ABSTRACT
The theory of simple shells is based on the direct approach to the mechanics of thin bodies, in which the shell-like body is modeled as a deformable surface endowed with a triad of orthonormal vectors connected to each material point of the surface.This idea was first proposed by Cosserat & Cosserat (1909). The definition of a simple shell has been given by Zhilin (1976) as a two-dimensional continuum in which the neighboring parts interact by means of forces and moments. This model has the advantage that it can be applied to shells with a complex internal structure and it allows the formulation of a shell theory with effective stiffness. Thus, the approach of simple shells has been employed to describe the effective properties of different classes of thin structures (Altenbach & Zhilin 1988, Zhilin 2006). Another direct approach for elastic shells consists in a surface with one deformable director (also called the Cosserat surface), which was discussed in details in the books of Naghdi (1972) and Rubin (2000).
