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2002 | 12 | 1 | 81-90
Tytuł artykułu

Non-smoothness in the asymptotics of thin shells and propagation of singularities. Hyperbolic case

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the limit behaviour of elastic shells when the relative thickness tends to zero. We address the case when the middle surface has principal curvatures of opposite signs and the boundary conditions ensure the geometrical rigidity. The limit problem is hyperbolic, but enjoys peculiarities which imply singularities of unusual intensity. We study these singularities and their propagation for several cases of loading, giving a somewhat complete description of the solution.
Rocznik
Tom
12
Numer
1
Strony
81-90
Opis fizyczny
Daty
wydano
2002
otrzymano
2001-09-01
poprawiono
2002-01-01
Twórcy
  • Laboratoire de Mécanique, Université de Caen, boulevard Maréchal Juin, 14032 Caen, France
  • Laboratoire de Mécanique, Université de Caen, boulevard Maréchal Juin, 14032 Caen, France
  • Laboratoire de Modélisation en Mécanique, Université Paris VI, 8 rue du capitaine Scott, 75015 Paris, France,
Bibliografia
  • Bernadou M. (1994): Methodes d'Elements Finis pour les Problèmes de Coques Minces. - Paris: Masson.
  • Chapelle D. and Bathe K.J. (1998): Fundamental considerations for thefinite element analysis of shell structures. - Comp. Struct., Vol. 66, No. 1, pp. 19-36.
  • Ciarlet P.G. (2000): Mathematical Elasticity, Vol. III, Theory of Shells. - Amsterdam: North Holland.
  • Egorov Yu.V. and Shubin M.A. (1992): Linear partial differential equations. Foundations of the classical theory, In: Encyclopaedia of Mathematical Sciences, Vol. 30 (Part. Diff. Eqs. I). - New York: Springer, pp. 345-375.
  • Gerard P. (1988): Solutions conormales analytiquesd'equations hyperboliques non lineaires. - Comm. Part. Diff. Eqns., Vol. 13, No. 3, pp. 345-375.
  • Gerard P. and Sanchez Palencia É. (2000): Sensitivity phenomena for certain thin elastic shells with edges. - Math. Meth. Appl.Sci., Vol.23, No. 4, pp. 379-399.
  • Goldenveizer A. L. (1962): Theory of Thin Elastic Shells. - New York: Pergamon.
  • Karamian P., Sanchez-Hubert J. and Sanchez Palencia É. (2000): Amodel problem for boundary layers of thin elastic shells. - Math. Modell.Num. Anal., Vol. 34, No. 1, pp. 1-30.
  • Karamian P. (1998a): Nouveaux resultats numeriques concernant les coques minces hyperboliques inhibees: Cas du paraboloide hyperbolique. - Compt. Rend. Acad. Sci., Paris, Serie IIb, Vol. 326, No. 11, pp. 755-760.
  • Karamian P. (1998b): Reflexion des singularites dans les coques hyperboliques inhibees. - Compt. Rend. Acad. Sci., Paris, Serie IIb, Vol. 326, No. 1, pp. 609-614.
  • Karamian P. (1999) Coques elastiques minces hyperboliques inhibees: calcul du problème limite par elements finis et non reflexion des singularites. - Ph. D. thesis, Universite de Caen.
  • Karamian P. and Sanchez-Hubert J. (2002): Boundary layers in thin elastic shells with developable middle surface. - Euro. J. Mech. Asolids, Vol. 21, No. 1, pp. 13-47.
  • Leguillon D., Sanchez-Hubert J. and Sanchez Palencia É. (1999): Model problem of singular perturbation without limit in the space off inite energy and its computation. - C. R. Acad. Sci. Paris, Serie IIb, Vol. 327, No. 5, pp. 485-492.
  • Lions J.L. (1973): Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal. - Berlin: Springer.
  • Pitkaranta J., Matache A.M. and Schwab C. (1998): Fourier mode analysis of layers in shallow shell deformation. - Res. Rep., No. 98-18, seminar fur Angewandte Mathematik, Technische Hochschule Zurich.
  • Sanchez-Hubert J. and Sanchez Palencia É. (1989), Vibration and Coupling of Continuous Systems. Asymptotic Methods. -Berlin: Springer.
  • Sanchez-Hubert J. and Sanchez Palencia É. (1998): Pathological phenomena in computation of thin elastic shells. - Trans. Can. Mech. Eng., Vol. 22, No. 4B, pp. 435-446.
  • Sanchez-Hubert J. and Sanchez Palencia É. (2001a): Singular perturbations with non-smooth limit and finite element approximation of layers for model problems of shells, In: Partial Differential Equations in Multistructures (F. Ali Mehmeti, J. von Below and S. Nicaise, Eds.). - New York: Dekker.
  • Sanchez-Hubert J. and Sanchez Palencia É. (2001b): An isotropic finite element estimates and local locking for shells: parabolic case. - Compt. Rend. Acad. Sci., Paris, Serie IIb, Vol. 329, No. 2, pp.153-159.
  • Sanchez-Hubert J. and Sanchez Palencia É (1997): Coques Elastiques Minces. Proprietes Asymptotiques. - Paris: Masson.
  • Sanchez Palencia É. (2000): On a singular perturbation going out of the energy space. - J. Math. Pures Appl., Vol. 79, No. 8, pp. 591-602.
  • Sanchez Palencia É. (2001) New cases of propagation of singularities along characteristic boundaries for model problems of shell theory. - Compt. Rend. Acad. Sci., Paris, Serie IIb, Vol. 329, No. 5, pp. 315-321.
Typ dokumentu
Bibliografia
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