Michell structures formed on surfaces of revolution

Structural and Multidisciplinary Optimization

Volumn 28, Issue 1, 2004, Pages 20-30

  Lewinski T ^a  

^a WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Michell structures; Michell's sphere

Indexed keywords

DATA COMPRESSION; ELASTICITY; MEMBRANES; PROBLEM SOLVING; STRESSES;

GRIDWORKS; MICHELL STRUCTURES; MICHELL'S SPHERE; REINFORCED MATERIAL;

STRUCTURAL ANALYSIS;

EID: 4444220603     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00158-004-0419-7     Document Type: Article

References (24)

1. Allaire, G.; 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
2. Bernadou, M. 1996: Finite element methods for thin shell problems. Chichester: Wiley
3. Chan, H.S.Y. 1967: Half-plane slip-line fields and Michell structures. Q. J. Mech. Appl. Math. 20, 453-469
4. Čyras, A. 1972: Optimization theory of perfectly locking bodies. Arch. Mech. 24, 203-210
5. Czarnecki, S. 2003: Compliance optimization of the truss structures. Comp. Ass. Mech. Eng. Sci. 10, 117-137
6. Dzierzanowski, G.; Lewiński, T. 2003: Layout optimization of two isotropic materials in elastic shells. J. Theor. Appl. Mech. 41, 459-472
7. Graczykowski, C.; Lewiński, T. 2003: Optimal Michell's cantilever transmitting a given point load to a circular support. Analysis of the exact solution. In: Szcześniak, W. (ed.) Theoretical Foundations of Civil Engineering - XI. Polish-Ukrainian Transactions. Warsaw: Oficyna Wydawnicza PW, 351-368
8. Hemp, W.S. 1973: Optimum Structures. Oxford: Clarendon
9. Lewiński, T. 2003: An elementary proof of the Michell sphere being the lightest among all the uniformly stressed shells loaded by two opposite torques. In: Proc. WCSMO-5 Lido di Jesolo, May 2003; CD ROM (6 pages) and Book of Abstracts (2 pages)
10. Lewiński, T.; Telega, J.J. 2000: Plates, laminates and shells. Asymptotic analysis and homogenization. Singapore, New Jersey, London, Hong Kong: World Scientific
11. Lewiński, T.; Telega, J.J. 2001: Michell-like grillages and structures with locking. Arch. Mech. 53, 303-331
12. Lewiński, T.; Telega, J.J. 2003: Optimal design of membrane shells. Homogenization-based relaxation of the two-phase lay-out problem. J. Theor. Appl. Mech. 41, 545-560
13. Lewinski, T.; Zhou, M.; 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; Part II: Unsymmetric cantilevers. Int. J. Mech. Sci., 399-419
14. Lewinski, T.; Zhou, M.; 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; Part II: Unsymmetric cantilevers. Int. J. Mech. Sci., 399-419
15. Love, A.E.H. 1888: The small free vibrations and deformation of a thin elastic shell. Phil. Trans. Roy. Soc. London. A 179, 491-546
16. Mazurkiewicz, Z.E. 1995: Thin Elastic Shells. Warszawa: Oficyna Wydawnicza PW (in Polish)
17. Michell, A.G.M. 1904: The limits of economy of material in frame structures. Phil. Mag. 8, 589-597
18. Novozhilov, V.V. 1970: Thin Shell Theory. Groningen: Walters-Nordhoff
19. Prager, W. 1959: On a problem of optimal design. In: Olszak, W. (ed.) Non-Homogeneity in Elasticity and Plasticity. Symp. IUTAM, Warsaw, 2-9 September 1958. London: Pergamon, pp. 125-132
20. Prager, W.; Shield, R.T. 1967: A general theory of optimal plastic design. J. Appl. Mech., Trans. ASME 34, 184-186
21. Rozvany, G.I.N. 1976: Optimal Design of Flexural Systems: Beams, Grillages, Slabs, Plates and Shells. Oxford: Pergamon
22. Rozvany, G.I.N. 1997: Some shortcomings in Michell's truss theory. Struct. Optim. 12, 244-255
23. Strang, G.; Kohn, R.V. 1983: Hencky-Prandtl nets and constrained Michell trusses. Comp. Meth. Appl. Mech. Eng. 36, 207-222
24. Telega, J.J.; Jemioło, S. 1998: Macroscopic behaviour of locking materials with microstructure. Part I. Primal and dual locking potential. Relaxation. Bull. Polon. Acad. Sci.; Tech. Sci. 46, 265-276