标题： Lamb问题的精确闭式解 显示英文标题

标题： Exact Closed-form Solutions for Lamb's Problem

摘要： 本文报告了一个精确的闭式解，该解描述了弹性半空间表面由于埋藏点源在其下方某处的作用而产生的位移。这通常被称为三维Lamb问题，对于该问题，先前的解仅限于源和接收器置于自由表面的情况。 通过互易定理，我们的解也应该可以作为当源置于自由表面时获得内部点位移的一种手段。我们通过将解表达为基本代数表达式以及椭圆积分来得到显式结果。 我们的研究基于泊松比0.25，从Johnson（1974）的积分解开始，这些积分解必须进行数值计算。最终，我们的闭式结果与Johnson（1974）的数值结果完全一致，这强烈证实了我们显式公式的正确性。 希望随着时间的推移，这些公式可以成为一个有价值的规范解，用作其他数值解比较和衡量的标准。 显示英文摘要

摘要： In this article, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem, for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's (1974) integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson (1974), which strongly confirms the correctness of our explicit formulas. It is hoped that in due time, these formulas may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.