The stress–strain state of symmetric three-layer cylindrical shells under nonstationary loads is considered. The equation of vibrations of a shell with a light core reinforced with stiffening ribs under axisymmetric impulsive loading is derived. The members of the elastic structure are analyzed using the model of Tymoshenko’s theory of shells and rods. Numerical results on the dynamics of the three-layer structure are obtained using the finite-element method. The significant effect of geometric and physical parameters of shell layers on the stress–strain state under axisymmetric internal impulsive loading is investigated.
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References
S. A. Ambartsumyan, General Theory of Anisotropic Shells [in Russian], Nauka, Moscow (1974).
A. E. Babev and V. D. Kubenko, “Nonstationary aeroelasticity of layered shells,” in: A. N. Kubenko (ed.), Dynamics of Structural Members, Vol. 9 of the 12-volume series Mechanics of Composite Materials [in Russian], ASK, Kyiv (1999), pp. 247–261.
M. Yu. Vakhrusheva, “Application of the variational-parametric method to obtain a linear system of algebraic equations in the design of three-layer shallow shells with a discrete inner layer,” in: Mathematical Modeling, Numerical Methods and Problem Complexes [in Russian], SPbGASU (1998), pp. 63–71.
Ya. M. Grigorenko, Isotropic and Anisotropic Layered Shells of Revolution with Variable Stiffness [in Russian], Naukova Dumka, Kyiv (1973).
V. N. Kobelev, L. M. Kovarskii, and S. I. Timofeev, Design of Three-Layer Structures [in Russian], Mashinostroenie, Moscow (1984).
P. Z. Lugovoi and V. F. Meish, “Numerical simulation of the dynamic behavior and strength analysis of multilayer shells under impulsive loading,” Strength of Materials, No. 4, 86–96 (2000).
P. Z. Lugovoi, V. F. Meish, Yu. A. Meish, and G. M. Zabolotnyi, “Forced oscillations of five-layer cylindrical shells with longitudinal-transverse discrete reinforcement under distributed loading,” in: Methods for Solving Applied Problems in Solid Mechanics [in Russian], Issue 12, DNU, Dnipropetrovsk (2011), pp. 203–209.
P. Z. Lugovyi, O. P. Shugailo, S. P. Orlenko, and V. M. Demenkov, “Vibrations of heat-insulating three-layer cylindrical pipes at operational loadings,” Yadern. Radiats. Bezopasn., No. 3, 55–61 (2020).
S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York (1959).
O. M. Ustarkhanov, Kh. M. Muselemov, and Z. K. Akaeva, “Calculation of parameters of a discrete core in the form of a truncated pyramid,” Vestn. Dag. Gos.Tekh. Univ., Tekh. Nauk., No. 19, 59–65 (2010).
Y. Frostig and O. Thomsen, “Higher-order free vibration of sandwich panels with a flexible core,” Int. J. Solids Struct., 1697–1724 (2004).
M. M. Kheirikhah, S. M. R. Khalili, and K. M. Fard, “Biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory,” European J. Mech. A/Solids, 31, No. 1, 54–66 (2012).
P. Z. Lugovyi, 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, V. F. Meish, and S. P. Orlenko, “Numerical simulation of the dynamics of spherical sandwich,” Int. Appl. Mech., 56, No. 5, 590–598 (2020).
P. Z. Lugovoi, Yu. V. Skosarenko, S. P. Orlenko, and O. 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).
V. F. Meish, Yu. A. Meish, and M. A. Belova, “Nonstationary dynamics of elliptic isotropic conical shells under distributed loads,” Int. Appl. Mech., 56, No. 4, 424–431 (2020).
V. F. Meish and S. E. 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).
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This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
Translated from Prikladnaya Mekhanika, Vol. 57, No. 4, pp. 23–34, July–August 2021.
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Lugovyi, P.Z., Gaidaichuk, V.V., Skosarenko, Y.V. et al. Stress–Strain State of Three-Layer Cylindrical Shells with Reinforced Light Core Under Nonstationary Loading*. Int Appl Mech 57, 395–404 (2021). https://doi.org/10.1007/s10778-021-01091-5
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DOI: https://doi.org/10.1007/s10778-021-01091-5