线载荷积分方程法分析桩顶受任意荷载的弹性斜桩

嵌在各向同性均匀弹性半空间的弹性斜桩顶部,受任意荷载的位移和应力,可分解为在倾斜平面xOz及其法平面yOz内进行分析.将Mindlin力作为基本虚载荷,令集度为未知函数X(t)、Y(t)、Z(t),分别平行于x、y、z轴,的基本载荷沿桩轴t的0,L]内分布,并在桩顶作用集中力Q_x,Q_y、Z,力偶矩M_y、M_x,根据弹性桩的边界条件,将问题归结为一组Fredholm-Volera型的积分方程.文中给出数值解.计算结果的精度可用功的互等定理来检查.

Analysis of Sloping Elastic Pile Under Arbitrary Loads by Line-Loaded Integral Equation Method

The analysis of displacement and stress of elastic sloping pile embedded in a homogeneous isotropic elastic half space under arbitrary loads at 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 and concentrated forces Q x,Q y,Z ,couples M y,M x at top of the pile, then, according to the boundary condtions of elastic pile, the problem is reduced to a set of Fredholm_Volterra type equations. Numerical solution is given and the accuracy of calculation can be checked by the reciprocal theorem of work.