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2002 | 12 | 1 | 91-100
Tytuł artykułu

The energy method for elastic problems with non-homogeneous boundary conditions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we propose the weighted energy method as a way to study estimates of solutions of boundary-value problems with non-homogeneous boundary conditions in elasticity. First, we use this method to study spatial decay estimates in two-dimensional elasticity when we consider non-homogeneous boundary conditions on the boundary. Some comments in the case of harmonic vibrations are considered as well. We also extend the arguments to a class of three-dimensional problems in a cylinder. A section is devoted to the study of an ill-posed problem. Some remarks are presented in the last section of the paper.
Rocznik
Tom
12
Numer
1
Strony
91-100
Opis fizyczny
Daty
wydano
2002
otrzymano
2001-09-01
poprawiono
2002-01-01
Twórcy
  • Matemática Aplicada 2, Universidad Politécnica de Catalunya, Colón, 11, Terrassa, Barcelona, Spain,
Bibliografia
  • Ames K.A. and Payne L.E. (2000): Saint-Venant type decay results for ill-posed elliptic problems. - Math. Models Meth. Appl. Sci., Vol. 10, No. 5, pp. 771-784.
  • Flavin J.N., Knops R.J. and Payne L.E. (1989): Decay estimates for the constrained elastic cylinder of variable cross section. - Quart. Appl. Math., Vol. XLVII, No. 2, pp. 325-350.
  • Franchi F. and Straughan B. (1994): Spatial decay estimates and continuous dependence on modelling for an equation from dynamotheory. - Proc. Roy. Society. Lond. A, Vol. 445, pp. 437-451.
  • Galdi G. and Rionero S. (1985): Weigthed Energy Methods in Fluid Dynamics and Elasticity. -Berlin: Springer.
  • Horgan C.O.(1989): Recent developments concerning Saint-Venant's principle: An update. - Appl. Mech. Rev., Vol. 42, No. 11, pp. 295-303.
  • Horgan C.O.(1996): Recent developments concerning Saint-Venant's principle: A second update. - Appl. Mech. Rev., Vol. 49, No. 10, pp. 101-111.
  • Horgan C.O. and Knowles J.K. (1983): Recent developments concerning Saint-Venant's principle, In: Advances in Applied Mechanics (J.W. Hutchinson, Ed.). - New York: Academic Press, pp. 179-269.
  • Horgan C.O. and Payne L.E. (1992): The influence of geometric perturbations on the decay of Saint-Venantend effects in linear isotropic elasticity, In: Partial Differential Equations with Real Analysis (H. Begrehr and A. Jeffrey, Eds.). - Essex: Longman, pp. 187-218.
  • Knops R.J. and Payne L.E. (1998): Spatial behaviour of energy in partially constrained thick elasticplates. - Atti dei Convegni Lincei, Vol. 140, pp. 77-104.
  • Lin C. and Payne L.E. (1993): On the spatial decay of ill-posed parabolic problems. - Math. Mod. Meth. Appl. Sci., Vol. 3, No. 4, pp. 563-575.
  • Quintanilla R. (1997a): Spatial decay estimates and upper bounds in elasticity for domains with unbounded cross-sections. - J. Elasticity, Vol. 46, No. 3, pp. 239-254.
  • Quintanilla R. (1997b): Directions of spatial decay in linear elasticity. - Manuscript (unpublished).
  • Quintanilla R. (1998): Comportamiento espacial en sólidos elasticos noacotados. - Anales de Ingenieria Mecanica, Vol.12, No. 1, pp.175-180.
  • Quintanilla R. (2000): Energy methods for problems with non homogeneous boundaryconditions. - Manuscript (unpublished).
  • Straughan B. (1982): Instability, Nonexistence and Weighted Energy Methods in Fluid Dynamics and Related Theories. -London: Longman.
  • Weinberger H.F. (1995): A First Course in Partial Differential Equations. -New York: Dover.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv12i1p91bwm
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