Analytic Solution for Finite Transversely Isotropic Circular Cylinders under the Axial Point Load Test

Abstract

An exact solution for stress distributions within a finite transversely isotropic cylinder for the axial point load strength test (PLST) is analytically derived. Lekhnitskii’s stress function is first used to uncouple the equations of equilibrium. Two different kinds of solutions corresponding to the real and the complex characteristic roots of the governing equation of the stress function are derived. The solution type to be used for stress analysis depends on the anisotropic parameters of the cylinder. The solution for isotropic cylinders under the axial PLST is recovered as a special case. Numerical results show that the pattern of stress distribution along the line joining the point loads does not depend on the degree of anisotropy of the cylinder, but the magnitude of the stress distributions does. In particular, the local maximum tensile stress, which is located near the point loads, may be either larger or smaller than that of isotropic cylinders. In general, the maximum tensile stress inside the cylinder increases with the ratio of Young’s moduli, but decreases with both the ratio of Poisson’s ratio and the ratio of the shear moduli. If anisotropy of the cylinder is ignored, the point load strength index may be overestimated when the ratio of Young’s moduli is greater than one, or when the ratios of Poisson’s ratio or of the shear moduli is smaller than one.