Efficient Approximate Analytic Solution for the Problem of Stability of a Three-Layer Conic Shell Under Combined Loading

Abstract

We propose a solution of the linear problem of behavior of an elastic three-layer conic shell under the combined action of several external force factors (uniform pressure, axial compression, and torque), which may lead to the loss of stability of the analyzed structure. The problem is reduced to the integration of the resolving singular sixth-order ordinary differential equation with variable coefficients. The solutions obtained by the methods of phase integrals (WKB method), hybrid WKB–Galerkin method, and finite-difference method are compared. We demonstrate the advantages of the asymptotic hybrid approach to the solution of the analyzed class of equations. The rational relationships between the thicknesses and elasticity moduli of layers of the shell required for attainment of the highest stability of the investigated structure under given external loads are analyzed. The problem of construction of the boundary surfaces separating the regions of stability and instability of the shell is discussed. The efficiency of three-layer shells as load-bearing elements aimed at improving stability is confirmed.