US

Abstract:

This paper presents a meshless Galerkin level-set method (MGLSM) for shape and topology optimization of compliant mechanisms of geometrically nonlinear structures. The design boundary of the mechanism is implicitly described as the zero level set of a Lipschitz continuous level set function of higher dimension. The moving least square (MLS) approximation is used to construct the meshless shape functions with the global Galerkin weak-form in terms of a set of arbitrarily distributed nodes. The MLS shape function is first employed to parameterize the level set function via the surface fitting rather than interpolation, and then used to implement the meshless approximations of the discrete state equations. Since the MLS shape function lacks of Kronecker delta function property, a constrained Galerkin global weak-form using the penalty method is applied to enforce the essential boundary conditions. In this way, the shape and topology optimization of the design boundary is just a question of advancing the discrete level set function in time by updating the unknown parameters for the parameterized size optimization. Compared to most conventional level set methods, the proposed MGLSM is able to (1) propagate the discrete level set function and solve the state equations at the same time with one unified set of meshes, (2) avoid numerical difficulties in solving the complicate Hamilton-Jacobi partial differential equations (PDEs), and (3) describe the implicit moving boundaries without remeshing for discontinuities. A benchmark numerical example is used to demonstrate the effectiveness of the proposed method. Copyright © 2012 Tech Science Press.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/22021