The lightest plane structures of a bounded stress level transmitting a point load to a circular support

Control and Cybernetics

Volumn 34, Issue 1, 2005, Pages 227-253

  Graczykowski, Cezary ^a   Lewiński, Tomasz ^b  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

^b WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Layout optimization; Michell cantilevers; Minimum weight design

Indexed keywords

EID: 25844493554     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. ACHTZIGER, W. (1997) Topology optimization of discrete structures. An introduction in view of computational and non-smooth aspects. In: Rozvany, G.I.N., ed., Topology Optimization in Structural Mechanics. Springer. Wien, 57-100.
2. ALLAIRE, G. and KOHN, R.V. (1993) Optimal design for minimum weight and compliance in plane stress using extremal microstructures. Eur. J. Mech. A/Solids 12, 839-878.
3. CHAN, H.S.Y. (1967) Half-plane slip-line fields and Michell structures. Q. J. Mech. Appl. Math. 20, 453-469.
4. CHAN, H.S.Y. (1975) Symmetric plane frameworks of least weight. In: A. Sawczuk and Z. Mróz, eds., Optimization in Structural Design. Springer, Berlin, 313-326.
5. CHERKAEV, A. (2000) Variational Methods for Structural Optimization. Springer. New York.
6. CZARNECKI, S. (2003) Compliance optimization of the truss structures. Comp. Ass. Mech. Eng. Sci. 10, 117-137.
7. GOLAY, F. and SEPPECHER, P. (2001) Locking materials and the topology of optimal shapes. Eur. J. Mech. A/Solids 20, 631-644.
8. GRACZYKOWSKI, C. and LEWIŃSKI, T. (2003) Optimal Michell's cantilever transmitting a given point load to a circular support. Analysis of the exact solution. In: W. Szcześniak, ed., Theoretical Foundations of Civil Engineering-XI. Oficyna Wydawnicza PW, Warszawa, 351-368.
9. HEMP, W.S. (1973) Optimum Structures. Oxford, Clarendon Press.
10. LEWIŃSKI, T. (2004) Michell structures formed on surfaces of revolution. Struct. Multidisc. Optimiz. 28, 20-30.
11. LEWIŃSKI, T. and TELEGA, J.J. (2000) Plates, laminates and shells. Asymptotic analysis and homogenization. World Scientific, Singapore, New Jersey, London, Hong Kong.
12. LEWIŃSKI, T. and TELEGA, J.J. (2001) Michell-like grillages and structures with locking. Arch. Mech. 53, 303-331.
13. LEWIŃSKI, T., ZHOU, M. and ROZVANY, G.I.N. (1994) Extended exact solutions for least-weight truss layouts - Part I: Cantilever with a horizontal axis of symmetry. Int. J. Mech. Sci. 36, 375-398;
14. Part II: Unsymmetric cantilevers, Int. J. Mech. Sci. 36, 399-419.
15. MAZURKIEWICZ, Z.E. (1995) Thin Elastic Shells. Oficyna Wydawnicza PW, Warszawa(in Polish).
16. MICHELL, A.G.M. (1904) The limits of economy of material in frame structures. Phil. Mag. 8, 589-597.
17. NOVOZHILOV, V.V. (1970) Thin Shell Theory. Walters-Nordhoff, Groningen, Russian Edition: Sudpromgiz, Leningrad 1962.
18. ROZVANY, G.I.N. (1976) Optimal Design of Flexural Systems: Beams, Grillages, Slabs, Plates and Shells. Oxford: Pergamon Press.
19. STRANG, G. and KOHN, R.V. (1983) Hencky-Prandtl nets and constrained Michell trusses. Comp. Meth. Appl. Mech. Engrg. 36, 207-222.
20. VEKUA, I.N. (1967) New Methods for Solving Elliptic Equations. North-Holland, Amsterdam.