The Generalized Membrane Problem for Linearly Elastic Shells with Hyperbolic or Parabolic-Middle Surface
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OpenAlex topics: Advanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Contact Mechanics and Variational Inequalities
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References (24)
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1. R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
2. D. Caillerie and E. Sanchez-Palencia, Elastic thin shells: asymptotic theory in the anisotropic and heterogeneous cases. Math. Models Methods Appl. Sci. 5(1995) 473-496.10.1142/S0218202595000280 ↗
3. P.G. Ciarlet, Mathematical Elasticity, Vol III: Theory of Shells, North Holland, Amsterdam, to appear.
4. P.G. Ciarlet and V. Lods, On the ellipticity of linear membrane shell equations. J. Math. Pures Appl 75(1996) 107-124.
5. P.G. Ciarlet and V. Lods, Asymptotic analysis of linearly elastic shells. I: Justification of membrane shell equations. Arch. Rational Mech. Anal. 136(1996) 119-161.10.1007/BF02316975 ↗
6. P.G. Ciarlet and V. Lods, Asymptotic analysis of linearly elastic shells: 'Generalized membrane shells'. Journal of Elasticity 43(1996) 147-188.10.1007/BF00042508 ↗
7. P.G. Ciarlet, V. Lods and B. Miara, Asymptotic analysis of linearly elastic shells. II: Justification of flexural shell equations. Arch. Rational Mech. Anal. 136(1996) 163-190.10.1007/BF02316976 ↗
8. P.G. Ciarlet and E. Sanchez-Palencia, an existence and uniqueness theorem for two-dimensional linear membrane shell equations. J. Math. Pures Appl. 75(1996) 51-67.
9. R. Courant and D. Hilbert, Methods of Mathematical Physics II, Wiley, New-York, 1989.
10. P. Destuynder, Sur une justification des modèles de plaques et de coques par les méthodes asymptotiques, Thèse, Université Pierre et Marie Curie, Paris, 1980.
11. P. Destuynder, A classification of thin shell theories. Acta Applicandae Mathematicae 4(1985) 15-63.10.1007/BF02293490 ↗
12. Y.V. Egorov and M.A. Shubin, Partial Differential Equations I, Springer-Verlag, Berlin, 1992.
13. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer Verlag, Berlin, 1983.
14. A.L. Goldenveizer, Derivation of an approximate theory of shells by means of asymptotic integration of the equations of the theory of elasticity. Prikl. Mat. Mech. 27(1963) 593-608.
15. A.L. Goldenveizer, The principles of reducing three-dimensional problems of elasticity to two-dimensional problems of the theory of plates and shells, in Proceedings of the Eleventh International Congress of Theoretical and Applied Mechanics (H. Görtler, editor), p. 306-311, Springer-Verlag, 1964.10.1007/978-3-662-29364-5_39 ↗
16. J.L. Lions and E. Sanchez-Palencia, Problèmes sensitifs et coques élastiques minces, Actes du Colloque à la memoire de Pierre Grisvard, Paris, 1995.
17. V. Lods and C. Mardare, The space of inextensional displacements for a partially clamped linearly elastic shell with an elliptic middle surface, to appear.
18. B. Miara and E. Sanchez-Palencia, Asymptotic analysis of linearly elastic shells. Asymptotic analysis 12(1996) 41-54.10.3233/ASY-1996-12103 ↗
19. E. Sanchez-Palencia, Statique et dynamique des coques minces. II: cas de flexion pure inhibée - Approximation membranaire. C.R. Acad. Sci.Paris, 309, série I, (1989) 531-537.
20. E. Sanchez-Palencia, Passages à la limite de l'élasticité tri-dimensionnelle à la théorie asymptotique des coques minces. C.R. Acad. SciParis, 311, série II, (1990) 909-916.
21. E. Sanchez-Palencia, On the membrane approximation for thin elastic shells in the hyperbolic case. Revista Matematica de la Universidad Complutense de Madrid 6(1993) 311-331.
22. M. Spivak, A Comprehensive Introduction to Differential Geometry III, Publish or Perish, Boston, 1979.
23. S.L. ¸Slicaru, Sur l'ellipticité de la surface moyenne d'une coque. C.R. Acad. Sci.Paris, 322, Série I, (1996) 97-100.
24. I.N. Vekua, Generalized Analytic Functions, Pergamon, 1962.