On the Diffusion of an Axial Load from an Infinite Cylindrical Bar Embedded in an Elastic Medium

Abstract

his investigation is concerned with the decay of the resultant axial force in an infinite cylindrical elastic bar that is completely bonded to an all around infinite elastic medium of distinct mechanical properties. The bar is subjected to an axial loading confined to, and uniformly distributed over, one of its cross-sections. First, a solution to this problem, exact within classical three-dimensional elastostatics, is obtained for the special case of a circular cylindrical bar. Next, an approximative solution scheme applicable to a cross-section of arbitrary shape is developed. This scheme is subsequently used to deduce an approximate solution for the bar of circular cross-section. The exact and the approximate solution appropriate to the circular bar are compared with each other, particular attention being given to their asymptotic behavior near the load and at large distances from the applied loading. The present work is preliminary to an approximate treatment of the physically more important problem pertaining to The diffusion of load from a transverse tension-bar that is immersed to a finite depth in an elastic halfspace. In addition, the results established here are of interest in connection with the study of fiber-reinforced materials.

Additional details