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Gaussian Curvature and Babuška’s Paradox in the Theory of Plates

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Rational Continua, Classical and New

Abstract

Within the functional framework of the trace spaces of H 2 functions on 2-D domains with corners, in this paper we discuss the geometrical reasons for the so-called Babuška’s paradox in the theory of plates and other related questions.

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References

  1. Babuska, I. (1961): Stability of the domain of definition with respect to fundamental problems in the theory of partial differential equations especially in connection with the theory of elasticity I, II. Czechoslovak Math. J. 11, 76–105;

    MathSciNet  Google Scholar 

  2. 165–203 (Russian)

    MathSciNet  Google Scholar 

  3. Babuska, L, Pitkäranta, J. (1990): The plate paradox for hard and soft simple support. SIAM J. Math. Anal. 21, 551–576

    Article  MathSciNet  MATH  Google Scholar 

  4. Babuska, L, Scapolla, T. (1989): Benchmark computation and performance evaluation for a rhombic plate bending problem. Internat. J. Numer. Methods Engrg. 28, 155–179

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Davini, C., Pitacco, I. (1998): Relaxed notions of curvature and a lumped strain method for elastic plates. SIAM J. Numer. Anal. 35, 677–691

    Article  MathSciNet  MATH  Google Scholar 

  6. Davini, C. (2002): T-convergence of external approximations in boundary value problems involving the bi-Laplacian. J. Comput. Appl. Math. To appear

    Google Scholar 

  7. Gagliardo, E. (1957): Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili. Rend. Sem. Mat. Univ. Padova, 27, 284–305

    MathSciNet  MATH  Google Scholar 

  8. Grisvard, P. (1985): Elliptic problems in non-smooth domains. Pitman, London

    Google Scholar 

  9. Grisvard, P. (1992): Singularities in boundary value problems. Springer, Berlin

    MATH  Google Scholar 

  10. Lions, J.L., Magenes, E. (1972): Non-homogeneous boundary value problems and applications. Vol. I, Springer, Heidelberg

    MATH  Google Scholar 

  11. Maz’ya, V.G., Nazarov, S.A. (1987): Paradoxes of limit passage in solutions of boundary value problems involving the approximation of smooth domains by polygonal domains. Math. USSR Izvestiya 29, 511–533

    Article  ADS  MATH  Google Scholar 

  12. Necas, J. (1967): Les méthodes directes en théorie des équations elliptiques. Masson, Paris

    MATH  Google Scholar 

  13. Pogorelov, A. V. (1978): The Minkowski multidimensional problem. Winston, Washington, DC

    MATH  Google Scholar 

  14. Suraci, S. (1997): Un nuovo metodo di approssimazione in analisi strutturale: applicazioni e confronti con il metodo degli elementi finiti. Thesis. Université degli Studi di Udine, Udine

    Google Scholar 

  15. Yakovlev, G.N. (1961): Boundary properties of functions of class W<Stack><Subscript>p</Subscript><Superscript>(1)</Superscript></Stack> on regions with angular points. Soviet Math. Dokl. 2, 1177–1180

    MATH  Google Scholar 

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© 2003 Springer-Verlag Italia, Milano

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Davini, C. (2003). Gaussian Curvature and Babuška’s Paradox in the Theory of Plates. In: Podio-Guidugli, P., Brocato, M. (eds) Rational Continua, Classical and New. Springer, Milano. https://doi.org/10.1007/978-88-470-2231-7_6

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  • DOI: https://doi.org/10.1007/978-88-470-2231-7_6

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-2233-1

  • Online ISBN: 978-88-470-2231-7

  • eBook Packages: Springer Book Archive

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