Analysis of initially stressed multilayered shells

Abstract

A refined non-linear first-order global approximation theory of initially stressed multilayered composite shells is developed. The material of each layer of the shell is assumed to be linearly elastic, anisotropic, homogeneous or fiber reinforced. The transverse shear and transverse normal effects are included. It is also assumed that the well-known three-dimensional partially non-linear Novozhilov's strain–displacement relationships are valid. As unknown functions, the tangential and transverse displacements of the top and bottom surfaces of the shell are selected. The paper focuses on two computational models for solving the non-linear problems of prestressed multilayered shells, namely, the axisymmetric deformation of initially stressed multilayered composite shells of revolution and non-axisymmetric deformation of these shells. The joint influence of anisotropy, initially stressed state response, geometrical non-linearity, transverse shear and transverse normal deformation response on the stress state of the shell is examined. It is shown that neglecting the effects of anisotropy and geometrical non-linearity leads to an incorrect description of the stress field in multilayered toroidal shells made of cord–rubber composites.