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IssuesArchive of Issues2014-2pp.187-195

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O.M. Palii, "A Version of Applied Theory of Thick Shells," Mech. Solids. 49 (2), 187-195 (2014)
Year 2014 Volume 49 Number 2 Pages 187-195
DOI 10.3103/S002565441$020083
Title A Version of Applied Theory of Thick Shells
Author(s) O.M. Palii (Krylov Shipbuilding Research Institute, Moskovskoe†sh.†44, St.†Petersburg, 196158 Russia, krylov@krylov.spb.ru)
Abstract A version of an applied theory of shells of large thickness based on the introduction of force and kinematic hypotheses completing and extending the set of Love-Kirchhoff and Timoshenko-Reissner hypotheses is discussed. The complete system of equations including the elasticity relations, the geometric relations (displacements and strains), and the equilibrium equations is written out. The obtained system of equations is verified in several special cases. It is noted that the error of this theory does not exceed the squared thickness-to-radius ratio compared with unity.
Keywords shell, relative thickness, kinematic and force hypotheses, displacement, strain, stress, system of equations
References
1.  V. V. Novoshilov, "On an Error of a Hypothesis in the Theory of Shells," Dokl. Akad. Nauk SSSR 38 (5-6), 174-179 (1943).
2.  V. V. Novoshilov and R. M. Finkel'shtein, "On an Error of Kirchhoff Hypothesis in the Theory of Shells," Prikl. Mat. Mekh. 7 (5), 331-340 (1943) [J. Appl. Math. Mech. (Engl. Transl.)].
3.  O. Yu. Kalekin, "To the Approximate Theory of Shells of Medium Thickness," Prikl. Mekh. 1 (12), 29-37 (1965) [Int. Appl. Mech. (Engl. Transl.)].
4.  V. V. Ponyatovskii, "On a Method for Constructing Two-Dimensional Theory of Shells by Using Legendre Polynomials," in Novozhilov Collection of Papers (Sudostroenie, St. Petersburg, 1992) [in Russian].
5.  V. V. Pikul, Applied Mechanics of Deformable Solid (Nauka, Moscow, 1989) [in Russian].
6.  V. A. Rodionova, B. F. Titaev, and K. F. Chernykh, Applied Theory of Anisotropic Plates and Shells (Izd-vo St. Petersburg Univ., St. Petersburg, 1996) [in Russian].
7.  O. M. Palii and V. E. Spiro, Anisotropic Shells in Shipbuilding (Sudostroenie, Leningrad, 1977) [in Russian].
8.  V. V. Novozhilov, Theory of Thin Shells (Izdat. St. Petersburg Univ., St. Petersburg, 2009) [in Russian].
Received 11 May 2011
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