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与传统的Lamb分析方法不同,本文利用在时间为Heaviside阶跃函数变化的圆形均布荷载作用下匀质各向同性弹性半空间表面圆心竖向位移的闭会解(此解答由本文前两作者得到,适用于任何泊松比值)以及突加谐和荷载的概念,首次得到了圆形均布谐和荷载作用下圆心位移的精确解。利用此精确解,作者提出了分析各种竖向谐和荷载作用下弹性半空间表面竖向位移的圆心位移影响函数法。 本文还提出了圆形及环形基础原面内外点位移及平均位移的具体计算式。由本文的圆心位移精确解及各种情况的具体计算式所得结果均以曲线图和表格示出,并与已有的理论结果作了广泛的对比。
Different from the traditional Lamb analysis method, this paper uses the closed solution of the vertical displacement of the center of the surface of a homogeneous isotropic elastic half-space under the action of a circular uniform load whose time is a change of the Heaviside step function. Obtained, applicable to any Poisson’s ratio value) and the concept of sudden harmonic loads, for the first time the exact solution of the center of the circle displacement under uniform harmonic loads is obtained. Using this exact solution, the author proposes a method to analyze the influence of center displacement on the vertical displacement of the elastic half-space under various vertical harmonic loads. In this paper, the specific calculation formulas of the point displacement and the average displacement in the inside and outside of the original surface of the circular and annular foundations are also proposed. The exact calculations of the center-displacement displacements of this paper and the specific calculation formulas of various situations are shown in graphs and tables, and are compared with the existing theoretical results extensively.