On the basis of the linear three-dimensional theory of elasticity, we consider the problem of equilibrium of nonthin isotropic cylindrical shells with dents under certain boundary conditions imposed on the end faces. To describe the cross section of the reference surface, we use the Pascal snail equation in polar coordinates. By the method of separation of variables, with the help of the approximation of functions by discrete Fourier series, we reduce the three-dimensional boundary-value problem to a one-dimensional problem, which is solved by the stable numerical method of discrete orthogonalization. We estimate the accuracy of the obtained solutions. The results of solving the problems are presented in the form of plots and tables.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 2, pp. 72–82, April–June, 2020.
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Grigorenko, Y.М., Rozhok, L.S. On the Equilibrium of Nonthin Cylindrical Shells with a Dent. J Math Sci 272, 80–92 (2023). https://doi.org/10.1007/s10958-023-06401-5
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DOI: https://doi.org/10.1007/s10958-023-06401-5