Two-dimensional linear model of elastic shell accounting for general anisotropy of material (original) (raw)

A two-dimensional linearly elastic model of shells made of an anisotropic material described by 21 elastic moduli is developed. For this aim, the generalized Timoshenko-Reissner hypotheses are used. In contrast to the ordinary shell models, the tangential stress-resultants here depend not only on the tangential strains but also on the transverse shear. An asymptotic analysis of the obtained equations is fulfilled. The typical stress-strain states, namely the membrane state, the edge effect state, and the boundary layer, are constructed. The system of the Donnell type is delivered. As an example of general anisotropy, a composite material consisting of a matrix reinforced by the system of fibers inclined to the mid-surface is studied. Certain simple static problems and free vibration problems are solved for a cylindrical shell made of this material.