Solution of the three forces problem in the case of two forces being mutually orthogonal

• Autorzy: Sokół T. , Lewiński T.
• Języki publikacji: EN

Abstrakty

EN

The present paper delivers some new numerical and exact solutions of the three forces problem that is one of fundamental problems of Michell’s truss theory. The present problem is to find the lightest fully stressed truss transmitting three self-equilibrated co-planar forces. In this study, we limit our considerations to the case of two forces being mutually orthogonal. The aim of this paper is to classify possible layouts of optimal trusses depending on the position of the applied lateral point load (the positions of the other two forces are fixed, which however does not restrict the scope of the study). The exact analytical solutions are obtained with a great help of numerical solutions that enable proper prediction of the optimal layouts.

Słowa kluczowe

EN

topology optimization; Michell’s trusses; three forces problem

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2016
• Tom: Vol. 64, iss. 4
• Strony: 485--491
• Opis fizyczny: Bibliogr. 11 poz., rys., wykr.

Twórcy

autor

Sokół T.

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

autor

Lewiński T.

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

Bibliografia

• 1. Chan H.S.Y., Minimum weight cantilever frames with specified reactions, University of Oxford, Department of Engineering Science, Eng. Laboratory, Parks Road, Oxford, no 1, 010.66, 1966.
• 2. Sokół T., Lewiński T., 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, doi: 10.1007/s00158-010-0556-0.
• 3. Sokół T., Lewiński T., On the three forces problem in truss topology optimization. Analytical and numerical solution, [in:] 9th World Congress on Structural and Multidisciplinary Optimization, WCSMO-9, http://pbl.eng.kagawa-u.ac.jp/kani/p/paper243 1.pdf.
• 4. Sokół T., Lewiński T., Optimal design of a class of symmetric plane frameworks of least weight, Structural and Multidisciplinary Optimization, 44(5): 729–734, 2011, doi: 10.1007/s00158-011-0704-1.
• 5. Sokół T., Rozvany G.I.N., New analytical benchmarks for topology optimization and their implications. Part I: bi-symmetric trusses with two point loads between supports, Structural and Multidisciplinary Optimization, 46(4): 477–486, 2012, doi: 10.1007/s00158- 012-0786-4.
• 6. Mazurek A., Geometrical aspects of optimum truss like structures for three-force problem, Structural and Multidisciplinary Optimization, 45(1): 21–32, 2012, doi: 10.1007/s00158- 011-0679-y.
• 7. Sokół T., Lewiński T., Simply supported Michell trusses generated by a lateral point load, Structural and Multidisciplinary Optimization, 54(5): 1209–1224, 2016, doi: 10.1007/s00158-016-1480-8.
• 8. Sokół T., 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, CRC Press, pp. 525–528, 2016.
• 9. Lewiński T., Zhou M., Rozvany G.I.N., 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, doi: 10.1016/0020-7403(94)90043-4.
• 10. He L., Gilbert M., Rationalization of trusses generated via layout optimization, Structural and Multidisciplinary Optimization, 52(4): 677–694, 2015, doi: 10.1007/s00158-015- 1260-x.
• 11. Smith Ch.J., Gilbert M., Todd I., Derguti F., Application of layout optimization to the design of additively manufactured metallic components, Structural and Multidisciplinary Optimization, 54(5): 1297–1313, 2016, doi: 10.1007/s00158-016-1426-1.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).