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Methoden zur Topologieoptimierung

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Optimierung mechanischer Strukturen

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Zusammenfassung

Die Topologie eines Bauteils, d. h. die Lage und Anordnung von Strukturelementen, kann das Strukturverhalten entscheidend beeinflussen. Eine Topologieoptimierung muss deshalb in einem sehr frühen Stadium des Entwurfsprozesses erfolgen. Die meisten heutigen Topologieoptimierungsverfahren liefern Design-Vorschläge basierend auf wenigen Vorgaben wie zulässiger Entwurfsraum, Lagerung und Belastung. In der Regel werden einfache Optimierungsfunktionale, wie das Gewicht und die mittlere Nachgiebigkeit (vgl. Abschn. 2.4) berücksichtigt. Diese Design-Vorschläge müssen dann in eine Konstruktion umgesetzt werden. In diesem Kapitel werden zunächst diese Verfahren behandelt. Die direkte Berücksichtigung aller in der Formoptimierung üblichen Optimierungsfunktionale ist nur mit der parametrischen Beschreibung der Bauteilränder möglich. Dies führt zu wesentlich aufwändigeren Verfahren, welche danach beschrieben werden.

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Literatur

  • Atrek E (1989) SHAPE: a program for shape optimization of continuum structures. In: Proceedings of the first international conference, Opti'89. Comp. Mechanics Publications. Springer, Berlin, S 135–144

    Google Scholar 

  • Beckers M (1999) Topology optimization using a dual method with discrete variables. Struct Optim 17:14–24

    Google Scholar 

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

    Google Scholar 

  • Bendsøe MP, Mota Soares CA (1993) Topology design of structures. Kluwer Academic, Dordrecht

    Book  Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology optimization – theory, methods and applications. Springer, Berlin

    MATH  Google Scholar 

  • Courant R, Robbins H (1962) Was ist Mathematik? Springer, Göttingen

    Book  Google Scholar 

  • Dienemann R (2018) Entwicklung einer Optimierungsmethodik für die Form- und Topologieoptimierung von tiefziehbaren Blechstrukturen. Dissertation an der Bergischen Universität Wuppertal, Shaker

    Google Scholar 

  • Dienemann R, Schumacher A, Fiebig S (2017) Using topology optimization for finding shell structures manufactured by deep-drawing. J Struct Multidiscip Optim 56:473–485

    Article  Google Scholar 

  • Dienemann R, Schumacher A, Fiebig S (2018) An element deactivation and reactivation scheme for the topology optimization based on the density method. In: Schumacher A, Vietor T, Fiebig S, Bletzinger K-U, Maute K (Hrsg) Advances in structural and multidisciplinary optimization, proceedings of the 12th world congress of structural and multidisciplinary optimization (WCSMO12). Springer Nature, Beijing, S 1127–1142

    Chapter  Google Scholar 

  • Dienemann R, Schumacher A, Fiebig S (2019) Considering linear buckling for 3D density based topology optimization. In: Rodrigues H et al (Hrsg) EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization. Springer Nature Switzerland, Cham, S 394–406

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Eschenauer HA, Kobelev VV, Schumacher A (1994) Bubble method for topology and shape optimization of structures. J Struct Optim 8:42–51

    Article  Google Scholar 

  • Franke T (2018) Fertigungsgerechte Bauteilgestaltung in der Topologieoptimierung auf Grundlage einer integrierten Gießsimulation. Logos, Berlin

    Google Scholar 

  • Hafsa S, Butt J, Schumacher A (2019) New geometric features in the topology optimization for adaptation of structures. In X Guo, H Huang (ed.) Advances in Structural and Multidisciplinary Optimization, ISBN 978-7-89437-207-9, S 258–263

    Google Scholar 

  • Hajela P, Lee E, Lin CY (1993) Genetic algorithms in structural topology optimization. In: Bendsøe MP, Mota Soares CA (Hrsg) Topology design of structures. Kluwer Academic Publishers, Netherlands, S 117–133

    Google Scholar 

  • Harzheim L, Graf G (2001) The importance of topology optimisation in the development process, Proceedings of NAFEMS world congress 2001 on the evolution of product simulation Vol. 1, Lake Como, Italy, 24–28 April 2001, S 361–372

    Google Scholar 

  • Harzheim L, Graf G, Klug S, Liebers J (1999) Topologieoptimierung im praktischen Einsatz. ATZ Automobiltech Z 101(7/8):530–539

    Article  Google Scholar 

  • Hassani B, Hinton E (1998) A review on homogenization and topology optimization: I. Homogenization theory for media with periodic structure. Comput Struct 69:707–717. II. Analytical and numerical solution of homogenization equations. Comput Struct 69:719–738, III. Topology optimization using optimality criteria. Comput Struct 69:739–756

    Google Scholar 

  • Hörnlein H (1994) Topologieoptimierung von Stabstrukturen, VDI/WZL-Seminar 32-63-08: Optimierungsstrategien mit der Finite Element Methode, Aachen

    Google Scholar 

  • Jäger J (1980) Elementare Topologie. Schöning, Paderborn

    MATH  Google Scholar 

  • Jänisch K (1980) Topologie. Springer, Berlin/Heidelberg

    Book  Google Scholar 

  • Kirsch U (1990) On the relationship between optimum structural and geometries. J Struct Optim 2:39–45

    Article  Google Scholar 

  • Kölsch G (1992) Diskrete Optimierungsverfahren zur Lösung konstruktiver Problemstellungen im Werkzeugmaschinenbau. Fortschr.-Ber. VDI-Reihe 1, Nr. 213, Düsseldorf

    Google Scholar 

  • Koumousis VK (1993) Layout and sizing design of civil engineering structures in accordance with the eurocodes. In: Bendsøe MP, Mota Soares CA (Hrsg) Topology design of structures. Kluwer Academic Publishers, Dordrecht, S 103–116

    Chapter  Google Scholar 

  • Mattheck C (1992) Design in der Natur – Der Baum als Lehrmeister. Rombach, Freiburg

    Google Scholar 

  • Michell AGM (1904) The limits of economy of materials in frame structures. Philos Mag, Series 6 8(47):589–597

    Article  Google Scholar 

  • Mußchelischwili NI (1971) Einige Grundaufgaben zur mathematischen Elastizitätstheorie. VEB Fachbuchverlag, Leipzig

    Google Scholar 

  • Neuber H (1985) Kerbspannungslehre. Springer, Berlin/Heidelberg

    Book  Google Scholar 

  • Padula S, Sandridge CA (1993) Passive/active strut placement by integer programming. In: Bendsøe MP, Soares M (Hrsg) Topology design of structures. Kluwer Academic, Dordrecht, S 145–156

    Chapter  Google Scholar 

  • Pederson P (1989) On optimal orientation of orthotropic materials. J Structural Optimization 1:101–106

    Article  Google Scholar 

  • Prager W (1974) A note on discretized Michell structures. Comput Methods Appl Mech Eng 3:349–355

    Article  Google Scholar 

  • Ramsaier M, Stetter R, Till M, Rudolph S, Schumacher A (2018) Automatic definition of density-driven topology optimization with graph-based design languages. In: Schumacher A, Vietor T, Fiebig S, Bletzinger K-U, Maute K (Hrsg) Advances in structural and multidisciplinary optimization. Springer Nature, Cham, S 1168–1184

    Chapter  Google Scholar 

  • Ramsaier M, Breckle T, Till M, Rudolph S, Schumacher A (2019) Automated evaluation of manufacturability and cost of steel tube constructions with graph-based design languages, 13th CIRP conference on intelligent computation in manufacturing engineering, Elsevier

    Google Scholar 

  • Ringertz UT (1986) A branch and bound – algorithm for topology optimization of truss structures. Eng Optim 10:111–124

    Article  Google Scholar 

  • Rodriguez J, Seireg A (1985) Optimizing the shape of structures via a rule-based computer program. Com Mech Eng:20–28

    Google Scholar 

  • Rozvany GIN, Zhou M, Rotthaus M, Gollub W, Spengemann F (1989) Continuum-type optimality criteria methods for large Finite Element Systems with a displacement constraints, Part I + II. J Struct Optim 1:47–72

    Google Scholar 

  • Russel DM, Manoochehri SP (1989) A two dimensional rule-based shape synthesis method. Proc ASME Advances Des Autom DE 19-2:217–224

    Google Scholar 

  • Sawin GN (1956) Spannungserhöhung am Rande von Löchern. VEB Verlag Technik, Berlin

    MATH  Google Scholar 

  • Schlosser M, Schumacher A, Bellendir K (2019) Effective modeling of load applications in composite structures – accuracy, complexity, computer time; selected papers from the „22 nd Symposium on Composites“, June 26–28, 2019, Kaiserslautern, Germany, S 461–466

    Google Scholar 

  • Schumacher A (1996) Topologieoptimierung von Bauteilstrukturen unter Verwendung von Lochpositionierungskriterien. Dissertation, Universität-GH Siegen, FOMAAS, TIM-Bericht T09-01.96

    Google Scholar 

  • Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidisc Optim 21:120–127

    Article  Google Scholar 

  • Sigmund O (2020) www.topopt.dtu.dk

  • Weider K, Schumacher A (2016) On the calculation of topological derivatives considering an exemplary nonlinear material model. Proc Appl Math Mech 16:717–718. 2016

    Article  Google Scholar 

  • Weider K, Schumacher A (2018) A topology optimization scheme for crash loaded structures using Topological Derivatives. In: Schumacher A, Vietor T, Fiebig S, Bletzinger K-U, Maute K (Hrsg) Advances in structural and multidisciplinary optimization, proceedings of the 12th world congress of structural and multidisciplinary optimization (WCSMO12). Springer Nature, Beijing, S 1601–1614

    Chapter  Google Scholar 

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  1. Fakultät 7, Lehrstuhl für Optimierung mechanischer Strukturen, Bergische Universität Wuppertal, Wuppertal, Deutschland

    Axel Schumacher

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  1. Axel Schumacher
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Schumacher, A. (2020). Methoden zur Topologieoptimierung. In: Optimierung mechanischer Strukturen. Springer Vieweg, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60328-4_8

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  • DOI: https://doi.org/10.1007/978-3-662-60328-4_8

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  • Online ISBN: 978-3-662-60328-4

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