nach oben

Structural and Multidisciplinary Optimization

Erschienen in:

01.10.2014 | RESEARCH PAPER

Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 4/2014

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

By using the finite element method and a “coarse to fine” two-stage genetic algorithm as the forward calculation method and the inverse search scheme, respectively, we perform both the unconstrained and constrained optimal design of the unit cell topology of the two-dimensional square-latticed solid phononic crystals (PnCs), to maximize the relative widths of the gaps between the adjacent energy bands of the PnCs. In the constrained optimizations, the maximization is subjected to the constraint of a predefined average density. In the numerical results, the variation patterns of the optimized structures with the order of the bandgap for both the out-plane shear and the in-plane mixed elastic wave modes are presented, and the effects of both the material contrast and the predefined average density on the obtained optimal structures are discussed.

Vorheriger Artikel Eigenvalue topology optimization of structures using a parameterized level set method

Nächster Artikel Sensitivity analysis of structural response to position of external applied load: in plane stress condition

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

Anderson C-M, Giapis K-P (1997) Symmetry reduction in group 4 mm photonic crystals. Phys Rev B 56:7313–7320CrossRef

Baker JE, Grefenstette JJ (1989) Proceedings of the third international confrenece on genetic algorithms. Morgan Kaufmann, Fairfax, p 20

Bilal OR, Hussein MI (2011) Ultrawide phononic band gap for combined in-plane and out-of-plane waves. Phys Rev E 84:065701CrossRef

Burger M, Osher SJ, Yablonovitch E (2004) Inverse problem techniques for the design of photonic crystals. IEICE Trans Electron E87C, pp 258–265

Cantú-Paz E (1998) A survey of parallel genetic algorithms. Res Sys Rep 10:141–170

Cox SJ, Dobson DC (1999) Maximizing band gaps in two dimensional photonic crystals. SIAM J Appl Math 59:2108–2120MathSciNetCrossRefMATH

Diaz AR, Haddow AG, Ma L (2005) Design of band-gap grid structures. Struct Multidisc Optim 29:418–431CrossRef

Du Q, Faber V, Gunzburger M (1999) Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev 41:637–676MathSciNetCrossRefMATH

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

Goldberg D (1989) Genetic algorithm in search, optimization and machine learning. Addison-Wesley Pub. Co., Reading

Halkjer S, Sigmund O, Jensen JS (2006) Maximizing band gaps in plate structures. Struct Multidisc Optim 32:263–275CrossRef

Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

Hussein MI, Hamza K, Hulbert G-M, Scoot RA, Saitou K (2006) Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics. Struct Multidiscip Optim 31:60–75CrossRef

Hussein MI, Hulbert G-M, Scoot RA (2007) Dispersive elastodynamics of 1D banded materials and structures: design. J Sound Vib 307:865–893CrossRef

Jong KD (1975) Analysis of the behavior of a class of genetic adaptive systems. University of Michigan Press, Ann Arbor

Khelif A, Houjaa AC, Benchabane S, Djafari-Rouhani B, Laude V (2004) Guiding and bending of acoustic waves in highly confined phononic crystal waveguides. Appl Phys Lett 84:4400–4402CrossRef

Kushwaha MS, Halevi P (1994) Band-gap engineering in periodic elastic composites. Appl Phys Lett 64:1085–108CrossRef

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

Li XF, Ni X, Feng L, Lu MH, He C, Chen YF (2011) Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode. Phys Rev Lett 106:084301CrossRef

Li JB, Wang YS, Zhang Ch (2012) Dispersion relations of a periodic array of fluid-filled holes embedded in an elastic solid. J Comput Acoust 20:1250014MathSciNetCrossRef

Liu YH, Chang CC, Chern RL, Chang CC (2007) Phononic band gaps of elastic periodic structures: a homogenization theory study. Phys Rev B 75:054104CrossRef

Malkova N, Kim S, Gopalan V (2002) Symmetrical perturbation analysis of complex two-dimensional photonic crystals. Phys Rev B 66:115113CrossRef

Malkova N, Kim S, Dilazaro T, Gopalan V (2003) Symmetrical analysis of complex two-dimensional hexagonal photonic crystals. Phys Rev B 67:125203CrossRef

Men H, Nguyen NC, Freund RM, Lim KM, Parrilo PA, Peraire J (2011) Design of photonic crystals with multiple and combined band gaps. Phys Rev E 83:046703CrossRef

Min R, Wu FG, Zhong LH, Zhong HL, Zhong S, Liu YY (2006) Extreme acoustic band gaps obtained under high symmetry in 2D phononic crystals. J Phys D 39:2272CrossRef

Preble S, Lipson M, Lipson H (2005) Two-dimensional photonic crystals designed by evolutionary algorithms. Appl Phys Lett 86:061111CrossRef

Richards D, Pines D (2003) Passive reduction of gear mesh vibration using a periodic drive shaft. J Sound Vib 264:317–342CrossRef

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

Shen LF, Zhou Y, He SL (2003) Design of two-dimensional photonic crystals with large absolute band gaps unsing a genetic algorithm. Phys Rev B 68:035109CrossRef

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

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

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

Su XX, Wang YF, Wang YS (2012) Effects of Poisson’s ratio on the band gaps and defect states in two-dimensional vacuum/solid porous phononic crystals. Ultrasonics 52:255–265CrossRef

Vesseur JO, Djafari-Rouhani B, Dobrzynski L, Kushwaha MS, 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 6:8759–8770CrossRef

Wang SY, Tai K (2005) Structural topology design optimization using genetic algorithms with a bit-array representation. Comput Methods Appl Mech Engng 194:3749–3770CrossRefMATH

Xu Z-L, Wu F-G, Mu Z-F (2007) Larger acoustic band gaps obtained by configurations of rods in two-dimensional phononic crystals. J Phys D Appl Phys 40:5584CrossRef

Zhong HL, Wu FG, Yao LN (2006) Application of genetic algorithm in optimization of band gap of two-dimensional phononic crystals. Acta Phy Sin 55:275–280

Zhou XZ, Wang YS, Zhang Ch (2009) Effects of materials parameters on elastic band gaps of phononic crystals. J Appl Phys 106:014903CrossRef

Titel: Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm
Publikationsdatum: 01.10.2014
Erschienen in: Structural and Multidisciplinary Optimization / Ausgabe 4/2014
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-014-1070-6

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 4/2014

The gradient projection method for structural topology optimization including density-dependent force

Element deformation scaling for robust geometrically nonlinear analyses in topology optimization

Eigenvalue topology optimization of structures using a parameterized level set method

Sensitivity analysis of structural response to position of external applied load: in plane stress condition

Bilevel multiobjective packaging optimization for automotive design

Seismic optimum design of triple friction pendulum bearing subjected to near-fault pulse-like ground motions

Premium Partner

Marktübersichten