Shells with thickness distension

International Journal of Solids and Structures

Volumn 38, Issue 6-7, 2001, Pages 1201-1225

  Dicarlo, A ^a   Podio Guidugli, P ^b   Williams, W O ^c  

^a ROMA TRE UNIVERSITY   (Italy)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

^c CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; PLATES (STRUCTURAL COMPONENTS); STRUCTURAL ANALYSIS; STRUCTURAL LOADS; TORQUE;

THICKNESS DISTENSION;

SHELLS (STRUCTURES);

EID: 0035254363     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(00)00082-2     Document Type: Article

References (35)

1. Antman, S.S., Osborne, J.E., 1979. The principle of virtual work and integral laws of motion. Archive for Rational Mechanics and Analysis 69, 231-262.
2. Antman, S.S., Marlow, R.S., 1991. Material constraints, Lagrange multipliers, and compatibility. Applications to rod and shell theories. Archive for Rational Mechanics and Analysis 116, 257-299.
3. Antman, S.S., 1995. Nonlinear Problems of Elasticity. Springer, New York, pp. 435-436.
4. Capriz, G., 1989. Continua with Microstructure. Springer, New York.
5. Cauchy, A.-L., 1827. De la pression ou tension dans un corps solide. In: Exercices de Mathématique, vol. 2, pp. 42-56. English translation of the quoted excerpt from: Truesdell, C. 1991. A First Course in Rational Continuum Mechanics, vol. 1, second edition, Academic Press, Boston, p. 150.
6. Cauchy, A.-L., 1827. De la pression ou tension dans un corps solide. In: Exercices de Mathématique, vol. 2, pp. 42-56. English translation of the quoted excerpt from: Truesdell, C. 1991. A First Course in Rational Continuum Mechanics, vol. 1, second edition, Academic Press, Boston, p. 150.
7. DeSimone, A., Podio-Guidugli, P., 1995. Centri di forza e oscillazioni di spessore nelle piastre. In: Atti del XII Congresso Nazionale di Meccanica Teorica e Applicata, vol. V, AIMETA, Napoli, pp. 99-104.
8. DiCarlo, A., 1996. A non-standard format for continuum mechanics. In: Batra, R.C., Beatty, M.F. (Eds.), Contemporary Research in the Mechanics and Mathematics of Materials, CIMNE, Barcelona, pp. 263-268.
9. DiCarlo, A., A clean direct theory of shells with distensible thickness, in preparation.
10. DiCarlo, A., Podio-Guidugli, P., Williams, W.O., Approximations within a hierarchical plate theory of a three-dimensional benchmark solution, in preparation.
11. Ericksen, J.L., Truesdell, C., 1958. Exact theory of stress and strain in rods and shells. Archive for Rational Mechanics and Analysis 1, 295-323.
12. Germain, P., 1972. Sur l'application de la méthode des puissances virtuelles en mécanique des milieux continus. Comptes Rendus de l'Académie des Sciences de Paris 274 (Série A), 1051-1055.
13. Germain, P., 1973a. La méthode des puissances virtuelles en mécanique des milieux continus. Première partie: Théorie du second gradient. Journal de Mécanique 12, 235-274.
14. Germain, P., 1973b. The method of virtual power in continuum mechanics. Part 2: Microstructure. SIAM Journal on Applied Mathematics 25, 556-575.
15. Green, A.E., Rivlin, R.S., 1964. Simple force and stress multipoles. Archive for Rational Mechanics and Analysis 16, 325-353.
16. Green, A.E., Naghdi, P.M., Wainwright, W.L., 1965. A general theory of a Cosserat surface. Archive for Rational Mechanics and Analysis 20, 287-308.
17. Green, A.E., Laws, N., Naghdi, P.M., 1968. Rods, plates and shells. Proceedings of the Cambridge Philosophical Society 64, 895-913.
18. Green, A.E., Naghdi, P.M., 1970. Non-isothermal theory of rods, plates and shells. International Journal of Solids and Structures 6, 209-244.
19. Green, A.E., Naghdi, P.M., 1971. Non-isothermal theory of rods, plates and shells. International Journal of Solids and Structures 7, 127.
20. Gurtin, M.E., 1972. The linear theory of elasticity. In: Truesdell, C. (Ed.), Encyclopedia of Physics, vol. VIa/2, Springer, Berlin, pp. 1-295.
21. Lembo, M., Podio-Guidugli, P., 1991. Plate theory as an exact consequence of three-dimensional linear elasticity. European Journal of Mechanics A/Solids 10, 485-516.
22. Levinson, M., 1985. The simply supported rectangular plate: an exact, three dimensional, linear elasticity solution. Journal of Elasticity 15, 283-291.
23. Maugin, G.A., 1980. The method of virtual power in continuum mechanics: applications to coupled fields. Acta Mechanica 35, 1-70.
24. Naghdi, P.M., 1972. The theory of shells and plates. In: Truesdell, C. (Ed.), Encyclopedia of Physics, vol. VIa/2, Springer, Berlin, pp. 425-640.
25. Naghdi, P.M., 1981. Finite deformation of elastic rods and shells. In: Carlson, D.E., Shield, R.T. (Eds.), Proceedings of the IUTAM Symposium on Finite Elasticity. Martinus Nijhoff Publishers, The Hague, pp. 47-103.
26. Nardinocchi, P., Podio-Guidugli, P., 1994. The equations of Reissner-Mindlin plates obtained by the method of internal constraints. Meccanica 29, 143-157.
27. Noll, W., 1963. La mécanique classique, basée sur un axiome de objectivité. In: La Méthode Axiomatique dans les Mécaniques Classiques et Nouvelles (Colloque International, Paris, 1959), Gauthier-Villars, Paris, pp. 47-56. Reprinted in: Noll, W., 1974. The Foundations of Mechanics and Thermodynamics. Springer, Berlin, pp. 135-144.
28. Noll, W., 1963. La mécanique classique, basée sur un axiome de objectivité. In: La Méthode Axiomatique dans les Mécaniques Classiques et Nouvelles (Colloque International, Paris, 1959), Gauthier-Villars, Paris, pp. 47-56. Reprinted in: Noll, W., 1974. The Foundations of Mechanics and Thermodynamics. Springer, Berlin, pp. 135-144.
29. Pan, E., 1991. An exact solution for transversely isotropic, simply supported and layered rectangular plates. Journal of Elasticity 25, 101-116.
30. Podio-Guidugli, P., 1989. An exact derivation of the thin plate equation. Journal of Elasticity 22, 121-133.
31. Podio-Guidugli, P., 1995. Local and global constraints. Paper presented at the Third Meeting on Current Ideas in Mechanics and Related Fields, Segovia.
32. Podio-Guidugli, P., Theory of Elastic Plates, in preparation.
33. Rogers, T.G., Watson, P., Spencer, A.J.M., 1992. An exact three-dimensional solution for normal loading of inhomogeneous and laminated anisotropic plates of moderate thickness. Proceedings of the Royal Society of London A 437, 199-213.
34. Teresi, L., Tiero, A., 1997. On variational approaches to plate models. Meccanica 32, 143-156.
35. Truesdell, C., Toupin, R.A., 1960. The classical field theories. In: Flügge, S. (Ed.), Encyclopedia of Physics, vol. III/1, Springer, Berlin, pp. 226-793.