Analysis of Sloping Elastic Pile Under Arbitrary Loads by Line-Loaded Integral Equation Method
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摘要: 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Qx,Qy、Z,力偶矩My、Mx,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.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 and concentrated forces Qx,Qy,Z,couples My,Mx 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 equations.Numerical solution is given and the accuracy of calculation can be checked by the reciprocal theorem of work.
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