Michell structures within L-shaped domains

• Autorzy: Bołbotowski Karol , Lewiński Tomasz , Sokół Tomasz

Identyfikatory

DOI

10.24423/cames.281

• Języki publikacji: EN

Abstrakty

EN

By recalling the main mathematical results concerning the theory of Michell structures,the present paper puts forward an interpretation of the selected numerical methods forconstructing their approximants, that is, trusses with a large number of nodes. The ef-ficiency of one of these methods: the ground structure method in its adaptive version isshown in the context of the L-shaped design domain problem. A large family of highlyaccurate truss approximants corresponding to the point loads acting at selected verticesis constructed and discussed.

Słowa kluczowe

EN

Michell structure; structural optimization; truss

PL

struktura Michell; optymalizacja konstrukcji; kratownica

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2020
• Tom: Vol. 27, no. 2-3
• Strony: 185--204
• Opis fizyczny: Bibliogr. 11 poz., rys., tab., wykr.

Twórcy

autor

Bołbotowski Karol

• Faculty of Civil Engineering Warsaw University of Technology al. Armii Ludowej 16, 00-637 Warsaw, Poland
• College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences University of Warsaw Stefana Banacha 2C, 02-097 Warsaw, Poland

autor

Lewiński Tomasz

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

autor

Sokół Tomasz

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

Bibliografia

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• 2. G. Bouchitté, I. Fragalà, Optimality conditions for mass design problems and applicationsto thin plates, Archive for Rational Mechanics and Analysis,184(2): 257–284, 2007.
• 3. G. Bouchitté, W. Gangbo, P. Seppecher, Michell trusses and lines of principal action, Mathematical Models and Methods in Applied Sciences,18(9): 1571–1603, 2008.
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• 5. W.S. Hemp, Optimum structures, Oxford, Clarendon Press, 1973.
• 6. T. Lewiński, G.I.N. Rozvany, Exact analytical solutions for some popular benchmark problems in topology optimization III: L-shaped domains, Structural and Multidisciplinary Optimization, 35(2): 165–174, 2008, doi: 10.1007/s00158-007-0157-8.
• 7. T. Lewiński, G.I.N. Rozvany, T. Sokół, K. Bołbotowski, Exact analytical solutions for somepopular benchmark problems in topology optimization III: L-shaped domains revisited, Structural and Multidisciplinary Optimization, 47(6): 937–942, 2013, doi: 10.1007/s00158-012-0865-6.
• 8. T. Lewiński, T. Sokół, C. Graczykowski, Michell structures, Springer International Publishing AG, Cham, Switzerland, 2019, doi: 10.1007/978-3-319-95180-5.
• 9. T. Sokół, Multi-load truss topology optimization using the adaptive ground structure approach, [in:] T. Łodygowski, J. Rakowski, P. Litewka [Eds], Recent advances in computational mechanics, pp. 9–16, CRC Press, London, 2014.
• 10. T. Sokół, A new adaptive ground structure method for multi-load spatial Michell struc-tures, [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.
• 11. G. Strang, R.V. Kohn, Hencky-Prandtl nets and constrained Michell trusses, Computer Methods in Applied Mechanics and Engineering, 36(2): 207–222, 1983.