Numerical simulation of the dynamics of a three-layer spherical shell with a discretely inhomogeneous filler

TitleNumerical simulation of the dynamics of a three-layer spherical shell with a discretely inhomogeneous filler
Publication TypeJournal Article
Year of Publication2020
AuthorsOrlenko, SP
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published3/2020

A constant interest in the widespread use of layered structures in the creation of modern supersonic aircraft and reusable space transport systems has appeared in recent years, and this trend continues and is currently being activated. The effective bearing capacity of three-layer shell structures with sufficient lightness makes them very useful in various engineering applications. The continuous development of new structural materials leads to increasingly complex structural constructions that require careful analysis. One of the common elements of these shell structures are three-layer spherical shells that are subjected to unsteady loads. In the literature, there are a sufficient number of studies on the dynamics of three-layer shells [1]. However, recently, the creation of special-purpose facilities, etc. leads to the need to develop structural three-layer shell elements with a filler with complicated geometric structure. The dynamic behavior of such shells has not been studied enough. In this paper, the kinematic and static hypotheses are applied to each layer of shells, which increases the general order of the system of equations, but allows a more detailed study of the dynamic behavior of a three-layer structure. The solution to the problem is based on the theory of shells and rods based on the Timoshenko shear model. To derive the equations of oscillations of a three-layer structure non-uniform in thickness, the variational principle of Hamilton—Ostrogradsky stationarity is used. The numerical simulation of the dynamics of a three-layer spherical shell with a discrete inhomogeneous filler is carried out using an explicit finite-difference scheme for integrating the equations. Numerical results of solving some specific problems are presented.

Keywordsdiscrete filler, non-stationary load, numerical method., three-layer spherical shell, Timoshenko theory of shells and rods

1. Lugovoi, P. Z.& Meish, V. F. (2017). Dynamics of Inhomogeneous Shell System Under Non-Stationary Loading (Surveys). Int. Appl. Mech., 53, No. 5, pp. 481-537. Doi:
2. Novozhilov, V. V. (1948). Fundamentals of the nonlinear theory of elasticity. Leningrad—Moscow: Gostekhizdat (in Russian).
3. Marchuk, G. I. (1977). Methods of Computational Mathematics. Moscow: Nauka (in Russian).
4. Samarsky, A. A. (1977). Theory of difference schemes. Moscow: Nauka (in Russian).
5. Meish, V. F. & Shtantsel 'S. É. (2002). Dynamic Problems in the Theory of Sandwich Shells of Revolution with a Discrete Core under Nonstationary Loads. Int. Appl. Mech., 38, No. 12, pp. 1501-1507. Doi:
6. Librescu, L., Oh a S.-Yo. & Hohe, J. (2006). Dynamic response of anisotropic sandwich flat panels to underwater and in-air explosions. Int. J. Solids and Structures, 43, pp. 3794-3816. Doi: