Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Kirichenko V. F., Misnik M. P., Samarkin P. A. Configuration Space in Second Boundary Value Problem of Non-classical Plate Theory. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 75-82. DOI: 10.18500/1816-9791-2013-13-4-75-82

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.12.2013
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Russian
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UDC: 
501.1

Configuration Space in Second Boundary Value Problem of Non-classical Plate Theory

Autors: 
Kirichenko Valerii Fedorovich, Saratov State University
Misnik Maria Petrovna, Saratov State University
Samarkin Pavel Alexsandrovich, Yuri Gagarin State Technical University of Saratov
Abstract: 

The article contains investigation of second boundary value problem for equilibrium equation «in mixed formulation» describing nonclassical mathematical model for hinged isotropic and uniform plate under generalized Timoshenko hypothesis taking into account initial irregularities. For this problem for the first time were proved the existance of generalized solution and weak compactness of the set of approximate solutions obtained with Bubnov–Galerkin method using V. Z. Vlasov scheme. Basing on functional spaces used to study existance of generalized solution and to investigate convergence of Bubnov–Galerkin method, there was defined configuration space corresponding to the boundary value problem.

References: 
  1. Arnold V. I. Mathematical Methods of Classical Mechanics. Springer-Verlag, 1989.
  2. Vilke V. G. Theoretical Mechanics. Saint Petersburg, Lan’, 2003 (in Russian).
  3. Vilke V. G. [Analytical and qualitative methods in the mechanics of systems with an infinite number of degrees of freedom]. Moscow, Izd-vo Moscow Univ. Press, 1986 (in Russian).
  4. Andronov A. A., Vitt A. A., Khaikin S. E. Theory of Oscillators. Dover Publ., Inc., 1987.
  5. Shestakov A. A. Obobshchennyy pryamoy metod Lyapunova dlya sistem s raspredelennymi parametrami. Moscow, Nauka, 2007. (in Russian).
  6. Kirichenko V. F., Samarkin P. A. Kachestvennyy analys evolucionnih uravneniy v neklassicheskoy teorii obolochek c nachalnymy nepravilnostyami [Qualitative analysis of the evolution equations in nonclassical theory of shallow shells with initial irregularities]. Vestnik Saratov. gos. tekhn. univ., 2011, no. 3 (57). iss. 1, pp. 33–40 (in Russian).
  7. Kirichenko V. F., Samarkin P. A. Ispolzovanie norm iz fazovogo prostranstva pri issledovanii dinamicheskoy ustoychivosti pologih obolochek [Application of the phase space norms in the analysis of dynamic buckling of shallow shells]. Vestnik Saratov. gos. tekhn. univ., 2011, no. 4 (60), iss. 2, pp. 70–76 (in Russian).
  8. Lions J. L. Quelques me´ thodes de re´ solution des proble´ mes aux limites non line´ aires [Some methods for solving nonlinear boundary value problems, in French]. Paris, Dunod, 1969.
  9. Ladyzhenskaya O. A. The Boundary Value Problems of Mathematical Physics. Applied Mathematical Sciences, 1985.
  10. Rektoris K. Variacionnye metody v matematicheskoj fizike i tehnike [Variational Methods in Mathematical Physics and Engineering]. Moscow, Mir, 1985 (in Russian).
  11. Ciarlet P. G., Rabier P. Les Equations de von K` arm` an [Von K`arm`an equations]. Springer, 1980 (in French).
  12. Vorovich I. I. Matematicheskie problemy nelineynoy teorii pologih obolochek [Mathematical problems of nonlinear theory of Shallow Shells]. Moscow, Nauka,1989 (in Russian).
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