Evolutionary topological design for phononic band gap crystals

Li, Yang Fan; Huang, Xiaodong; Meng, Fei; Zhou, Shiwei

doi:10.1007/s00158-016-1424-3

Cited by 108 publications

(35 citation statements)

References 36 publications

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“…The material design at the micro-scale assumes that the material is constructed by periodic unit cells (PUC), thus its effective properties can be calculated by the numerical homogenization theory [9]. The efficient material distribution on the micro-scale enriches the capacity of topology optimization method for more extensive advanced designs and applications [10,11]. However, whether it is structural-oriented or material-oriented topology optimization, it is difficult to obtain optimal design of structure and material at the same time.…”

Section: Introductionmentioning

confidence: 99%

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Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with imprecise probability is integrated into the multi-scale concurrent topology optimization (CTO) framework. To describe the imprecise probabilistic uncertainty efficiently, the type I hybrid interval random model is adopted. An improved hybrid perturbation analysis (IHPA) method is formulated to estimate the expectation and stand variance of the objective function in the worst case. Combined with the bi-directional evolutionary structural optimization (BESO) framework, the robust designs of the structure and its composite material are carried out. Several 2D and 3D numerical examples are presented to illustrate the effectiveness of the proposed method. The results show that the proposed method has high efficiency and low precision loss. In addition, the proposed RCTO approach remains efficient in both of linear static and dynamic structures, which shows its extensive adaptability.where J Y and J Y denote the lower and upper bounds of interval vector J Y . The symbol m J Y is the mean value of J Y , which can be calculated by averaging the lower and upper bounds value as shown in Eq. (16b). I J Y denotes the variation interval of J Y , which depends on the difference of the lower and upper bound values as shown in Eq. (16c). The deviation J Y  of the symmetrical interval can be acquired by averaging the upper and lower bounds of J Y as shown in Eq. (16d). In the combined form, the J-th hybrid interval random parameter( ) JJ X Y can be formulated as RCTO Volume fraction of solid: 95.6% Volume fraction of Phase 1: 70.3% DCTO Volume fraction of solid: 95.1% Volume fraction of phase 1: 70.7% 33 (b) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 93.0% Volume fraction of phase 1: 72.4% DCTO Volume fraction of solid: 92.7% Volume fraction of phase 1: 72.7% (c) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 90.4% Volume fraction of phase 1: 74.9% DCTO Volume fraction of solid: 88.9% Volume fraction of phase 1: 76.3%JJ J ee JJ J J J J e J J e J J JJ J e e J J J J J J J J e J J e 2 2 J J J J JK J e e J J J J J J J J J J J J J e J J JJ JJ e J J J J JJ J J e J J J J e JJ e J J J J 3m d I e J J J J x X X e J J e J J e J J e J J e J J e J J e e e e J J J J e J J J J e J J J J H T A a J J J J H a J J J J pT A J J J J A e J J J J A e J J J J J J J J a i A Y J J J J p a i A Y J J J J a i J J J J a i A Y J J J J p a i A Y J J J J Ne ia A i J J J J a i J J J J Ne ia A i J J J J

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Section: Introductionmentioning

confidence: 99%

“…,(15b)where M and N represent the number of random and interval parameters, respectively. For each11 interval vector, J Y can be expressed as follows mI , ,…”

mentioning

confidence: 99%

Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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“…[10][11][12][13]) some of which addressed porous topologies [14,15]. Two other works reported optimized porous topologies for maximized RBW of asymmetric guided wave modes through genetic algorithm (GA) [16] and gradient based [17] approaches.…”

Section: Introductionmentioning

confidence: 99%

Optimization and experimental validation of stiff porous phononic plates for widest complete bandgap of mixed fundamental guided wave modes

Hedayatrasa

Kersemans

Abhary

et al. 2018

Mechanical Systems and Signal Processing

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“…After that, Halkjær et al proposed the solid isotropic material with penalization method for the topology optimization of the plate structures with maximal BGs. The bidirectional evolutionary structural optimization was developed to optimize the design of PnC with maximum BG width (BGW) under the volume constraint . Meanwhile, Li et al used the bidirectional evolutionary structural optimization in conjunction with the homogenization method for the topology optimization of cellular PnCs with a bulk or shear modulus constraint.…”

Section: Introductionmentioning

confidence: 99%

“…The bidirectional evolutionary structural optimization was developed to optimize the design of PnC with maximum BG width (BGW) under the volume constraint. 49 Meanwhile, Li et al 50 used the bidirectional evolutionary structural optimization in conjunction with the homogenization method for the topology optimization of cellular PnCs with a bulk or shear modulus constraint. Recently, Lu et al 51 used the gradient-based topology optimization (GTO) method to obtain 3D PnCs with ultrawide normalized all-angle and all-mode BGs.…”

Section: Introductionmentioning

confidence: 99%

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

Xie

Liu

Huang

et al. 2018

Numerical Meth Engineering

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Summary The design and analysis of phononic crystals (PnCs) are generally based on the deterministic models without considering the effects of uncertainties. However, uncertainties that existed in PnCs may have a nontrivial impact on their band structure characteristics. In this paper, a sparse point sampling–based Chebyshev polynomial expansion (SPSCPE) method is proposed to estimate the extreme bounds of the band structures of PnCs. In the SPSCPE, the interval model is introduced to handle the unknown‐but‐bounded parameters. Then, the sparse point sampling scheme and the finite element method are used to calculate the coefficients of the Chebyshev polynomial expansion. After that, the SPSCPE method is applied for the band structure analysis of PnCs. Meanwhile, the checkerboard and hinge phenomena are eliminated by the hybrid discretization model. In the end, the genetic algorithm is introduced for the topology optimization of PnCs with unknown‐but‐bounded parameters. The specific frequency constraint is considered. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

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Evolutionary topological design for phononic band gap crystals

Cited by 108 publications

References 36 publications

Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

Optimization and experimental validation of stiff porous phononic plates for widest complete bandgap of mixed fundamental guided wave modes

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

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