Numerical simulation of oscillations of a three-layer conical shell with a discre-tesymmetric inhomogeneous filler

Abstract

The constant interest in the widespread use and creation of modern structural materials often leads to the need for the simultaneous implementation of a number of sometimes contradictory requirements for multilayer structures, in which each layer performs only one or, better, several functions. The layers can differ both in thickness and in physical and mechanical properties, i.e., the package can be significantly inhomogeneous. The effective load-bearing capacity of three-layer shell structures with lightweight filler makes them very useful with sufficient ease in various engineering applications. It has been experimentally proved that the reinforcement of a lightweight filler with discrete-symmetric rigid elements significantly increases the strength and resistance strength of three-layer structures. The continuous development of new structural materials leads to increasingly complex structural structures that require a careful analysis. One of the common elements of these shell structures are three-layer conical shells, which are subjected to non-stationary loads. There is a sufficient amount of works in the literature about studying the dynamics of three-layer shells [1]. However, the recent creation of special purpose facilities, etc. leads to the need to develop constructive three-layer shell elements with a filler of a complicated geometric structure [2]. The issues of the dynamic behavior of such shells are insufficiently studied. In this paper, kinematic and static hypotheses are applied to each layer of shells, which increases the general order of the system of equations, but allows us to study the dynamic behavior of the three-layer structure in more details. The solution of the problem is based on the theory of shells and rods, based on the Timoshenko landslide model. The Hamilton–Ostrogradsky stationarity variational principle is used to derive the equations of oscillations of a three-layer structure of inhomogeneous thickness. The numerical simulation of the dynamics of a three-layer conical shell with discrete-symmetric lightweight filler is performed using the finite element method. Numerical results of solving the specific problems are given, and some new mechanical effects are revealed.