Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

doi:10.1007/s11465-019-0534-1

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

Ψ

maps 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

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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