Abstract
An approach is proposed to solving linear boundary-value problems for shells of revolution that are closed in the circumferential direction, with complex boundary conditions in which the coefficients of the solving functions depend on the circumferential coordinate. The approach relies on reduction of the boundary-value problem to a number of boundary-value problems for systems of ordinary differential equations and systems of algebraic equations. We solve a specific problem for the stressed state of a conical shell with one of its ends supported by an elastic foundation with a variable modulus.
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References
Ya. M. Grigorenko, Isotropic and Anisotropic Layered Shells of Revolution with Variable Rigidity [in Russian], Kiev (1973).
Ya. M. Grigorenko and A. T. Vasilenko, Theory of Variable Rigidity Shells, Vol. 4, Methods for Computation of Shells [in Russian], Kiev (1981).
Additional information
Institute of Mechanics, Ukrainian Academy of Sciences. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 85–93, 1989.
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Vasilenko, A.T., Polishchuk, T.I. Solving some problems in the theory of thin shells of revolution with complex boundary conditions. J Math Sci 69, 1437–1442 (1994). https://doi.org/10.1007/BF01250588
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DOI: https://doi.org/10.1007/BF01250588