Structural topology optimization for frequency response problem using model reduction schemes

Yoon, Gil Ho

doi:10.1016/j.cma.2010.02.002

Cited by 188 publications

(78 citation statements)

References 27 publications

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“…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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“…Maximization of the fundamental frequency or frequency gaps of a vibrating structure have been studied for many years (Diaz and Kikuchi, 1992;Xie and Steven, 1996;Pedersen, 2000;Du and Olhoff, 2007b). In some other works, various dynamic responses of the structure are taken as the objective function of the optimization model, including the dynamic compliance (Ma et al, 1995;Min et al, 1999;Jensen, 2007;Yoon, 2010), vibration amplitude (Jog, 2002;Kang et al, 2012) and sound pressure (Luo and Gea, 2003;Yoon et al, 2007;Du and Olhoff, 2010;Shu et al, 2011a). Also, dynamic properties of structures under active attitude control have also been considered in topology optimization problems (Kang et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

“…For instance, Larsen et al (2009) considered the optimal material layout of plates for minimizing the global vibration level and maximizing the energy transport. Yoon (2010) compared several model reduction techniques in the SIMP-based structural topology optimization for frequency responses. Olhoff (2007a, 2010) studied topology optimization for reducing vibration level and sound radiation of bi-material structures under harmonic excitations.…”

Section: Introductionmentioning

confidence: 99%

Vibration suppression using integrated topology optimization of host structures and damping layers

Zhang

Kang

2014

Journal of Vibration and Control

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It is often desirable to simultaneously optimize the damping and stiffness distribution in the design of shell structures incorporating damping material layers for achieving the best vibration mitigation performance. This paper investigates the integrated topology optimization of host structures and damping layers for reducing the vibration level in the presence of harmonic excitations. Therein, the global damping matrix is a nonproportional one due to distributed damping effects. For an efficient frequency response analysis of the system with nonproportional damping, reduced-order equations are obtained by using lower-order eigenvectors of the undamped system, and then the method of complex mode superposition is employed for solving the dynamic equations in the state space. In the optimization model, the vibration amplitudes at specified positions are taken as the objective function. The relative densities of the elements are considered as design variables, and an artificial damping material model relating the local damping properties to the elemental density variables is employed. The Rational Approximation of Material Properties model is adopted to avoid localized modes in low-density areas during the optimization process. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed framework.

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“…for avoiding the possibility of internal resonance. The active point-of-view is to 5 design structures with specific eigenfrequencies to maximize vibrations i.e. by utilizing the resonance phenomena.…”

Section: Introductionmentioning

confidence: 99%

“…Beams, plates and 3D continua are treated and different numerical tools (penalization's) to obtain 1 -0 designs are applied. Among these papers are [2], [3], [4], [5], [6] and [7]. Note, that 1 -0 optimal designs is not the goal of the here presented research, that may be classified as traditional size optimization, where stiffness interpolation should be viewed instead from a physical point of view.…”

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confidence: 99%

Eigenfrequency optimized 3D continua, with possibility for cavities

Pedersen¹,

Pedersen²

2015

Journal of Sound and Vibration

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Eigenfrequency optimization for 3D continua is formulated and exemplified by the geometry and boundary conditions of a thick plate. Numerical finite element models are based on four node tetrahedra and results from subspace iterations give directly the basis for the continuum redesign. The 3D modeling with a large number of elements has the possibility in optimal design to obtain (as found) not only holes but also cavities in the continuum. Sensitivity analysis is presented on the element level with simple physical interpretation of the involved terms. This general result has general value for control of eigenfrequencies. It is found that in the combination of partial differentiation with the chain rule of differentiation, a specific notation is needed and a suggestion is presented.The optimization method is based on a derived optimality criterion, and as such the maximization problem change to a problem of determining a design with uniform values of this criterion. Non-linear stiffness interpolation may be a physical reality. A two parameter interpolation function is incorporated analytical, also in the sensitivity analysis and the optimality criterion, but without focusing on 1-0 optimal solutions. Two cases of boundary conditions, two cases of total amount of material, and cases of linear and non-linear stiffness interpolation are studied.

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Structural topology optimization for frequency response problem using model reduction schemes

Cited by 188 publications

References 27 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

Vibration suppression using integrated topology optimization of host structures and damping layers

Eigenfrequency optimized 3D continua, with possibility for cavities

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