Buckling problems of a cylindrical shell made of anisotropic material
The 2D model of a cylindrical shell made of an anisotropic material with 21 elastic modules is presented. It is established that as the Kirchhoff-Love hypotheses, so the Timoshenko-Reissner hypotheses do not lead to correct 2D models. To deliver the 2D equations the generalized cinematic Timoshenko-Reissner hypotheses are used. In contrast to the ordinary shell models here the tangential stress-resultants depend not only on the tangential strains but also on the transversal shear. The asymptotic analysis of the obtained system is fulfilled. The system of 2D equations of the 8th order similar to a system of equations of shallow shells of Donnell type is built. Some simplest buckling for cylindrical shells is studied, namely the buckling problems under the action of external lateral compression, of torsion, and of axial compression. The obtained results are compared with the well-known results for an isotropic shell. The most essential difference is marked in the problem of axial compression. If for the isotropic shell a lot of buckling modes correspond to a critical compression then for the studied anisotropic shell the buckling mode is single. As an example the composite material consisting of matrix reinforced by a system of fibers is used.