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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

Postal Subscription Code 80-975

2018 Impact Factor: 0.989

Front. Mech. Eng.    2019, Vol. 14 Issue (2) : 222-234    https://doi.org/10.1007/s11465-019-0534-1
RESEARCH ARTICLE
Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency
Manman XU, Shuting WANG(), Xianda XIE
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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Abstract

Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.

Keywords topology optimization      level set method      isogeometric analysis      eigenfrequency     
Corresponding Author(s): Shuting WANG   
Just Accepted Date: 28 December 2018   Online First Date: 18 February 2019    Issue Date: 22 April 2019
 Cite this article:   
Manman XU,Shuting WANG,Xianda XIE. Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency[J]. Front. Mech. Eng., 2019, 14(2): 222-234.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-019-0534-1
https://academic.hep.com.cn/fme/EN/Y2019/V14/I2/222
Fig.1  Geometrical mapping Ψmaps the common parameter space (ξ,η) onto the physical space
Fig.2  Flowchart of the optimization procedure
Fig.3  Design domain of a cantilever beam structure
Method Number of elements Number of DOFs Time of each iteration/s Time of solution of system equation/s
IGA-L 256×128 67080 873.26 713.68
FEA-L 256×128 263682 1580.42 1237.16
IGA-L 128×64 17160 30.06 25.31
FEA-L 128×64 66306 54.17 43.97
IGA-L 64×32 4488 6.41 5.18
FEA-L 64×32 16770 8.55 6.85
Tab.1  Comparison of IGA- and FEA-based LSM TO
Fig.4  Optimized results obtained by using IGA and FEA methods with 128 × 64 elements
Fig.5  Comparison of IGA and FEA in terms of convergence history
Fig.6  Comparison of IGA and FEA in terms of eigenfrequency history
Fig.7  Design domain of a clamped beam structure
Fig.8  Optimal layouts obtained by using (a) 64×16 meshes, (b) 128×32 meshes, and (c) 256×64 meshes
Fig.9  Convergence history
Fig.10  Iteration history of the first three eigenfrequencies
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