nach oben

Structural and Multidisciplinary Optimization

Erschienen in:

04.03.2016 | RESEARCH PAPER

Evolutionary topological design for phononic band gap crystals

verfasst von: Yang fan Li, Xiaodong Huang, Fei Meng, Shiwei Zhou

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 3/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Phononic band gap crystals are made of periodic inclusions embedded in a base material, which can forbid the propagation of elastic and acoustic waves within certain range of frequencies. In the past two decades, the systematic design of phononic band gap crystals has attracted increasing attention due to their wide practical applications such as sound insulation, waveguides, or acoustic wave filtering. This paper proposes a new topology optimization algorithm based on bi-directional evolutionary structural optimization (BESO) method and finite element analysis for the design of phononic band gap crystals. The study on the maximizing gap size between two adjacent bands has been systematically conducted for out-of-plane waves, in-plane waves and the coupled in-plane and out-of-plane waves. Numerical results demonstrate that the proposed optimization algorithm is effective and efficient for the design of phononic band gap crystals and various topological patterns of optimized phononic structures are presented. Several new patterns for phononic band gap crystals have been successfully obtained.

Vorheriger Artikel A variable-accuracy metamodel-based architecture for global MDO under uncertainty

Nächster Artikel A full-space barrier method for stress-constrained discrete material design optimization

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

Bendsoe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer Science & Business Media, BerlinMATH

Bilal OR, Hussein MI (2011) Optimization of phononic crystals for the simultaneous attenuation of out-of-plane and in-plane waves. In: ASME 2011 International Mechanical Engineering Congress and Exposition, Denver, Colorado, USA, 2011. ASME, Denver, pp 969–972

Bilal OR, Hussein MI (2012) Topologically evolved phononic material: breaking the world record in band gap size. In: SPIE OPTO, 2012. International Society for Optics and Photonics, Bellingham, pp 826911–826917

Dong HW, Su XX, Wang YS, Zhang C (2014) Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm. Struct Multidisc Optim 50:593–604MathSciNetCrossRef

Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidisc Optim 34:91–110MathSciNetCrossRefMATH

Gazonas GA, Weile DS, Wildman R, Mohan A (2006) Genetic algorithm optimization of phononic bandgap structures. Int J Solids Struct 43:5851–5866CrossRefMATH

Huang X, Xie YM (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43:1039–1049CrossRef

Huang X, Xie YM (2009) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43:393–401MathSciNetCrossRefMATH

Huang X, Xie YM (2010) Evolutionary topology optimization of continuum structures: methods and applications. John Wiley & Sons, ChichesterCrossRefMATH

Huang X, Zuo Z, Xie YM (2010) Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Comput Struct 88:357–364CrossRef

Huang X, Radman A, Xie YM (2011) Topological design of microstructures of cellular materials for maximum bulk or shear modulus. Comput Mater Sci 50:1861–1870CrossRef

Huang X, Xie YM, Jia B, Li Q, Zhou S (2012) Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity. Struct Multidisc Optim 46:385–398MathSciNetCrossRefMATH

Huang X, Zhou S, Sun G, Li G, Xie YM (2015) Topology optimization for microstructures of viscoelastic composite materials. Comput Methods Appl Mech Eng 283:503–516CrossRef

Hussein MI, Hamza K, Hulbert GM, Scott RA, Saitou K (2005) Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics. Struct Multidisc Optim 31:60–75CrossRef

Hussein MI, Hamza K, Hulbert GM, Saitou K (2007) Optimal synthesis of 2D phononic crystals for broadband frequency isolation. Waves Random Complex Media 17:491–510MathSciNetCrossRefMATH

Jensen JS, Pedersen NL (2006) On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases. J Sound Vib 289:967–986CrossRef

Kittel C, McEuen P, McEuen P (1976) Introduction to solid state physics, vol 8. Wiley, New York

Kushwaha MS (1996) Classical band structure of periodic elastic composites. Int J Mod Phys B 10:977–1094CrossRef

Kushwaha MS, Halevi P, Dobrzynski L, Djafari-Rouhani B (1993) Acoustic band structure of periodic elastic composites. Phys Rev Lett 71:2022–2025CrossRef

Kushwaha MS, Halevi P, Martínez G, Dobrzynski L, Djafari-Rouhani B (1994) Theory of acoustic band structure of periodic elastic composites. Phys Rev B 49:2313–2322CrossRef

Liu Y-H, Chang CC, Chern R-L, Chang CC (2007) Phononic band gaps of elastic periodic structures: a homogenization theory study. Phys Rev B 75:054104CrossRef

Liu Y, Su JY, Xu YL, Zhang XC (2009) The influence of pore shapes on the band structures in phononic crystals with periodic distributed void pores. Ultrasonics 49:276–280CrossRef

Liu Z, Wu B, He C (2014) Band-gap optimization of two-dimensional phononic crystals based on genetic algorithm and FPWE. Waves Random Complex Media 24:286–305MathSciNetCrossRef

Lu MH, Feng L, Chen YF (2009) Phononic crystals and acoustic metamaterials. Mater Today 12:34–42CrossRef

Men H, Nguyen NC, Freund RM, Parrilo PA, Peraire JJ (2010) Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods. Comput Phys 229(10):3706–3725MathSciNetCrossRefMATH

Pennec Y, Vasseur JO, Djafari-Rouhani B, Dobrzyński L, Deymier PA (2010) Two-dimensional phononic crystals: examples and applications. Surf Sci Rep 65:229–291CrossRef

Querin OM, Young V, Steven GP, Xie YM (2000) Computational efficiency and validation of bi-directional evolutionary structural optimisation. Comput Methods Appl Mech Eng 189:559–573CrossRefMATH

Rupp CJ, Evgrafov A, Maute K, Dunn ML (2007) Design of phononic materials/structures for surface wave devices using topology optimization. Struct Multidisc Optim 34:111–121MathSciNetCrossRefMATH

Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163:489–528MathSciNetCrossRefMATH

Seyranian AP, Lund E, Olhoff N (1994) Multiple eigenvalues in structural optimization problems. Struct Optim 8:207–227CrossRef

Sigalas M, Economou E (1992) Elastic and acoustic wave band structure. J Sound Vib 158:377–382CrossRef

Sigalas M, Economou EN (1993) Band structure of elastic waves in two dimensional systems. Solid State Commun 86:141–143CrossRef

Sigmund O, Hougaard K (2008) Geometric properties of optimal photonic crystals. Phys Rev Lett 100:153904CrossRef

Sigmund O, Jensen J (2003) Systematic design of phononic band-gap materials and structures by topology optimization. Philos Trans R Soc London, Ser A 361:1001–1019MathSciNetCrossRefMATH

Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16:68–75CrossRef

Vasseur J, Djafari-Rouhani B, Dobrzynski L, Kushwaha M, Halevi P (1994) Complete acoustic band gaps in periodic fibre reinforced composite materials: the carbon/epoxy composite and some metallic systems. J Phys Condens Matter 6:8759CrossRef

Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246MathSciNetCrossRefMATH

Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49:885–896CrossRef

Xie YM, Steven GP (1997) Basic evolutionary structural optimization. Springer, London

Yang X, Xie YM, Steven G, Querin O (1999) Bidirectional evolutionary method for stiffness optimization. AIAA J 37:1483–1488CrossRef

Titel: Evolutionary topological design for phononic band gap crystals
verfasst von: Yang fan Li
Xiaodong Huang
Fei Meng
Shiwei Zhou
Publikationsdatum: 04.03.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Structural and Multidisciplinary Optimization / Ausgabe 3/2016
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-016-1424-3

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 3/2016

Topology optimization for crashworthiness of thin-walled structures under axial impact using hybrid cellular automata

A multiscale method for optimising surface topography in elastohydrodynamic lubrication (EHL) using metamodels

Topology optimization of a coupled thermal-fluid system under a tangential thermal gradient constraint

A full-space barrier method for stress-constrained discrete material design optimization

Implementing a structural continuity constraint and a halting method for the topology optimization of energy absorbers

Representative surrogate problems as test functions for expensive simulators in multidisciplinary design optimization of vehicle structures

Premium Partner

Marktübersichten