Level set based structural topology optimization for minimizing frequency response

Shu, Lei; Wang, Michael Yu; Fang, Zongde; Ma, Zheng-Dong; Peng, Wei

doi:10.1016/j.jsv.2011.07.026

Cited by 124 publications

(39 citation statements)

References 31 publications

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“…Ma et al [8] minimized structure dynamic compliance under harmonic loads using the homogenization method. Shu et al [9] studied the topology optimization for minimizing frequency response using level set method. Yoon [10] conducted a comprehensive investigation for three model reduction schemes namely mode displacement method (MDM), Ritz vector method and quasi-static Ritz vector method in topology optimization under harmonic loads.…”

Section: Introductionmentioning

confidence: 99%

A MAC based excitation frequency increasing method for structural topology optimization under harmonic excitations

Liu

Zhu

et al. 2017

Int. J. Simul. Multisci. Des. Optim.

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-This work is focused on the topology optimization of structures that are subjected to harmonic force excitation with prescribed frequency and amplitude. As an important objective of such a design problem, the natural resonance frequency of the structure is driven far away from the prescribed excitation frequency for the purpose of avoiding resonance and reducing the vibration level. Therefore when the excitation frequency is higher than the natural resonance frequency of the structure, the natural resonance frequency will decrease, then the optimum topology configuration will be distorted with large amount of gray elements. A MAC (Modal Assurance Criteria) based excitation frequency increasing method is proposed to obtain a desired configuration. MAC is adopted here to track the natural resonance frequency which can provide the baseline reference for the current excitation frequency during the optimum iterative procedure. Then the excitation frequency increases progressively up to its originally prescribed value. By means of numerical examples, the proposed formulation can generate effective topology configurations which can avoid resonance.

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Section: Introductionmentioning

confidence: 99%

A MAC based excitation frequency increasing method for structural topology optimization under harmonic excitations

Liu

Zhu

et al. 2017

Int. J. Simul. Multisci. Des. Optim.

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“…Thus, among several other sub-areas, during the latest decades, topology optimization of continuum structures has been developed and applied in the following sub-areas of dynamic and vibro-acoustic topological design, & dynamic compliance and response (Ma et al 1995;Min et al 1999;Shu et al 2011;Kang et al 2012;Yang and Li 2013;Zhang and Kang 2014;Zhao and Wang 2015;Xu et al 2015;Jung et al 2015;Liu et al 2015;Olhoff and Niu 2015), & vibro-acoustic response (Jog 2002a, b, Olhoff andDu 2006;Jensen 2007;Calvel and Mongeau 2007;Du and Olhoff 2007a;Niu et al 2010;Yoon 2010;Nandy and Jog 2011;Du et al 2011;Yang and Du 2012;Du and Yang 2015), and & eigenfrequencies, eigenfrequency gaps, and band-gaps (Sigmund 2001;Sigmund and Jensen 2003;Jensen 2003;Halkjaer et al 2006;Olhoff 2007a, b, c, Olhoff et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Generalized incremental frequency method for topological designof continuum structures for minimum dynamic compliance subject to forced vibration at a prescribed low or high value of the excitation frequency

Olhoff

2016

Struct Multidisc Optim

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This paper deals with topological design optimization of elastic, continuum structures without damping that are subjected to time-harmonic, design-independent external dynamic loading with prescribed excitation frequency, amplitude and spatial distribution. The admissible design domain, the boundary conditions, and the available amount(s) of material(s) for single-or bi-material structures are given. An important objective of such a design problem is often to drive the resonance frequencies of the structure as far away as possible from the given excitation frequency in order to avoid resonance and to reduce the vibration level of the structure. In the present paper, the excitation frequency is defined to be 'low' for positive values up to and including the fundamental resonance frequency of the structure, and to be 'high' for values beyond that. Our paper shows that it may be very important to consider different design paths in problems of minimum dynamic compliance in order to obtain desirable solutions for prescribed excitation frequencies, and a socalled 'incremental frequency technique' (IF technique) is applied for this. Subsequently, the IF technique is integrated into an extended, systematic method named as the 'generalized incremental frequency method' (GIF method) that is developed for gradient based dynamic compliance minimization for not only 'low', but also 'high' excitation frequencies of the structure. The GIF method performs search for and determination of the solution to the minimum dynamic compliance design problem, but this is subject to the complexity that problems with prescribed high excitation frequencies exhibit disjointed design sub-spaces. Each of these sub-spaces is associated with a local minimum value of the dynamic compliance, so in general the 'global optimum solution' will have to be selected as the 'best' solution from among a number of local candidate solutions. Illustrative examples of application of the IF technique and the GIF method are presented in the paper.

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“…This approach found the distribution of material properties that minimized a cost function involving the eigenvalues of the structure. Recently, Shu et al [3] presented an approach for structural topology optimization using level set method to minimize the frequency response of the structure. Heidari et al [4] presented a method to minimize the peak power input to a truss by varying the cross-sectional areas of the truss elements while keeping the total mass of the truss constant.…”

Section: Summary Of Publications and Presentationsmentioning

confidence: 99%

Estimating the Effects of Damping Treatments on the Vibration of Complex Structures

McDaniel¹,

Bridgeo²,

Öztürk³

2012

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Level set based structural topology optimization for minimizing frequency response

Cited by 124 publications

References 31 publications

A MAC based excitation frequency increasing method for structural topology optimization under harmonic excitations

A MAC based excitation frequency increasing method for structural topology optimization under harmonic excitations

Generalized incremental frequency method for topological designof continuum structures for minimum dynamic compliance subject to forced vibration at a prescribed low or high value of the excitation frequency

Estimating the Effects of Damping Treatments on the Vibration of Complex Structures

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