Mechanics of Anisotropic Heterogeneous Shells: Fundamental Relations for Different Models

Abstract

Elastic bodies in the form of thin and thick-walled anisotropic shells are considered. The shells may be made both of homogeneous and inhomogeneous materials with discrete (multilayer) structure or of continuously inhomogeneous materials (functionally gradient materials). The stationary deformation of such shells is analyzed by using various mechanical models. The basic relations of the theory of elasticity, which include equilibrium equations of motion, geometrical, and physical relations, are presented. By using classical and refined shell theories, the original three-dimensional problem is reduced to a two-dimensional one. The basic equations of the classical (Kirchhoff-Love) shell theory, which are based on the hypothesis of undeformed normals, are presented. It is assumed that all of the shell layers are stiffly joined and operate mutually without sliding and separation. Moreover, geometrical and mechanical parameters of the shells and mechanical loads applied to them are such that, considering the shell as a unit stack, the hypothesis of undeformed normals is valid. In the case of laminated shells made of new composite materials with low shearing stiffness, where anisotropy and inhomogeneity of the mechanical properties of the layers vary considerably, the refined model based on the straight-line hypothesis is used. The basic equations of the model are presented and various physically consistent boundary conditions at the bonded surfaces of the shells are specified.