The equations of vibrations of a stringer-reinforced spherical sandwich shell under unsteady loading are obtained. In analyzing the elements of the elastic structure, the models of the Timoshenko theory of shells and rods are used. The numerical method for solving the obtained equations is based on the application of the integro-interpolation method for constructing finite-difference schemes for equations with discontinuous coefficients. The problem of the dynamic behavior of a spherical sandwich shell under unsteady loading is solved taking into account the discreteness of the ribs. Numerical results are plotted and analyzed.
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References
K. G. Golovko, P. Z. Lugovoi, and V. F. Meish, Dynamics of Inhomogeneous Shells under Nonstationary Loads [in Russian], Poligr. Tsentr “Kievskii Universitet,” Kyiv (2012).
P. Z. Lugovoi, M. I. Mikhailova, D. F. Meish, S. P. Malashenkov, I. I. Anik’ev, and E. A. Sushchenko, “Interaction of complex objects with shock waves,” Strength of Materials, 35, No. 6, 581–587 (2003).
G. I. Marchuk, Methods ùà Computational Mathematics [in Russian], Nauka, Moscow (1977).
V. F. Meish, V. K. Stryuk, and L. V. Cat, “Unsteady behavior of discrete-reinforced sandwich shells of rotation under longitudinal impulse loading,” Visn. Kyiv. Univ. Ser. Fiz.-Mat. Nauky, No. 3, 171–175 (1999).
A. N. Guz (ed.), Mechanics of Composite Materials and Structural Members [in Russian], in 3 vols., Vol. 3, Applied Research, Naukova Dumka, Kyiv (1982–1983).
V. V. Novozhilov, Foundations of the Nonlinear Theory of Elasticity, Dover, New York (1999).
A. A. Samarskii, The Theory of Difference Schemes, Marcel Dekker, New York (2001).
V. I. Tsypkin, A. G. Ivanov, V. I. Mineev, and A. N. Shitov, “Effect of scale, geometry, and filler on the strength of steel vessels to internal pulsed loads,” Soviet Atomic Energy, 41, No. 5, 944–950 (1976).
À. N. Guz and V. À. Zarutskii (eds.), Experimental Research of Thin-Walled Structures [in Russian], Naukova Dumka, Kyiv (1984).
I. I. Anik’ev, M. I. Mikhailova, and E. A. Sushchenko, “Dynamic loading of cylindrical and spherical bodies interacting with a shock wave,” Int. Appl. Mech., 40, No. 12, 1405–1410 (2004).
E. Carrera, “On the use of the Murakami’s zig-zag function in the modeling of layered plates and shells,” Comp. Struct., 82, No. 7–8, 541–554 (2004).
R. Li, A. Kardomateas, and G. J. Simitses, “Nonlinear response of a shallow sandwich shell with the compressible core to blast loading,” J. Appl. Mech., 75, No. 6, 061023 (2008).
L. Librescu, S. Yo. Oh, and J. Hohe, “Dynamic response of anisotropic sandwich flat panels to underwater and in-air explosions,” Int. J. Solids Struct., No. 43, 3794–3816 (2006).
P. Z. Lugovoi and V. F. Meish, “Dynamics of inhomogeneous shell systems under nonstationary loading (survey),” Int. Appl. Mech., 53, No. 5, 481–537 (2017).
P. Z. Lugovoi, V. F. Meish, Yu. A. Meish, and S. P. Orlenko, “Dynamic design of compound shell structures of revolution under nonstationary loads,” Int. Appl. Mech., 56, No. 1, 22–32 (2020).
P. Z. Lugovoi, A. P. Shugailo, Ya. D. Kruglyiy, and A. V. Kolupaev, “Effect of sludge on the stress-strain state of heat-exchange tubes of a steam generator,” Int. Appl. Mech., 55, No. 1, 86–94 (2019).
P. Z. Lugovoi, Yu. V. Skosarenko, S. P. Orlenko, and A. P. Shugailo, “Application of the spline-collocation method to solve problems of statics and dynamics for multilayer cylindrical shells with design and manufacturing features,” Int. Appl. Mech., 55, No. 5, 524–533 (2019).
D. A. Maturi, A. J. M. Ferreira, A. M. Zenkour, and D. S. Mashat, “Analysis of laminated shells by Murakami’s zig-zag theory and radial basis functions collocation,” J. Appl. Math., Article ID 123465 (2013).
V. F. Meish, Yu. A. Meish, and N. V. Arnauta, “Numerical analysis of nonstationary vibrations of discretely reinforced multilayer shells of different geometry,” Int. Appl. Mech., 55, No. 4, 426–433 (2019).
V. F. Meish and S. É. Shtantsel’, “Dynamic problems in the theory of sandwich shells of revolution with a discrete core under nonstationary loads,” Int. Appl. Mech., 38, No. 12, 1501–1507 (2002).
M. S. Qatu, Vibration of Laminated Shells and Plates, Academic Press, New-York (2004).
M. S. Qatu, E. Asadi, and W. Wang, “Review of recent literature on static analyses of composite shells: 2000–2010,” Open J. Compos. Mater., 2, No. 3, 61–86 (2012).
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Translated from Prikladnaya Mekhanika, Vol. 56, No. 5, pp. 78–88, September–October 2020.
This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK).
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Lugovoi, P.Z., Meish, V.F. & Orlenko, S.P. Numerical Simulation of the Dynamics of Spherical Sandwich Shells Reinforced with Discrete Ribs Under a Shockwave*. Int Appl Mech 56, 590–598 (2020). https://doi.org/10.1007/s10778-020-01037-3
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DOI: https://doi.org/10.1007/s10778-020-01037-3