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Erschienen in: Structural and Multidisciplinary Optimization 5/2014

01.11.2014 | EDUCATIONAL ARTICLE

GRAND — Ground structure based topology optimization for arbitrary 2D domains using MATLAB

verfasst von: Tomás Zegard, Glaucio H. Paulino

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 5/2014

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Abstract

The present work describes in detail an implementation of the ground structure method for non–orthogonal unstructured and concave domains written in MATLAB, called GRAND — GRound structure ANalysis and Design. The actual computational implementation is provided, and example problems are given for educational and testing purposes. The problem of ground structure generation is translated into a linear algebra approach, which is inspired by the video–game literature. To prevent the ground structure generation algorithm from creating members within geometric entities that no member should intersect (e.g. holes, passive regions), the concept of “restriction zones” is employed, which is based on collision detection algorithms used in computational geometry and video–games. The aim of the work is to provide an easy–to–use implementation for the optimization of least–weight trusses embedded in any domain geometry.

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Literatur
Zurück zum Zitat Achtziger W (2007) On simultaneous optimization of truss geometry and topology. Struct Multidiscip Optim 33(4–5):285– 304MathSciNetCrossRefMATH Achtziger W (2007) On simultaneous optimization of truss geometry and topology. Struct Multidiscip Optim 33(4–5):285– 304MathSciNetCrossRefMATH
Zurück zum Zitat Bendsøe M, Sigmund O (2003) Topology optimization: theory, methods and applications, 2nd edn. Springer, Berlin Bendsøe M, Sigmund O (2003) Topology optimization: theory, methods and applications, 2nd edn. Springer, Berlin
Zurück zum Zitat Christensen P, Klarbring A (2009) An introduction to structural optimization. Springer, BerlinMATH Christensen P, Klarbring A (2009) An introduction to structural optimization. Springer, BerlinMATH
Zurück zum Zitat Dorn W, Gomory R, Greenberg H (1964) Automatic design of optimal structures. J Mecanique 3(1):25–52 Dorn W, Gomory R, Greenberg H (1964) Automatic design of optimal structures. J Mecanique 3(1):25–52
Zurück zum Zitat Ericson C (2004) Real-time collision detection. Morgan Kaufmann, San Francisco Ericson C (2004) Real-time collision detection. Morgan Kaufmann, San Francisco
Zurück zum Zitat Gilbert M, Tyas A (2003) Layout optimization of large-scale pin-jointed frames. Eng Comput 20(8):1044–1064CrossRefMATH Gilbert M, Tyas A (2003) Layout optimization of large-scale pin-jointed frames. Eng Comput 20(8):1044–1064CrossRefMATH
Zurück zum Zitat Graczykowski C, Lewiński T (2005) The lightest plane structures of a bounded stress level transmitting a point load to a circular support. Control Cybern 34(1):227–253MATH Graczykowski C, Lewiński T (2005) The lightest plane structures of a bounded stress level transmitting a point load to a circular support. Control Cybern 34(1):227–253MATH
Zurück zum Zitat Heath M (1998) Scientific computing. An introductory survey, 2nd edn. McGraw Hill, New York Heath M (1998) Scientific computing. An introductory survey, 2nd edn. McGraw Hill, New York
Zurück zum Zitat Hemp W (1973) Optimum Structures. Oxford University Press, Oxford Hemp W (1973) Optimum Structures. Oxford University Press, Oxford
Zurück zum Zitat Hencky H (1923) Über einige statisch bestimmte Fälle des Gleichgewichts in plastischen Körpern. Z Angew Math Mech 747:241–251CrossRef Hencky H (1923) Über einige statisch bestimmte Fälle des Gleichgewichts in plastischen Körpern. Z Angew Math Mech 747:241–251CrossRef
Zurück zum Zitat Kicher TP (1966) Optimum design-minimum weight versus fully stressed. ASCE J Struct Div 92(ST 6):265–279 Kicher TP (1966) Optimum design-minimum weight versus fully stressed. ASCE J Struct Div 92(ST 6):265–279
Zurück zum Zitat Kirsch U (1993) Structural optimization: fundamentals and applications. Springer, BerlinCrossRef Kirsch U (1993) Structural optimization: fundamentals and applications. Springer, BerlinCrossRef
Zurück zum Zitat Lewiński T, Rozvany GIN, Sokół T, Bołbotowski K (2013) Exact analytical solutions for some popular benchmark problems in topology optimization III: L-shaped domains revisited. Struct Multidiscip Optim 47(6):937–942MathSciNetCrossRef Lewiński T, Rozvany GIN, Sokół T, Bołbotowski K (2013) Exact analytical solutions for some popular benchmark problems in topology optimization III: L-shaped domains revisited. Struct Multidiscip Optim 47(6):937–942MathSciNetCrossRef
Zurück zum Zitat Michell AGM (1904) The limits of economy of material in frame-structures. Phil Mag Ser 6 8(47):589–597CrossRefMATH Michell AGM (1904) The limits of economy of material in frame-structures. Phil Mag Ser 6 8(47):589–597CrossRefMATH
Zurück zum Zitat Ohsaki M (2010) Optimization of finite dimensional structures. CRC Press, Boca RatonCrossRef Ohsaki M (2010) Optimization of finite dimensional structures. CRC Press, Boca RatonCrossRef
Zurück zum Zitat Olson L (2013) Personal communication Olson L (2013) Personal communication
Zurück zum Zitat Rozvany G (2001) On design-dependent constraints and singular topologies. Struct Multidiscip Optim 21(2):164–172CrossRef Rozvany G (2001) On design-dependent constraints and singular topologies. Struct Multidiscip Optim 21(2):164–172CrossRef
Zurück zum Zitat Rozvany G, Sokół T (2013) Validation of numerical methods by analytical benchmarks, and verification of exact solutions by numerical methods. In: Topology optimization in structural and continuum mechanics. Springer, Vienna, Austria Rozvany G, Sokół T (2013) Validation of numerical methods by analytical benchmarks, and verification of exact solutions by numerical methods. In: Topology optimization in structural and continuum mechanics. Springer, Vienna, Austria
Zurück zum Zitat Smith ODS (1998) Generation of ground structures for 2D and 3D design domains. Eng Comput 15(4):462–500CrossRefMATH Smith ODS (1998) Generation of ground structures for 2D and 3D design domains. Eng Comput 15(4):462–500CrossRefMATH
Zurück zum Zitat Sokół T (2011) A 99 line code for discretized Michell truss optimization written in Mathematica. Struct Multidiscip Optim 43(2):181–190CrossRefMATH Sokół T (2011) A 99 line code for discretized Michell truss optimization written in Mathematica. Struct Multidiscip Optim 43(2):181–190CrossRefMATH
Zurück zum Zitat Sved G (1954) The minimum weight of certain redundant structures. Aust J Appl Sci 5:1–9 Sved G (1954) The minimum weight of certain redundant structures. Aust J Appl Sci 5:1–9
Zurück zum Zitat Sved G, Ginos Z (1968) Structural optimization under multiple loading. Int J Mech Sci 10:803–805CrossRef Sved G, Ginos Z (1968) Structural optimization under multiple loading. Int J Mech Sci 10:803–805CrossRef
Zurück zum Zitat Talischi C, Paulino GH, Pereira A, Menezes IFM (2012a) PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab. Struct Multidiscip Optim 45(3):309– 328MathSciNetCrossRefMATH Talischi C, Paulino GH, Pereira A, Menezes IFM (2012a) PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab. Struct Multidiscip Optim 45(3):309– 328MathSciNetCrossRefMATH
Zurück zum Zitat Talischi C, Paulino GH, Pereira A, Menezes IFM (2012b) PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. Struct Multidiscip Optim 45(3):329–357MathSciNetCrossRefMATH Talischi C, Paulino GH, Pereira A, Menezes IFM (2012b) PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. Struct Multidiscip Optim 45(3):329–357MathSciNetCrossRefMATH
Zurück zum Zitat Wright M (2005) The interior-point revolution in optimization: history, recent developments, and lasting consequences. Bull Am Math Soc 42(1):39–56CrossRefMATH Wright M (2005) The interior-point revolution in optimization: history, recent developments, and lasting consequences. Bull Am Math Soc 42(1):39–56CrossRefMATH
Metadaten
Titel
GRAND — Ground structure based topology optimization for arbitrary 2D domains using MATLAB
verfasst von
Tomás Zegard
Glaucio H. Paulino
Publikationsdatum
01.11.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 5/2014
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-014-1085-z

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