On the fundamental problem of optimum design of anisotropic plates

• Autorzy: Lewiński T.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the free material design problem of minimum compliance of an anisotropic clastic plate loaded in-plane. All the characteristics of the plate stiffness tensor or of the form of the Hookc tensor for plane case, are treated as design variables. The cost function is expressed in terms of the Kelvin moduli. The necessary conditions of optimality are discussed. They imply that the deformation state within the optimal plate must satisfy the condition of colinearity of stress and strain tensors.

Słowa kluczowe

EN

free material design; compliance minimization; optimum design; elastic plate

PL

podatność; konstrukcja optymalna; płyta sprężysta

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Civil and Environmental Engineering
• Rocznik: 2006
• Tom: No. 7
• Strony: 215--226
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Lewiński T.

• Warsaw University of Technology Faculty of Civil Engineering Tel.: [phone] fax: [phone],

Bibliografia

• 1. Allaire G.: Shape optimisation by the homogenisation method, New York, Springcr 2002.
• 2. Banichuk N.V.: Optimization of anisotropic propcrties for continuum bodies and structural elements using spectral methods of tensor analysis. Mech.Struct.Mach, 24 (1996) 71-87.
• 3. Bendsoe M.P., Guedes J.M., Habcr R.B., Pedersen P., Taylor J.E.: Ań analyti-cal rnodel to predict optimal materiał properties in the context of optimal structural design. J.Appl.Mech. Trans. ASME, 61( 1994) 930-937.
• 4. Cherkaev A.: Yariational methods for structural optimization, New York, Springer 2000.
• 5. Cowin S.C.: Optimization of the strain cncrgy density in linear anisotropic elasticity. J.Elasticity 34 (1994) 45-68. |
• 6. Du J., Taylor J.E.: Application of an cnergy-based model for thc optimal de-sign of structural matcrials and topology. Struci.Mullidisc. Optimiz. 24 (2002) 277-292.
• 7. Hornlein H.R.E.M., Koćvara M., Wcrner R.: Materiał optimization: bridging the gap between conceptual and preliminary design, Aeorosp. Sci. Technol. 5(2001)541-554.
• 8. Jemioło S.: Optimum orientations of a non-homogcneous orthotropic materiał. Ed.: W.Szcześniak, Theoretical Foundation^ of dvii Engineering. Polish-Ukrainian Transactions. Pridncprovsk, June-July 2001, Oficyna Wydawnicza PW, Warszawa (in Polish), 269-274.
• 9. Jemioło S., Szwed A.: Application of convex isotropic functions in failure theory for isotropic materiał s. Yield criteria for metal s. Prace Naukowe Politechniki Warszawskiej, Budownictwo, z. 133 (1999) pp 5-51 (in Polish)
• 10. Kolm R.V., Strang G.: Oplimal design and relaxation of variational problems. Comm.Pure AppiMath. 39 (1986), pp. 113-137,139-183,353-379.
• 11. J.S.Li, G.T.Parks, P.J.CIarkson, Metamorhic development: a new topology optimization method for continuum structures. Struct.Mulńdisc. Optimiz. 20( 2000) 288-300.
• 12. Luric K.A., Chcrkacv A.V.: Effeclivc charactcristics of composite matcrials and optimum design of structural mcmbers. Adv. Mech. (Uspekhi Mekhaniki) 9, 1986,pp.3-81 (inRussian).
• 13. Łukasiak T.: Invariant representations of the constitutive tensors, Master's Thesis (K.H.Żmijewski, supervisor) Warsaw University of Technology, Faculty of Ci vii Enginecring, Warsaw 1989 (in Polish)
• 14. Mróz Z., Garstecki A.: Optimal loading conditions in thc design and identificalion of structurcs. Part 1: discrctc formulation. Struci. Mullidisc. Optimiz. 2006, in press
• 15. Pedersen, P.: On optimal orientation of orthotropic rnaterials. Struci. Optimiz. 1(1989) 101-106.
• 16. Ringertz U.T.: On finding the optimal distribution of materiał propcrties. Struct.Oplimiz. 5(1993) 265- 267.
• 17. Rychlewski J.: Mathematical structure of elastic bodies. Report of the Institute of Problems in Mechanics of the Academy of Sciences of the USSR, No 217, Moscow 1983, pp 113.(in Russian)
• 18. Rychlewski J.: On Hooke's law, Prikl.Mat.Mekh. 48 (1984) 420-435 (in Russian)
• 19. Rychlewski J.: On thermoclastic constants,Arch.Mech. 36 (1984) 77-95.
• 20. Rychlewski J.: Uncotwentional approach to linear elasticity, Arch.Mech. 47(1995) 149-171.
• 21. Rychlewski J.: A qualitative approach to Hooke's tensor. Part I, Arch.Mech. 52(2000) 737-759; Part II, ibidem 53(2001), 45-63.
• 22. Sutcliffe S.: Spectral decomposition of the elasticity tensor, J.AppLMech. Trans. ASME, 59(1992) 762-773
• 23. Taylor J.E.: Ań cnergy model for the optimal design of linear continuum structurcs. truct.Optimiz, 16(1998) 116-127.
• 24. Theocaris P.S., Sokolis D.P.: Spectral decomposition of the compliance tensor for anisotropic plates. J. Elasticity 51(1998) 89-103.
• 25. Vannucci P., Ycrchcry G.: Sliffness design of laminates using the polar method, Int. J.Solidt.Struct. 38( 2001) 9281-9294.
• 26. Yinccnti A., P.Yannucci P.: Tailoring cxpansion cocfficients of laminates: a new generał optimal approach based upon the polar-genetic method, Eds: J.Herskovits, S.Mazorche, A.Canelas. CD-Rom Proceedings of the 6th World Congress of Structural and Multidisciplinary Optimization (WCSMO-6) Rio de Janeiro, 30 May-3 June 2005, Brazil.