刚性斜桩顶部受任意力的位移的线载荷积分方程法的分析

Analysis of Displacement of Rigid Sloping Pile Under Arbitrary Loads at Top by Line-loaded Integral Equation Method

刚性斜桩顶部受任意力作用的位移分析可以分解为在倾斜平面xoz及其法平面yoz内受力的位移分析.xoz(或yoz)平面内的位移分析,可以用集度为未知函数X(t)(或Y(t))和Z(t)的Mindlin水平点力(平行x轴(或y轴)),垂直点力,在xoz(或yoz)平面内沿桩轴[0,L]内分布,根据边界条件,可将问题归结为Fredholm第一种积分方程.用离散的方法可获数值解.文中给出数值计算的例子.计算的精度用功的互等定理来检查,并将直桩的结果与别人的直桩结果作比较.

The analysis of displacement of rigid sloping pile under arbitrary loads at top can be decomposed into two plane systems, i. e, the inclined plane xoz and its normal plane yoz. The analysis of displacement in xoz (or yoz) plane can be done by the distribution of Mindlin's horizontal force with unknown intensity function X(t) (or Y(t)) parallel to the x-axis (or y-axis) and vertical force with unknown intensity function Z(t) (for xoz plane only) along the axis of the pile in [0. L],then,the problem, according to the boundary conditions, is reduced to Fredholm integral equations of the first kind. Numerical solution can be obtained by discrete method. Numerical examples are given. The accuracy of calculation is checked by the reciprocal theorem of work, and the result of vertical pile is compared with other's.