Topology optimization for metastructures with quasi-zero stiffness and snap-through features

Lu, Y; Luo, Q; Tong, L

Topology optimization for metastructures with quasi-zero stiffness and snap-through features

Lu, Y Luo, Q

Tong, L

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Publisher:: ELSEVIER SCIENCE SA
Publication Type:: Journal Article
Citation:: Computer Methods in Applied Mechanics and Engineering, 2025, 434
Issue Date:: 2025-02-01

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Field	Value	Language
dc.contributor.author	Lu, Y
dc.contributor.author	Luo, Q https://orcid.org/0000-0001-5727-9290
dc.contributor.author	Tong, L
dc.date.accessioned	2025-08-04T00:51:34Z
dc.date.available	2025-08-04T00:51:34Z
dc.date.issued	2025-02-01
dc.identifier.citation	Computer Methods in Applied Mechanics and Engineering, 2025, 434
dc.identifier.issn	0045-7825
dc.identifier.issn	1879-2138
dc.identifier.uri	http://hdl.handle.net/10453/188991
dc.description.abstract	Quasi-zero stiffness (QZS) is highly demanded in passive vibration isolators. Most of the existing design methods of QZS vibration isolators are typically based on mechanism designs, where pre-defined structural configurations, components, or mechanisms with certain features, such as negative stiffness, are required to synthesize the designs. This work introduces topology optimization for QZS structure designs, enabling the design of structures without pre-definitions and resulting in single-part designs rather than structural assemblies. We propose novel mathematical formulations of the objective function based on the QZS force-displacement curve and generic mathematical formulations of the optimization problem. An extended moving isosurface threshold method is used to solve the formulated optimization problem. In addition, topology optimization of metastructures with snap-through features and an alternative design method that synthesizes QZS metastructures by combining snap-through structures with positive stiffness elements are also presented. The optimized snap-through metastructures are numerically validated by nonlinear finite element analysis (NFEA) and experiment, which shows negative stiffness and snap-through characteristics. Numerical examples and investigations are presented for the QZS structures designed by both optimization and synthesis methods. The NFEA results reveal the QZS designs obtained from the two methods can achieve approximately constant stiffness of 0.502 N/mm over a 17 mm displacement range and 0.402 N/mm over a 12 mm displacement range, respectively.
dc.language	English
dc.publisher	ELSEVIER SCIENCE SA
dc.relation.ispartof	Computer Methods in Applied Mechanics and Engineering
dc.relation.isbasedon	10.1016/j.cma.2024.117587
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	01 Mathematical Sciences, 09 Engineering
dc.subject.classification	Applied Mathematics
dc.subject.classification	40 Engineering
dc.subject.classification	49 Mathematical sciences
dc.title	Topology optimization for metastructures with quasi-zero stiffness and snap-through features
dc.type	Journal Article
utslib.citation.volume	434
utslib.for	01 Mathematical Sciences
utslib.for	09 Engineering
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	open_access	*
dc.rights.license	This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/
dc.date.updated	2025-08-04T00:51:30Z
pubs.publication-status	Published
pubs.volume	434

Abstract:

Quasi-zero stiffness (QZS) is highly demanded in passive vibration isolators. Most of the existing design methods of QZS vibration isolators are typically based on mechanism designs, where pre-defined structural configurations, components, or mechanisms with certain features, such as negative stiffness, are required to synthesize the designs. This work introduces topology optimization for QZS structure designs, enabling the design of structures without pre-definitions and resulting in single-part designs rather than structural assemblies. We propose novel mathematical formulations of the objective function based on the QZS force-displacement curve and generic mathematical formulations of the optimization problem. An extended moving isosurface threshold method is used to solve the formulated optimization problem. In addition, topology optimization of metastructures with snap-through features and an alternative design method that synthesizes QZS metastructures by combining snap-through structures with positive stiffness elements are also presented. The optimized snap-through metastructures are numerically validated by nonlinear finite element analysis (NFEA) and experiment, which shows negative stiffness and snap-through characteristics. Numerical examples and investigations are presented for the QZS structures designed by both optimization and synthesis methods. The NFEA results reveal the QZS designs obtained from the two methods can achieve approximately constant stiffness of 0.502 N/mm over a 17 mm displacement range and 0.402 N/mm over a 12 mm displacement range, respectively.

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http://hdl.handle.net/10453/188991