Analysis of Stress-Strain State of a Cylinder with Variable Elasticity Moduli Based on Three-Dimensional Equations of Elasticity Theory

Introduction. Functionally graded materials are of great use, because heterogeneity properties enables to control the strength and rigidity structures. This has caused interest in topic world scientific literature. The construction solutions such problems depends significantly on type boundary conditions. In this paper, we consider equilibrium a thin-walled circular cylinder whose mechanical change along radius. Homogeneous conditions were set cylindrical surfaces that had not been considered before, effect was ends. mathematical formulation problem carried out linear theory elasticity framework axisymmetric deformation. Expressions constructed for components stress-strain state cylinder, which some coefficients found from solution resulting system algebraic equations. Materials Methods. material linearly elastic, elastic modulus depended radial coordinate. basic research method asymptotic method, half logarithm ratio outer inner radii acted as small parameter. Iterative processes used construct characteristics cylinder. Results. value obtained functionally gradient hollow An analysis these made it possible reveal nature wall. For purpose, an out, relations displacements stresses obtained. It determined those corresponded layer, while their first terms Saint-Venant edge similar plate theory. Discussion Conclusion. analytical inhomogeneous radius by expansion can be numerical specific problem. this, is required solve systems equations determine corresponding coefficients. representations provide analyzing three-dimensional state. selection number makes calculate with given degree accuracy. useful assessing adequacy applied calculation methods engineering practice.