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

Abstract

Using multi-layers method (MLM), a semi-analytical solution have been derived for determination of displacements and stresses in a thick cylindrical shell with variable thickness under non-uniform pressure. Three different profiles (convex, linear and concave) are  considered for the variable thickness cylinder. Given the existence of shear stress in the thick cylindrical shell due to thickness and pressure changes along the axial direction, the governing equations are obtained based on first-order shear deformation theory (FSDT). These  equations are in the form of a set of general differential equations with variable coefficients. Given that the thick cylinder with variable thickness is divided into n homogenous disks, n sets of differential equations with constant coefficients are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. Finally, some numerical results are presented to study the effects of applied pressure, thickness profile type, and angular velocity on the mechanical behavior of the cylindrical shell.