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Enhanced growth method for topology and geometry optimization of truss structures

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Abstract

In this paper, we present an enhanced growth method based on virtual displacements and strains fields for generating optimal design in terms of topology and geometry of plane trusses without the need of a generation of so-called ground structure. The method has been applied to the single load case problem with stress and size constraints in plastic design. In order to demonstrate the reliability and accuracy of the proposed method, three examples are carried out: Hemp cantilever, Chan cantilever and McConnel structure.

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Notes

  1. The algorithm allows for using different values of \(\sigma _T\) and \(\sigma _C\), but for the sake of simplicity of presented examples it was assumed that both of these values are equal to \(\sigma _{ 0 }\).

References

  • Achtziger W (1997) Topology optimization of discrete structures. In: Rozvany GIN (ed) Topology optimization in structural mechanics, vol 374. International Centre for Mechanical Sciences (Courses and Lectures). Springer, Vienna, pp 57–100

    Chapter  Google Scholar 

  • Achtziger W (1998) Multiple-load truss topology and sizing optimization: Some properties of minimax compliance. J Optim Theory Appl 98(2):255–280

    Article  MathSciNet  Google Scholar 

  • Achtziger W (2007) On simultaneous optimization of truss geometry and topology. Struct Multidisc Optim 33(4–5):285–304

    Article  MathSciNet  Google Scholar 

  • Chan ASL (1960) The design of Michell optimum structures. Tech. rep, Cranfield College of Aeronautics

    Google Scholar 

  • Chan HSY (1963) Optimum Michell frameworks for three parallel forces. Tech. rep, Cranfield College of Aeronautics

    Google Scholar 

  • Dorn WS, Gomory RE, Greenberg HJ (1964) Automatic design of optimal structures. J de Mecanique 3:25–52

    Google Scholar 

  • Eichhammer E (2018) QCustomPlot 2.0.1 documentation. https://www.qcustomplot.com/documentation/

  • Fairclough HE, Gilbert M, Pichugin AV, Tyas A, Firth I (2018) Theoretically optimal forms for very long-span bridges under gravity loading. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474(2217):20170726

    Article  MathSciNet  Google Scholar 

  • Fairclough HE, He L, Pritchard TJ, Gilbert M (2021) Layopt: an educational web-app for truss layout optimization. Struct Multidisc Optim 64, 2805–2823 . https://www.layopt.com

  • Gilbert M, Tyas A (2003) Layout optimization of large-scale pin-jointed frames. Eng Comput 20(8):1044–1064

    Article  Google Scholar 

  • Graczykowski C, Lewiński T (2010) Michell cantilevers constructed within a half strip. tabulation of selected benchmark results. Struct Multidisc Optim 42(6):869–877

    Article  Google Scholar 

  • He L, Gilbert M (2015) Rationalization of trusses generated via layout optimization. Struct Multidisc Optim 52(4):677–694

    Article  MathSciNet  Google Scholar 

  • Hemp WS (1974) Michell framework for uniform load between fixed supports. Eng Optim 1(1):61–69

    Article  Google Scholar 

  • Lewiński T, Sokół T, Graczykowski C (2018) Michell structures. Springer

  • Martinez P, Marti P, Querin OM (2007) Growth method for size, topology, and geometry optimization of truss structures. Struct Multidisc Optim 33(1):13–26

    Article  Google Scholar 

  • Mazurek A (2012) Geometrical aspects of optimum truss like structures for three-force problem. Struct Multidisc Optim 45(1):21–32

    Article  MathSciNet  Google Scholar 

  • McConnel RE (1974) Least-weight frameworks for loads across span. J Eng Mech 100:10872

    Google Scholar 

  • Michell AGM (1904) The limits of economy of material in frame-structures. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 8(47):589–597

    Article  Google Scholar 

  • MosekAps: MOSEK Fusion API for C++. Version 9.2.38. (2021). https://docs.mosek.com/9.2/cxxfusion/index.html

  • Nocedal J, Wright S (2006) Numerical optimization. Springer Science & Business Media, New York

    MATH  Google Scholar 

  • Prager W, Rozvany GIN (1977) Optimization of structural geometry. Dynamical systems pp. 265–293

  • Prata S (2011) C++ primer plus. Addison-Wesley Professional

  • Pritchard TJ, Gilbert M, Tyas A (2005) Plastic layout optimization of large-scale frameworks subject to multiple load cases, member self-weight and with joint length penalties. Proc of 6th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil

  • QtGroup: Qt framework documentation (2021). https://doc.qt.io/

  • Rozvany GIN (1976) Optimal design of flexural systems: beams, grillages, slabs, plates and shells. Pergamon Press, Oxford

  • Sokół T (2015) Multi-load truss topology optimization using the adaptive ground structure approach. In: Łodygowski T, Rakowski J, Litewka P (eds) Recent advances in computational mechanics. CRC Press, London, pp 9–16

    Google Scholar 

  • Sokół T (2017) On the numerical approximation of Michell trusses and the improved ground structure method. In: Schumacher A, Vietor T, Fiebig S, Bletzinger KU, Maute K (eds) Advances in Structural and Multidisciplinary Optimization. WCSMO, Springer, Cham

    Google Scholar 

  • Sokół T, Lewiński T (2010) On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight. Struct Multidisc Optim 42(6):835–853

    Article  MathSciNet  Google Scholar 

  • Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106(1):25–57

    Article  MathSciNet  Google Scholar 

  • Weldeyesus AG, Gondzio J (2018) A specialized primal-dual interior point method for the plastic truss layout optimization. Comput Optim Appl 71(3):613–640

    Article  MathSciNet  Google Scholar 

  • Williams A (2019) C++ concurrency in action, vol. 2. Manning Publications

  • Wright SJ (1997) Primal-dual interior-point methods. SIAM, Thailand

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Acknowledgements

The paper was prepared within the Research Grant no 2019/33/B/ST8/00325 financed by the National Science Centre (Poland), entitled: Merging the optimum design problems of structural topology and of the optimal choice of material characteristics. The theoretical foundations and numerical methods.

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Authors and Affiliations

  1. Department of Structural Mechanics and Computer Aided Engineering, Faculty of Civil Engineering, Warsaw University of Technology, Al.Armii Ludowej 16, 00-637, Warsaw, Poland

    Grzegorz Kozłowski & Tomasz Sokół

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  1. Grzegorz Kozłowski
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  2. Tomasz Sokół
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Correspondence to Tomasz Sokół.

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The starting points used to generate all numerical examples are available in the Electronic Supplementary Material.

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Kozłowski, G., Sokół, T. Enhanced growth method for topology and geometry optimization of truss structures. Struct Multidisc Optim 65, 220 (2022). https://doi.org/10.1007/s00158-022-03317-7

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  • DOI: https://doi.org/10.1007/s00158-022-03317-7

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