ON THE PROBLEM OF THE THEORY OF ELASTICITY FOR THE RADIALLY INHOMOGENEOUS TRANSVERSAL ISOTROPIC CYLINDER WITH A FIXED LATERAL SURFACE

Abstract

Using the method of asymptotic integration of the equations of the theory of elasticity, the axisymmetric problem of the theory of elasticity for a radially inhomogeneous transversally isotropic cylinder of small thickness is studied. Suppose that the elastic moduli are arbitrary continuous functions of the radius of the cylinder. It is assumed that the side part of the cylinder is fixed, and stresses are set at the ends of the cylinder, leaving the cylinder in equilibrium. Solutions have been determined having the nature of a boundary layer and are localized at the ends of the cylinder. The first terms of its asymptotic expansion coincide with the Saint-Venant edge effect in the theory of plates. The nature of the stress-strain state has been studied. It is shown that some boundary layer solutions may not be extinguished by propagating far from the ends.