Skip to main content
Erschienen in: Structural and Multidisciplinary Optimization 6/2013

01.06.2013 | Research Paper

Symmetry properties in structural optimization: some extensions

verfasst von: Xu Guo, Zongliang Du, Gengdong Cheng, Changhui Ni

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 6/2013

Einloggen

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

search-config
loading …

Abstract

In the present paper, some extensions of the previous theoretical results about the symmetry properties of structural optimization problems are reported. It is found that generally the condition of convexity can be relaxed to quasi-convexity in order to guarantee the existence of symmetry global optima. Furthermore, some new results about the symmetry properties of robust and discrete structural optimization problems are also presented. Numerous concrete examples illustrate the claims made in the present work explicitly.

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!

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!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
Zurück zum Zitat Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press
Zurück zum Zitat Cheng GD, Liu XF (2011) Discussion on symmetry of optimum topology design. Struct Multidisc Optim 44:713–717MathSciNetCrossRef Cheng GD, Liu XF (2011) Discussion on symmetry of optimum topology design. Struct Multidisc Optim 44:713–717MathSciNetCrossRef
Zurück zum Zitat Guo X, Bai W, Zhang WS, Gao XX (2009) Confidence structural robust design and optimization under stiffness and load uncertainties. Comput Methods Appl Mech Eng 198:3378–3399MathSciNetMATHCrossRef Guo X, Bai W, Zhang WS, Gao XX (2009) Confidence structural robust design and optimization under stiffness and load uncertainties. Comput Methods Appl Mech Eng 198:3378–3399MathSciNetMATHCrossRef
Zurück zum Zitat Guo X, Ni CH, Cheng GD, Du ZL (2012) Some symmetry results for optimal solutions in structural optimization. Struct Multidisc Optim 46:631–645MathSciNet Guo X, Ni CH, Cheng GD, Du ZL (2012) Some symmetry results for optimal solutions in structural optimization. Struct Multidisc Optim 46:631–645MathSciNet
Zurück zum Zitat Guo X, Zhang WS, Zhang L (2013) Robust structural topology optimization considering boundary uncertainties. Comput Methods Appl Mech Eng 253:356–368CrossRef Guo X, Zhang WS, Zhang L (2013) Robust structural topology optimization considering boundary uncertainties. Comput Methods Appl Mech Eng 253:356–368CrossRef
Zurück zum Zitat Healey TJ (1989) Symmetry and equivalence in nonlinear elastostatics part I. Arch Ration Mech Anal 105:205–228MathSciNetCrossRef Healey TJ (1989) Symmetry and equivalence in nonlinear elastostatics part I. Arch Ration Mech Anal 105:205–228MathSciNetCrossRef
Zurück zum Zitat Kang JS, Suh MH, Lee TY (2004) Robust economic optimization of process design under uncertainty. Eng Optim 36:51–75MathSciNetCrossRef Kang JS, Suh MH, Lee TY (2004) Robust economic optimization of process design under uncertainty. Eng Optim 36:51–75MathSciNetCrossRef
Zurück zum Zitat Kangwai RD, Guest SD, Pellegrino S (1999) An introduction to the analysis of symmetric structures. Comput Struct 71:671–688MathSciNetCrossRef Kangwai RD, Guest SD, Pellegrino S (1999) An introduction to the analysis of symmetric structures. Comput Struct 71:671–688MathSciNetCrossRef
Zurück zum Zitat Rozvany GIN (2011a) On symmetry and non-uniqueness in exact topology optimization. Struct Multidisc Optim 43:297–317MathSciNetCrossRef Rozvany GIN (2011a) On symmetry and non-uniqueness in exact topology optimization. Struct Multidisc Optim 43:297–317MathSciNetCrossRef
Zurück zum Zitat Rozvany GIN (2011b) Author’s reply to a discussion by Gengdong Cheng and Xiaofeng Liu of the review article “On symmetry and non-uniqueness in exact topology optimization” by George I.N. Rozvany (2011, Struct Multidisc Optim 43:297–317). Struct Multidisc Optim 44:719–721MathSciNetCrossRef Rozvany GIN (2011b) Author’s reply to a discussion by Gengdong Cheng and Xiaofeng Liu of the review article “On symmetry and non-uniqueness in exact topology optimization” by George I.N. Rozvany (2011, Struct Multidisc Optim 43:297–317). Struct Multidisc Optim 44:719–721MathSciNetCrossRef
Zurück zum Zitat Sandgren E, Cameron TM (2002) Robust design optimization of structures through consideration of variation. Comput Struct 80:1605–1613CrossRef Sandgren E, Cameron TM (2002) Robust design optimization of structures through consideration of variation. Comput Struct 80:1605–1613CrossRef
Zurück zum Zitat Seepersad CC, Allen JK, McDowell DL, Mistree F (2006) Robust design of cellular materials with topological and dimensional imperfections. J Mech Des Trans ASME 128:1285–1297CrossRef Seepersad CC, Allen JK, McDowell DL, Mistree F (2006) Robust design of cellular materials with topological and dimensional imperfections. J Mech Des Trans ASME 128:1285–1297CrossRef
Zurück zum Zitat Sigmund O (2009) Manufacturing tolerant topology optimization. Acta Mech Sin 25:227–239CrossRef Sigmund O (2009) Manufacturing tolerant topology optimization. Acta Mech Sin 25:227–239CrossRef
Zurück zum Zitat Stolpe M (2010) On some fundamental properties of structural topology optimization problems. Struct Multidisc Optim 41:661–670CrossRef Stolpe M (2010) On some fundamental properties of structural topology optimization problems. Struct Multidisc Optim 41:661–670CrossRef
Zurück zum Zitat Stolpe M, Svanberg K (2001) On trajectories of penalization for topology optimization. Struct Multidisc Optim 21:128–139CrossRef Stolpe M, Svanberg K (2001) On trajectories of penalization for topology optimization. Struct Multidisc Optim 21:128–139CrossRef
Zurück zum Zitat Takezawa A, Nii S, Kitamura M, Kogiso N (2011) Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system. Comput Methods Appl Mech Eng 200:2268–2281MathSciNetMATHCrossRef Takezawa A, Nii S, Kitamura M, Kogiso N (2011) Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system. Comput Methods Appl Mech Eng 200:2268–2281MathSciNetMATHCrossRef
Zurück zum Zitat Watada R, Ohsaki M, Kanno Y (2011) Non-uniqueness and symmetry of optimal topology of a shell for minimum compliance. Struct Multidisc Optim 43:459–471CrossRef Watada R, Ohsaki M, Kanno Y (2011) Non-uniqueness and symmetry of optimal topology of a shell for minimum compliance. Struct Multidisc Optim 43:459–471CrossRef
Zurück zum Zitat Zingoni A (2009) Group-theoretic exploitation of symmetry in computational solid and structural mechanics. Int J Numer Methods Eng 79:253–289MathSciNetMATHCrossRef Zingoni A (2009) Group-theoretic exploitation of symmetry in computational solid and structural mechanics. Int J Numer Methods Eng 79:253–289MathSciNetMATHCrossRef
Metadaten
Titel
Symmetry properties in structural optimization: some extensions
verfasst von
Xu Guo
Zongliang Du
Gengdong Cheng
Changhui Ni
Publikationsdatum
01.06.2013
Verlag
Springer-Verlag
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 6/2013
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-012-0877-2

Weitere Artikel der Ausgabe 6/2013

Structural and Multidisciplinary Optimization 6/2013 Zur Ausgabe

    Marktübersichten

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