Quasi-static bending of a cylindrical elastic bar partially embedded in a saturated elastic half-space

Abstract

This paper presents the quasi-static behavior of a circular cylindrical elastic bar which is partially embedded in a saturated elastic half-space. The bar is subjected to a lateral force and a moment at a top end. The material of the half-space is governed by Biot's consolidation theory. The problem is decomposed into two systems; namely, an extended half-space and a fictitious bar with a Young's modulus equal to the difference between the Young's moduli of the real bar and the half-space. The governing equation, which is formulated under the approximation that the slope of the fictitious bar is equal to the corresponding average over a circular area in the extended half-space, is found to be a Fredholm integral equation of the second kind, and solved by an appropriate numerical method for initial and final solutions.