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IssuesArchive of Issues2007-3pp.429-436

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B. V. Nerubailo and V. P. Ol’shanskii, "Asymptotic method for analysis of a conical shell under local loading," Mech. Solids. 42 (3), 429-436 (2007)
Year 2007 Volume 42 Number 3 Pages 429-436
Title Asymptotic method for analysis of a conical shell under local loading
Author(s) B. V. Nerubailo (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993, Russia, prof_nebo@mail.ru)
V. P. Ol’shanskii (National Technical University “Kharkiv Polytechnical Institute”, Frunze 21, Kharkov, 61002, Ukraine)
Abstract Differential equations of the general theory describing the stress-strain state of conical shells are very complicated, and when computing the exact solution of the problem by analytic methods one encounters severe or even so far insurmountable difficulties. Therefore, in the present paper we develop an approach based on the method of asymptotic synthesis of the stressed state, which has already proved efficient when solving similar problems for cylindrical shells [1, 2]. We essentially use the fourth-order differential equations obtained by Kan [3], which describe the ground state and the boundary effect. Earlier, such equations have already been used to solve problems concerning force and thermal actions on weakly conical shells [4–6]. By applying the asymptotic synthesis method to these equations, we manage to obtain sufficiently accurate closed-form solutions.
References
1.  I. F. Obraztsov, B. V. Nerubailo, and I. V. Andrianov, Asymptotic Methods in the Structal Mechanics of Thin-Walled Structures (Mashinostroenie, Moscow, 1991) [in Russian].
2.  B. V. Nerubailo, Local Strength Problems for Cylindrical Shells (Mashinostroenie, Moscow, 1983) [in Russian].
3.  S. N. Kan, Structural Mechanics of Shells (Mashinostroenie, Moscow, 1966) [in Russian].
4.  V. A. Sibiryakov, "Analysis of an Orthotropic Conical Shell for an Arbitrary External Load by V. Z. Vlasov's Method," Izv. Vyssh. Uchebn. Zaved. Aviats. Tekhnika, No. 2, 72-82 (1959).
5.  V. A. Sibiryakov, "Determining Thermal Stresses in a Conical Shell," Izv. Vyssh. Uchebn. Zaved. Aviats. Tekhnika, No. 1, 72-82 (1960).
6.  B. V. Nerubailo, "On the Solution of Differential Equations of Conical Shells with Singular Right-Hand Side," PMTF 37 (2), 157-161 (1996).
7.  S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959; Fizmatgiz, Moscow, 1963).
8.  I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Nauka, Moscow, 1971) [in Russian].
Received 01 June 2004
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