Analysis of sloping elastic pile under arbitrary loads by line-loaded integral equation method

Abstract

For analysis of displacement and stress, an elastic sloping pile embedded in a homogeneous isotropic elastic half space under arbitrary loads at the top can be decomposed into two plane systems, i.e., the inclined plane xOz and its normal plane yOz. Let Mindlin's forces be the fundamental loads with unknown intensity function X(t), Y(t), Z(t), parallel to x, y, z-axis respectively, be distributed along the t-axis of the pile in [0, L] and concentrated forces Q_x, Q_y, Z, couples M_y, M_x at top of the pile. Then, according to the boundary conditions of elastic pile, the problem is reduced to a set of Fredholm-Volterra type euations. Numerical solution is given and the accuracy of calculation can be checked by the reciprocal theorem of work.