nach oben

Structural and Multidisciplinary Optimization

Erschienen in:

16.03.2017 | RESEARCH PAPER

Topology optimization using the p-version of the finite element method

verfasst von: Tam H. Nguyen, Chau H. Le, Jerome F. Hajjar

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 3/2017

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

A multiresolution topology optimization approach is proposed using the p-version finite element method (p-version FEM). Traditional topology optimization, where a density design variable is assigned to each element, is suitable for low-order h-version FEM. However, it cannot take advantage of the higher accuracy of higher-order p-version FEM analysis for generating results with higher resolution. In contrast, the proposed method separates density variables and finite elements so that the resolution of the density field, which defines the structure, can be higher than that of the finite element mesh. Thus, the method can take full advantage of the higher accuracy of p-version FEM.

Vorheriger Artikel A surrogate modeling approach for reliability analysis of a multidisciplinary system with spatio-temporal output

Nächster Artikel Optimal shape design of functionally graded thickness inversion tubes subjected to oblique loading

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

Aage N, Lazarov BS (2013) Parallel framework for topology optimization using the method of moving asymptotes. Struct Multidiscip Optim 47(4):493–505MathSciNetCrossRefMATH

Aage N, Nobel-Jørgensen M, Andreasen CS, Sigmund O (2013) Interactive topology optimization on hand-held devices. Struct Multidiscip Optim 47(1):1–6CrossRef

Aage N, Andreassen E, Lazarov BS (2014) Topology optimization using PETSc: an easy-to-use, fully parallel, open source topology optimization framework. Struct Multidiscip Optim 51(3):565–572MathSciNetCrossRef

Amir O, Bendsøe MP, Sigmund O (2009) Approximate reanalysis in topology optimization. Int J Numer Methods Eng 78(12):1474–1491MathSciNetCrossRefMATH

Amir O, Stolpe M, Sigmund O (2010) Efficient use of iterative solvers in nested topology optimization. Struct Multidiscip Optim 42(1):55–72CrossRefMATH

Amir O, Aage N, Lazarov BS (2014) On multigrid-CG for efficient topology optimization. Struct Multidiscip Optim 49(5):815–829MathSciNetCrossRef

Bendsoe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetCrossRefMATH

Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9):635–654MATH

Borrvall T, Petersson J (2001) Large-scale topology optimization in 3D using parallel computing. Comput Methods Appl Mech Eng 190(46–47):6201–6229CrossRefMATH

Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26–27):3443–3459CrossRefMATH

Challis VJ, Roberts AP, Grotowski JF (2014) High resolution topology optimization using graphics processing units (GPUs). Struct Multidiscip Optim 49(2):315–325CrossRef

Cook RD, Malkus DS, Plesha ME, Witt RJ (2007) Concepts and Applications of Finite Element Analysis, John Wiley & Sons, New York

Costa JCA Jr, Alves MK (2003) Layout optimization with h-adaptivity of structures. Int J Numer Methods Eng 58(1):83–102CrossRefMATH

Diaz A, Sigmund O (1995) Checkerboard patterns in layout optimization. Struct Multidiscip Optim 10(1):40–45CrossRef

Düster A, Bröker H, Rank E (2001) The p-version of the finite element method for three-dimensional curved thin walled structures. Int J Numer Methods Eng 52(7):673–703CrossRefMATH

Düster A, Parvizian J, Yang Z, Rank E (2008) The finite cell method for three-dimensional problems of solid mechanics. Comput Methods Appl Mech Eng 197(45):3768–3782MathSciNetCrossRefMATH

Evgrafov A (2014) State space Newton’s method for topology optimization. Comput Methods Appl Mech Eng 278:272–290MathSciNetCrossRef

Evgrafov A, Rupp CJ, Maute K, Dunn ML (2008) Large-scale parallel topology optimization using a dual-primal substructuring solver. Struct Multidiscip Optim 36(4):329–345MathSciNetCrossRefMATH

Guest JK, Smith Genut LC (2010) Reducing dimensionality in topology optimization using adaptive design variable fields. Int J Numer Methods Eng 81(8):1019–1045MATH

Guest J, Prévost J, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238–254MathSciNetCrossRefMATH

Guo X, Zhang W, Zhong W (2014) Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J Appl Mech 81(8):081009CrossRef

Jog CS, Haber RB (1996) Stability of finite element models for distributed-parameter optimization and topology design. Comput Methods Appl Mech Eng 130(3–4):203–226MathSciNetCrossRefMATH

Kim JE, Jang GW, Kim YY (2003) Adaptive multiscale wavelet-Galerkin analysis for plane elasticity problems and its applications to multiscale topology design optimization. Int J Solids Struct 40(23):6473–6496CrossRefMATH

Kim TS, Kim JE, Kim YY (2004) Parallelized structural topology optimization for eigenvalue problems. Int J Solids Struct 41(9–10):2623–2641CrossRefMATH

Le C, Norato J, Bruns T, Ha C, Tortorelli D (2010) Stress-based topology optimization for continua. Struct Multidiscip Optim 41(4):605–620CrossRef

Le C, Bruns T, Tortorelli D (2011) A gradient-based, parameter-free approach to shape optimization. Comput Methods Appl Mech Eng 200(9):985–996MathSciNetCrossRefMATH

Matsui K, Terada K (2004) Continuous approximation of material distribution for topology optimization. Int J Numer Methods Eng 59(14):1925–1944MathSciNetCrossRefMATH

Maute K, Ramm E (1995) Adaptive topology optimization. Struct Multidiscip Optim 10(2):100–112CrossRefMATH

Mello LAM, De Sturler E, Paulino GH, Silva ECN (2010) Recycling Krylov subspaces for efficient large-scale electrical impedance tomography. Comput Methods Appl Mech Eng 199(49–52):3101–3110MathSciNetCrossRefMATH

Nguyen TH (2010) System reliability-based design and multiresolution topology optimization. Ph.D thesis, University of Illinois at Urbana-Champaign

Nguyen TH, Paulino GH, Song J, Le CH (2010a) A computational paradigm for multiresolution topology optimization (MTOP). Struct Multidiscip Optim 41(4):525–539MathSciNetCrossRefMATH

Nguyen TH, Song J, Paulino GH (2010b) Single-loop system reliability-based design optimization using matrix-based system reliability method: theory and applications. J Mech Des 132(1):011005CrossRef

Nguyen TH, Song J, Paulino GH (2010c) Challenges and advances in system reliability based optimization of structural topology. In: Proceedings of the 19th Analysis and Computation Specialty Conference, ASCE Conf. Proc. doi:10.1061/41131(370)42

Nguyen TH, Song J, Paulino GH (2011) Single-loop system reliability-based topology optimization considering statistical dependence between limit-states. Struct Multidiscip Optim 44(5):593–611MathSciNetCrossRefMATH

Nguyen TH, Paulino GH, Song J, Le CH (2012) Improving multiresolution topology optimization via multiple discretizations. Int J Numer Methods Eng 92(6):507–530MathSciNetCrossRefMATH

Nguyen TH, Le CH, Hajjar JF (2013) High-order finite elements for topology optimization. In: 10th world congress on structural and multidisciplinary optimization, Orlando

Norato JA, Bendsøe MP, Haber RB, Tortorelli DA (2007) A topological derivative method for topology optimization. Struct Multidiscip Optim 33(4):375–386MathSciNetCrossRefMATH

Olhoff N, Bendsøe MP, Rasmussen J (1991) On CAD-integrated structural topology and design optimization. Comput Methods Appl Mech Eng 89(1):259–279CrossRefMATH

Parvizian J, Düster A, Rank E (2012) Topology optimization using the finite cell method. Optim Eng 13(1):57–78MathSciNetCrossRefMATH

Rozvany G (1996) Some shortcomings in Michell’s truss theory. Struct Multidiscip Optim 12(4):244–250MathSciNetCrossRef

Rozvany G (1998) Exact analytical solutions for some popular benchmark problems in topology optimization. Struct Multidiscip Optim 15(1):42–48CrossRefMATH

Rozvany G, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Multidiscip Optim 4(3):250–252CrossRef

Schmidt S, Schulz V (2012) A 2589 line topology optimization code written for the graphics card. Comput Vis Sci 16:249–256MathSciNet

Sigmund O (2000) Topology optimization: a tool for the tailoring of structures and materials. Philos Trans R Soc London, Ser A 358:211–227MathSciNetCrossRefMATH

Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4):401–424MathSciNetCrossRef

Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Multidiscip Optim 16(1):68–75CrossRef

Stainko R (2006) An adaptive multilevel approach to the minimal compliance problem in topology optimization. Commun Numer Methods Eng 22(2):109–118MathSciNetCrossRefMATH

Sutradhar A, Paulino GH, Miller MJ, Nguyen TH (2010) Topological optimization for designing patient-specific large craniofacial segmental bone replacements. Proc Natl Acad Sci 107(30):13222–13227CrossRef

Suzuki K, Kikuchi N (1991) A homogenization method for shape and topology optimization. Comput Methods Appl Mech Eng 93(3):291–318CrossRefMATH

Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATH

Szabo BA, Babuska I (1991) Finite element analysis. Wiley, New YorkMATH

Szabó B, Düster A, Rank E (eds) (2004) The p-Version of the Finite Element Method vol 1. Encyclopedia of Computational Mechanics

Takezawa A, Kitamura M (2012) Geometrical design of thermoelectric generators based on topology optimization. Int J Numer Methods Eng 90(11):1363–1392CrossRefMATH

Toogood R, Zecher J (2013) Creo Parametric 2.0 Tutorial. SDC Publications

Vatanabe SL, Paulino GH, Silva ECN (2012) Influence of pattern gradation on the design of piezocomposite energy harvesting devices using topology optimization. Compos Part B 43(6):2646–2654CrossRef

Wang S, Sturler E, Paulino GH (2007) Large-scale topology optimization using preconditioned Krylov subspace methods with recycling. Int J Numer Methods Eng 69(12):2441–2468MathSciNetCrossRefMATH

Zhang W, Yuan J, Zhang J, Guo X (2016) A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model. Struct Multidiscip Optim 53(6):1243–1260

Titel: Topology optimization using the p-version of the finite element method
verfasst von: Tam H. Nguyen
Chau H. Le
Jerome F. Hajjar
Publikationsdatum: 16.03.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Structural and Multidisciplinary Optimization / Ausgabe 3/2017
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-017-1675-7

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 3/2017

Topology optimization of freely vibrating continuum structures based on nonsmooth optimization

Shape and topology optimization of acoustic lens system using phase field method

A decoupling approach for evidence-theory-based reliability design optimization

Boundary shape design by using PDE filtered design variables

Global sensitivity analysis for fiber reinforced composite fiber path based on D-MORPH-HDMR algorithm

Optimal shape design of functionally graded thickness inversion tubes subjected to oblique loading

Premium Partner

Marktübersichten