Analysis of the Deformation of Multi-layered Orthotropic Cylindrical Elastic Shells Using the Direct Approach

In this paper we analyze the deformation of cylindrical multi-layered elastic shells using the direct approach to shell theory. In this approach, the thin shell-like bodies are modeled as deformable surfaces with a triad of vectors (directors) attached to each point. This triad of directors rotates during deformation and describes the rotations of the thickness filament of the shell. We consider a general set of constitutive equations which can model orthotropic multi-layered shells. For this type of shells we investigate the equilibrium of thin-walled tubes (not necessarily circular) subjected to external body loads and to resultant forces and moments applied to the end edges. We present a general procedure to derive the analytical solution of this problem. We consider that the external body loads are given polynomials in the axial coordinate, which coefficients can be arbitrary functions of the circumferential coordinate. We illustrate our method in the case of circular cylindrical three-layered shells and obtain the solution in closed form. For isotropic shells, the solution is in agreement with classical known results.