A Semi-Analytical Solution of Thick Truncated Cones Using Matched Asymptotic Method and Disk Form Multilayers

Abstract

In this article, the thick truncated cone shell is divided into disk-layers form with their thickness corresponding to the thickness of the cone. Due to the existence of shear stress in the truncated cone, the equations governing disk layers are obtained based on first shear deformation theory. These equations are in the form of a set of general differential equations. Given that the truncated cone is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. The results obtained have been compared with those obtained through the analytical solution and the numerical solution. For the purpose of the analytical solution, use has been made of matched asymptotic method (MAM) and for the numerical solution, the finite element method (FEM).

Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading

“…In their work, they converted a hollow cylinder with variable thickness into some disk layers and assumed the thickness to be constant in each disk. In other work, they derived an elastic solution for the purpose of determining displacements and stresses in a thick pressure vessel which MLM has been used for solution (Nejad et al, 2014a(Nejad et al, , 2014b. They obtained the MLM is very suitable for the purpose of calculation of radial stress, circumferential stress, shear stress and radial displacement, but it is not useful for axial stress and not useful at all for axial displacement.…”

Elastic Analysis of Rotating Thick Cylindrical Pressure Vessels under Non-Uniform Pressure: Linear and Non-Linear Thickness

“…Thick cylindrical shells with variable thickness have widely been applied in many fields such as space fight, rocket, aviation, and submarine technology [15]. Given the limitations of the classic theories of thick wall shells, very little attention has been paid to the analytical and semi-analytical solutions of these shells [16]. Assuming the transverse shear effect, Naghdi and Cooper [12], formulated the theory of shear deformation.…”