Applications of Michell’s theory in designof high-rise buildings, large-scale roofs and long-span bridges

• Autorzy: Graczykowski Cezary , Lewiński Tomasz

Identyfikatory

DOI

10.24423/cames.288

• Języki publikacji: EN

Abstrakty

EN

This paper analyzes the relations between the theory of Michell structures, which is one ofthe most important theories in structural optimization, and some remarkable engineeringstructures, including selected high-rise buildings, large-scale roof coverings and long-span bridges. The first part of this study briefly presents the development of Michell’s theory, its basic concepts, assumptions, and examples and fundamental features of Michellstructures. Then, several untypical engineering structures that make use of said conceptsare presented, including skyscrapers proposed by the Polish structural designer W. Zalewski and the international architectural office of Skidmore, Owings and Merill (SOM). Next, large-scale roof coverings of “Spodek” arena in Poland as well as selected bridgesare thoroughly analyzed in the context of similarity to Michell structures. The conductedstudy reveals that considered structural forms of the analyzed structures follow some ofthe concepts known from Michell’s theory and thus possess many features of the optimalstructural designs.

Słowa kluczowe

EN

topology optimization; Michell's structure; high-rise building; large-scale roof; long-span bridges

PL

optymalizacja topologii; konstrukcja Michell; wieżowiec; dach wielkoformatowy; most dużej rozpiętości

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2020
• Tom: Vol. 27, no. 2-3
• Strony: 133--154
• Opis fizyczny: Bibliogr. 31 poz., il., wykr.

Twórcy

autor

Graczykowski Cezary

• Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5b, 02-106 Warsaw, Poland

autor

Lewiński Tomasz

• Faculty of Civil Engineering Warsaw University of Technologyal. Armii Ludowej 16, 00-637 Warsaw, Poland

Bibliografia

• 1. A.G.M. Michell, The limits of economy of material in frame structures, The London, Edinburgh, and Dublin Philosophical Magazine Series 6, 8 (47): 589–597, 1904, doi: 10.1080/14786440409463229.
• 2. H.S.Y. Chan, Minimum weight cantilever frames with specified reactions, June, No 1,010.66, 11pp, University of Oxford. Depart. of Eng. Sci. Eng. Laboratory, Oxford, 1966.
• 3. H.S.Y. Chan, Half-plane slip-line fields and Michell structures, The Quarterly Journal of Mechanics and Applied Mathematics, 20 (4): 453–469, 1967.
• 4. H.L. Cox, The design of structures of least weight, Pergamon Press, Oxford, 1965.
• 5. W.S. Hemp, Optimum Structures, Clarendon Press, Oxford, 1973.
• 6. T. Lewiński, M. Zhou, G.I.N. Rozvany, Extended exact solutions for least-weight truss layouts – Part I: Cantilever with a horizontal axis of symmetry, International Journal of Mechanical Sciences, 36 (5): 375–398, 1994.
• 7. T. Lewiński, M. Zhou, G.I.N. Rozvany, Extended exact solutions for least-weight truss layouts – Part II: Unsymmetric cantilevers, International Journal of Mechanical Sciences, 36 (5): 399–419, 1994.
• 8. G.I.N. Rozvany, Some shortcomings in Michell’s truss theory, Structural Optimization, 12 (4): 244–250, 1996.
• 9. G.I.N. Rozvany, T. Sokół, Exact truss topology optimization: allowance for support costs and different permissible stresses in tension and compression – extensions of a classical solution by Michell, Structural and Multidisciplinary Optimization, 45 (3): 367–376, 2012.
• 10. M. Gilbert, A. Tyas, Layout optimization of large-scale pin-jointed frames, Engineering Computations, 20 (8): 1044–1064, 2003
• 11. T. Sokół, A 99 line code for discretized Michell truss optimization written in Mathematica, Structural and Multidisciplinary Optimization, 43 (2): 181–190, 2011.
• 12. T. Sokół, T. Lewiński, On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight, Structural and Multidisciplinary Optimization, 42 (6): 835–853, 2010.
• 13. A.V. Pichugin, A. Tyas, M. Gilbert, On the optimality of Hemp’s arch with vertical hangers. Structural and Multidisciplinary Optimization, 46 : 17–25, 2012.
• 14. A.V. Pichugin, A. Tyas, M. Gilbert, L. He, Optimum structure for a uniform load over multiple spans, Structural and Multidisciplinary Optimization, 52 : 1041–1050, 2015.
• 15. T. Sokół, T. Lewiński, Michell Cantilever on Circular Support for Unequal Permissible Stresses in Tension and Compression, Proceedings of the SOLMECH 2018 Conference, Warsaw, Poland, 2018.
• 16. T. Lewiński, T. Sokół, C. Graczykowski, Michell Structures, Springer, 2019.
• 17. L.L. Beghini, J. Carrion, A. Beghini, A. Mazurek, W.F. Baker, Structural optimization using graphic statics, Structural and Multidisciplinary Optimization, 49 : 351–366, 2014.
• 18. T. Sokół, A new adaptive ground structure method for multi-load spatial Michell structures, [in:] M. Kleiber, T. Burczyński, K. Wilde, J. Górski, K. Winkelmann, Ł. Smakosz [Eds], Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues, pp. 525–528, CRC Press, 2016.
• 19. G.I.N Rozvany, W. Prager, A new class of structural optimization problems: optimal archgrids, Computer Methods in Applied Mechanics and Engineering, 19 (1): 127–150, 1979.
• 20. R. Czubacki, T. Lewiński, Optimal archgrids: a variational setting, Structural and Multidisciplinary Optimization, 2020, doi: 10.1007/s00158-020-02562.
• 21. W. Zalewski, W. Zabłocki, Engineering inspirations in shaping tall buildings, [in:] Lightweight Structures in Civil Engineering, Proceedings of the International Symposium, Warsaw, Poland, 24–28 June, pp. 109–118, 2002.
• 22. W. Zalewski, Strength and lightness – The muses of a structural designer [in Polish: Moc i lekkość: muzy projektanta konstrukcji], Architektura, 74 (11): 94–95, 2000.
• 23. W. Zabłocki, Optimization of structures and new forms of tall buildings [in Polish: Optymalizacja konstrukcji a nowe formy architektoniczne budynków wysokościowych], Architektura, 74 (11): 96–98, 2000.
• 24. E. Allen, W. Zalewski, Boston Structures Group, Form and forces. Designing efficient expressive structures, Wiley, New Jersey, 2010.
• 25. T. Zegard, C. Hartz, A. Mazurek, W.F. Baker, Advancing building engineering through structural and topology optimization, Structural and Multidisciplinary Optimization, 2020, doi: 10.1007/s00158-020-02506-6.
• 26. W. Zalewski, Construction of the supermarket roof in Warsaw [in French: Construction de la toiture du supermarket a Varsovie], [in:] N. Esquillan, Y. Saillard [Eds], Hanging roofs: Proceedings of the IASS Colloquium on Hanging Roofs, Continuous Metallic Shell Roofs and Superficial Lattice Roofs, Paris 9–11 July, 1962
• 27. W. Zalewski, Constancy of force as a criterion of the rational form of a construction [in French: Constance de la force comme critere de la forme ationelle d’une construction], 1963.
• 28. W. Zalewski, Some new structural forms created in the period 1950–60 [in Polish], 1964.
• 29. W. Zalewski, E. Allen, Shaping structures: Statics, Wiley, New York, 1998.
• 30. M. Pelczarski, Considerations from interviews with W. Zalewski, Architectus, 2 (34): 69– 82, 2013.
• 31. H.E. Fairclough, M. Gilbert, A.V. Pichugin, A. Tyas, I. Firth, Theoretically optimal forms for very long-span bridges under gravity loading, Proceeding of the Royal Society A, 474 (2217): 20170726, 2018, doi: 10.1098/rspa.2017.0726.