3-D analytical solution of non-homogeneous transversely isotropic thick closed cylindrical shells

Abstract

This paper presents an effective analytical method based on displacement potential functions (DPF) for solving 3D static problem of thick and multilayer transversely isotropic cylindrical shells with simply supported end boundary conditions. By using the DPF method, the three-dimensional elasticity equations are simplified and decoupled into two linear partial differential equations of fourth and second order as governing differential equations. The governing equations are solved by the separation of variable method in terms of fields that exactly satisfy end boundary conditions and the continuity of a closed cylinder in the hoop direction. The analysis covers a straightforward solution process for handling problems on multilayered cylindrical shells of transversely isotropic material, adopting all boundary and continuity conditions. Extensive sets of general radial loads located on the inner and outer faces of the cylindrical shell may be stated and examined with in a systematic manner. Comparisons are performed to other existing analytical results for one and multilayered cylindrical shells, and show excellent agreement for different materials, thicknesses and aspect ratios of the shell. In addition, various more involved problems are studied and solved analytically for single and three-layered shells of transversely isotropic material with different sets of radial loading functions at the outer and inner shell surfaces. The results of the present study can be used as benchmark solutions for other studies.