Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Structural and Multidisciplinary Optimization
Erschienen in: Structural and Multidisciplinary Optimization 2/2013

01.02.2013 | Research Paper

Shape optimization of continua using NURBS as basis functions

verfasst von: Hideyuki Azegami, Shota Fukumoto, Taiki Aoyama

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 2/2013

Einloggen

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

search-config
loading …

Abstract

The present paper introduces a numerical solution to shape optimization problems of domains in which boundary value problems of partial differential equations are defined. In the present paper, the finite element method using NURBS as basis functions in the Galerkin method is applied to solve the boundary value problems and to solve a reshaping problem generated by the H1 gradient method for shape optimization, which has been developed as a general solution to shape optimization problems. Numerical examples of linear elastic continua illustrate that this solution works as well as using the conventional finite element method.
Vorheriger Artikel Structural optimization of composite structures with limited number of element properties
Nächster Artikel Conservative multi-objective optimization considering design robustness and tolerance: a quality engineering design approach

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
Literatur
Azegami H (1994) A solution to domain optimization problems. Trans Jpn Soc Mech Eng, Ser A 60:1479–1486 (in Japanese)CrossRef
Azegami H, Kaizu S, Takeuchi K (2011) Regular solution to topology optimization problems of continua. JSIAM Lett 3:1–4
Azegami H, Shimoda M, Katamine E, Wu ZC (1995) A domain optimization technique for elliptic boundary value problems. In: Hernandez S, El-Sayed M, Brebbia CA (eds) Computer aided optimization design of structures IV, structural optimization. Computational Mechanics Publications, Southampton, pp 51–58
Azegami H, Takeuchi K (2006) A smoothing method for shape optimization: traction method using the Robin condition. Int J Comput Methods 3(1):21–33MathSciNetMATHCrossRef
Azegami H, Yokoyama S, Katamine E (2002) Solution to shape optimization problems of continua on thermal elastic deformation. In: Tanaka M, Dulikravich GS (eds) Inverse problems in engineering mechanics III, chap. 2, sec. 1. Elsevier, Tokyo, pp 61–66CrossRef
Belegundu AD, Rajan SD (1988) A shape optimization approach based on natural design variables and shape functions. Comput Methods Appl Mech Eng 66:87–106MATHCrossRef
Cea J (1981a) Problems of shape optimization. In: Haug EJ, Cea J (eds) Optimization of distributed parameter structures, vol 2. Sijthoff & Noordhoff, Alphen aan den Rijn, pp 1005–1048
Cea J (1981b) Numerical methods of shape optimal design. In: Haug EJ, Cea J (eds) Optimization of distributed parameter structures, vol 2. Sijthoff & Noordhoff, Alphen aan den Rijn, pp 1049–1088
Cho S, Ha SH (2009) Isogeometric shape design optimization: exact geometry and enhanced sensitivity. Struct Multidisc Optim 38:53–70MathSciNetCrossRef
Choi KK, Kim NH (2005) Structural sensitivity analysis and optimization, vol 1. Springer, New York
Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis toward integration of CAD and FEA. Wiley, New York
Ha SH, Choi KK, Cho S (2010) Numerical method for shape optimization using t-spline based isogeometric method. Struct Multidisc Optim 42:417–428CrossRef
Haslinger J, Mäkinen RAE (2003) Introduction to shape optimization: theory, approximation and computation. Society for Industrial and Applied Mathematics, PhiladelphiaMATHCrossRef
Haslinger J, Neittaanmäki P (1988) Finite element approximation for optimal shape design: theory and application. Wiley, Chichester
Haslinger J, Neittaanmäki P (1996) Finite element approximation for optimal shape, material and topology design. Wiley, ChichesterMATH
Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4194MathSciNetMATHCrossRef
Inzarulfaisham AR, Azegami H (2004) Solution to boundary shape optimization problem of linear elastic continua with prescribed natural vibration mode shapes. Struct Multidisc Optim 27(3):210–217CrossRef
Iwai T, Sugimoto A, Aoyama T, Azegami H (2010) Shape optimization problem of elastic bodies for controlling contact pressure. JSIAM Lett 2:1–4
Iwata Y, Azegami H, Aoyama T, Katamine E (2010) Numerical solution to shape optimization problems for non-stationary navier-stokes problems. JSIAM Lett 2:37–40
Kaizu S, Azegami H (2006) Optimal shape problems and traction method. Trans Jpn Soc Ind Appl Math 16(3):277–290
Katamine E, Azegami H, Hirai M (2006) Solution of shape identification problems on thermoelastic solids. Int J Comput Methods 3(3):279–293MathSciNetMATHCrossRef
Katamine E, Azegami H, Tsubata T, Itoh S (2005) Solution to shape optimization problems of viscous flow fields. Int J Comput Fluid Dyn 19(1):45–51MathSciNetMATHCrossRef
Katamine E, Kawase Y, Azegami H (2008) Shape optimization of thermal forced convection fields. Heat Tran Asian Res 37(5):313–328CrossRef
Katamine E, Nagatomo Y, Azegami H (2009) Shape optimization of 3d viscous flow fields. Inverse Probl Sci Eng 17(1):105–114MATHCrossRef
Li K, Qian X (2011) Isogeometric analysis and shape optimization via boundary integral. Comput-Aided Des 43:1427–1437CrossRef
Manh ND, Evgrafov A, Gersborg AR, Gravesen J (2011) Isogeometric shape optimization of vibrating membranes. Comput Methods Appl Mech Eng 200:1343–1353MathSciNetMATHCrossRef
Mohammadi B, Pironneau O (2001) Applied shape optimization for fluids. Oxford University Press, OxfordMATH
Nagy AP, Abdalla MM, Gürdal Z (2011) Isogeometric design of elastic arches for maximum fundamental frequency. Struct Multidisc Optim 43:135–149CrossRef
Qian X, Sigmund O (2011) Isogeometric shape optimization of complex geometry via multiple compatible coons patches. Comput Methods Appl Mech Eng 200:2237–2255MathSciNetMATHCrossRef
Scherer M, Denzer R, Steinmann P (2010) A fictitious energy approach for shape optimization. Int J Numer Methods Eng 82:269–302MathSciNetMATH
Seo YD, Kim HJ, Youn SK (2010) Shape optimization and its extension to topological design based on isogeometric analysis. Int J Solids Struct 47:1618–1640MATHCrossRef
Shimoda M, Azegami H, Sakurai T (1998) Numerical solution for min-max problems in shape optimization: minimum design of maximum stress and displacement. JSME Int J Ser A 41(1):1–9CrossRef
Shimoda M, Tsuji J, Azegami H (2005) Minimum weight shape design for the natural vibration problem of plate and shell structures. In: Hernandez S, Brebbia CA (eds) Computer aided optimum design in engineering IX. WIT Press, Southampton, pp 147–156
Shimoda M, Tsuji J, Azegami H (2007) Non-parametric shape optimization method for thin-walled structures under strength criterion. In: Hernandez S, Brebbia CA (eds) Computer aided optimum design in engineering X. WIT Press, Southampton, pp 179–188CrossRef
Silva CAC, Bittencourt ML (2007) Velocity fields using nurbs with distortion control for structural shape optimization. Struct Multidisc Optim 33:147–159CrossRef
Simon J (1980) Differentiation with respect to the domain in boundary value problems. Numer Funct Anal Optim 2(7–8):649–687MathSciNetMATHCrossRef
Sokolowski J, Zolésio JP (1992) Introduction to shape optimization: shape sensitivity analysis. Springer, New YorkMATH
Yamada T, Izui K, Nishiwaki S, Takezawa A (2010) A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput Methods Appl Mech Eng 199:2876–2891MathSciNetMATHCrossRef
Yao TM, Choi KK (1989) 3-d shape optimal design and automatic finite element regridding. Int J Numer Methods Eng 28:369–384MATHCrossRef
Zolésio JP (1981a) The material derivative (or speed) method for shape optimization. In: Haug EJ, Cea J (eds) Optimization of distributed parameter structures, vol 2. Sijthoff & Noordhoff, Alphen aan den Rijn, pp 1089–1151
Zolésio JP (1981b) Domain variational formulation for free boundary problems. In: Haug EJ, Cea J (eds) Optimization of distributed parameter structures, vol 2. Sijthoff & Noordhoff, Alphen aan den Rijn, pp 1152–1194
Metadaten
Titel
Shape optimization of continua using NURBS as basis functions
verfasst von
Hideyuki Azegami
Shota Fukumoto
Taiki Aoyama
Publikationsdatum
01.02.2013
Verlag
Springer-Verlag
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 2/2013
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-012-0822-4

Weitere Artikel der Ausgabe 2/2013

Structural and Multidisciplinary Optimization 2/2013 Zur Ausgabe

Industrial Application

Optimization of variable blank holder force trajectory for springback reduction via sequential approximate optimization with radial basis function network

Research Paper

Comparison study between probabilistic and possibilistic methods for problems under a lack of correlated input statistical information

Research Paper

Microstructural topology optimization with respect to sound power radiation

Research Paper

Structural optimization of composite structures with limited number of element properties

Research Paper

Multi-objective design method based on evolution game and its application for suspension

Industrial Application

Optimization of the box section of the main girder of the bridge crane with the rail placed above the web plate

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
    Bildnachweise