On the problems of Almansi and Michell for anisotropic Cosserat elastic shells

Abstract

This paper investigates the equilibrium of cylindrical elastic shells under the action of prescribed body loads, external loads on the lateral edges, and resultant forces and moments on the end edges. We consider anisotropic and inhomogeneous cylindrical shells with arbitrary (open or closed) cross-sections, and we employ the linear theory of Cosserat surfaces. We present a method to construct the solutions to the problems of Almansi and Michell. Then, we apply these results to study the deformation of orthotropic and homogeneous circular cylindrical tubes and Cosserat plates.