STRESS STATE PROBLEM OF THREE-LAYERED SOLID CYLINDERS WITH CONTINUOUSLY NONHOMOGENEOUS FILLER UNDER DIFFERENT END BOUNDARY CONDITIONS

The article examines the axisymmetric problem of the linear theory of elasticity concerning the stress state of three-layered solid cylinders with a continuously nonhomogeneous filler subjected to uniform normal loading on the lateral surface under two types of end constraints: simply supported and rigidly clamped. The problem is considered for two types of end constraints: simply supported and rigidly clamped. The solution is obtained using a numerical-analytical approach based on spline approximation of the solution along the longitudinal coordinate. This approach reduces the original two- dimensional boundary value problem for a system of partial differential equations to a one-dimensional boundary value problem described by a system of ordinary differential equations, which is solved using a stable numerical method of discrete orthogonalization. Additionally, the method addresses the indeterminacy of certain factors in the system of ordinary differential equations at the geometrically singular point (r = 0).The study considers three-layered cylinders with isotropic load-bearing layers that have different mechanical properties. The filler material is assumed to be continuously nonhomogeneous along the radial coordinate, with its elastic modulus varying according to quadratic and linear laws. The Poisson’s ratio of the filler is taken as the arithmetic mean of the corresponding Poisson’s ratios of the adjacent layers. The layers are assumed to be perfectly bonded without slipping or separation, and at the interfaces, the filler’s elastic modulus matches that of the adjacent layer.The accuracy and reliability of the results are verified by comparing the spline-approximation-based solution with the exact solution for the case of simply supported ends and by varying the number of spline functions.The obtained solutions are presented in the form of graphical distributions of circumferential and longitudinal stress fields along the cylinder radial coordinate. The study establishes the dependencies of the stress state characteristics on the variation of the filler’s elastic modulus, the thickness of the middle layer, and the type of end constraints.