عنوان مقاله [English]
This work considers an effective analytical method based on displacement potential function (DPF) for solving 3D thick and multilayer transversely isotropic linearly elastic cylindrical shells (non-homogeneous in radial direction) with simply supported- simply supported end boundary conditions. Axisymmetric radial loads are applied in the inner and outer faces of the cylindrical shell. Three dimensional elasticity equations are simplified using displacement potential function result in one single linear partial differential equation of fourth order as governing differential equation in term of displacement potential functions. The governing equation are solved by separation of variable method with exact satisfaction of two end boundary condition include stress and displacement boundary conditions, stresses at inner and outer surfaces of the shell and the continuity conditions of the displacement and tractions on the interfacial surfaces of the multilayer cylindrical shell and after determining displacement potential function, all other functions such as stresses and displacements can be obtained at each points of the examined shell. Comparison of the results with existing analytical results show excellent agreement of the method for different thickness ratio and aspect ratios of the shells. Some practical problems are solved for one layer and three layer cylindrical shell. For this purpose, three types of materials are defined for one layer cylindrical shell such as a composite material, Graphite epoxy, as well as metallic substance, Zinc and an isotropic material, Aluminum. Also two combinations of materials are considered for three layers cylindrical shell so that the inner and outer layers of the shell are made of transversely isotropic materials (Graphite epoxy) and the middle layer of isotropic material such as Aluminum and Foam. The values of the non-dimensional functions, containing the stress and displacement components are calculated for these problems to show the effect of thickness ratio and anisotropy of the shell on the distribution of the stresses and displacements.