2018
DOI: 10.1002/nme.5829
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Eigenvalue topology optimization via efficient multilevel solution of the frequency response

Abstract: Summary The article presents an efficient solution method for structural topology optimization aimed at maximizing the fundamental frequency of vibration. Nowadays, this is still a challenging problem mainly because of the high computational cost required by spectral analyses. The proposed method relies on replacing the eigenvalue problem with a frequency response one, which can be tuned and efficiently solved by a multilevel procedure. Connections of the method with multigrid eigenvalue solvers are discussed … Show more

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Cited by 44 publications
(24 citation statements)
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References 68 publications
(136 reference statements)
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“…Despite using the element removal scheme, the remaining small regions with intermediate volume fractions ν(x) ∈ (ε r , 1) gave rise to spurious eigenmodes due to the ersatz material model. To combat this, we follow Ferrari et al (2018) and set the lower bound δ 0 to a relatively large value δ 0 = 10 −3 . This choice of δ 0 increases the magnitude of the spurious eigenfrequencies such that they do not obstruct the optimization.…”
Section: Consideration Of Low Volume Fraction Elementsmentioning
confidence: 99%
“…Despite using the element removal scheme, the remaining small regions with intermediate volume fractions ν(x) ∈ (ε r , 1) gave rise to spurious eigenmodes due to the ersatz material model. To combat this, we follow Ferrari et al (2018) and set the lower bound δ 0 to a relatively large value δ 0 = 10 −3 . This choice of δ 0 increases the magnitude of the spurious eigenfrequencies such that they do not obstruct the optimization.…”
Section: Consideration Of Low Volume Fraction Elementsmentioning
confidence: 99%
“…A multilevel concept is exploited also here, with the main focus on cheaply computing a satisfactory approximation to some buckling modes without ever solving an eigenvalue problem on the fine discretization. However, in contrast to [27], the approximate buckling modes and their associated load factors estimated by means of the Rayleigh quotient, are now directly used to run the optimization. We emphasize that this multilevel approach helps filtering the aforementioned unphysical artifacts and localized buckling modes originating on the fine grid, thus significantly simplifying and speeding up the optimization process.…”
Section: Introductionmentioning
confidence: 99%
“…The topology optimization for eigenfrequencies of a non-rotating plate has attracted continuous attention [17][18][19][20][21][22] since the pioneering work of Bendsøe and Kikuchi [23]. Nevertheless, no studies have been reported so far for the topology optimization for eigenfrequencies of a rotating thin plate.…”
Section: Introductionmentioning
confidence: 99%
“…Nevertheless, no studies have been reported so far for the topology optimization for eigenfrequencies of a rotating thin plate. Most of the previous topology optimization approaches are based on the variable densities [19][20][21] or level set functions [24], which may contain many design variables, especially for large-scale problems. A large number of design variables will increase the computation cost associated with the sensitivity analysis and optimization solution.…”
Section: Introductionmentioning
confidence: 99%
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