Numerical analysis of the stress state of non-thin corrugated cylindrical shells made of continuous-inhomogeneous materials

Cylindrical shells of circular and non-circular cross-section are used as structural elements in many branches of economy. To increase the reliability of operation of such elements, continuous non-homogeneous materials are used. This research investigates non-thin cylindrical shells with corrugated as cross sections made of the continuously inhomogeneous materials. The shells are subjected to internal pressure under conditions of simple support on the ends.The subject of the study is the stressed state of the shells and, as a consequence, the establishment of dependencies between its characteristics and the geometric parameters of the reference surface, the thickness of the shells, and the law of change of the modulus of elasticity of the material. The aim of the work is numerical analysis of the stress state of shells of such class depending on the amplitude of the corrugation, the thickness of the shells and the law of variation of elastic properties of their material. The solution of the problem is based on reduction of the original three-dimensional boundary value problem for the system of partial differential equations with variable coefficients to a one-dimensional boundary value problem for a system of ordinary differential equations with constant coefficients of higher order. At the same time, the analytical method of separating variables in two coordinate directions is used, together with approximation of functions by discrete Fourier series. The one-dimensional boundary value problem is solved by the stable numerical method of discrete orthogonalization. An analysis of the stress state of the considered shells was carried out depending on the amplitude of the corrugation, the thickness of the shells and the law of change of the elastic characteristics of the material. It is shown that with a slight deviation of the shape of the cross-section from the circular one, for a certain thickness of the shells, the presence of corrugations can be neglected when choosing the calculation model.In addition, the presence of corrugations causes a redistribution of the values of displacements and stresses in the characteristic sections of the shells, which must be taken into account when calculating the strength and reliability of the structures under consideration.