A spherical tank, being perfect as far as weight is concerned, is used in spacecraft, where the thin-walled elements (shells) are united by frames. Obviously, local actions on the shell and hence the stress concentration in the shell cannot be avoided. Attempts to make weight structure of the spacecraft perfect inevitably decrease the safetymargin of the components, which is possible only if the stress-strain state of the components is determined with a controlled error. A mathematical model of shell deformation mechanics is proposed for this purpose, and its linear differential equations are obtained with an error that does not exceed the error of Kirchhoff assumptions in the theory of shells. The algorithm for solving these equations contains procedures for estimating the convergence of the Fourier series and the series of the hypergeometric function with a prescribed error, and the problem can be solved analytically.
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Ya.M. Grigorenko, L. A. Il’in, and A. D. Kovalenko, Theory of Thin Conical Shells and Their Applications in Machine Engineering (Nauka, Moscow, 1992) [in Russian].
G. B. Men’kov, Solution of Problems of Mechanics of Shell Deformation by the Method of Functional Normalization, Candidate’s Dissertation in Mathematics and Physics (Kazan, 1999) [in Russian].
Yu. N. Vinogradov and G. B. Men’kov, A Method for Functional Normalization for Boundary Value Problems in the Theory of Shells (Editorial URSS,Moscow, 2001) [in Russian].
A. P. Filin, Elements of the Theory of Shells (Stroiizdat, Leningrad Division, Leningrad, 1975) [in Russian].
V. V. Novozhilov, Theory of Thin Shells (St. Petersburg Univ., St. Petersburg, 2010) [in Russian].
A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, 2nd. ed. (Chapman & Hall/CRC, Boca Raton, 2003).
Yu. Luke, Mathematical Functions and Their Approximations (Academic Press, New York–San Francisco–London, 1975;Mir,Moscow, 1980).
K. Aomoto and M. Kita, Theory of Hypergeometric Functions (Springer, 2011).
E. Madenci and I. Guven, The Finite Element Method and Applications in Engineering Using ANSYS (Springer, 2006).
Original Russian Text © Yu.N. Vinogradov, M.V. Konstantinov, 2016, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2016, No. 2, pp. 109–120.
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Vinogradov, Y.N., Konstantinov, M.V. Analysis of a spherical tank under a local action. Mech. Solids 51, 223–233 (2016). https://doi.org/10.3103/S0025654416020102