摘要
用布希涅斯克定义的弹性半空间内的垂直位移包括两项积分,除了积分号前面系数的差别之外,第一项积分是单层位势而第二项积分为双层位势。若扁壳基础是正高斯曲率的几何曲面,则壳底与半空间表面间的挤压强度就是半空间表面作用的分布垂直荷载。当越过边界时,双层势位的函数值和单层势位的法向导数值发生跳跃。利用这些性质,本文得出布希涅斯克积分的反演公式,从而避开要求解偏微分—积分方程组的巨大数学困难而易于得出解析解。以椭园抛物面扁壳为例说明本文方法的应用。
The Boussinesq's integral defining the vertical deflection of an elastic half-space and the normal pressure exerted on a part of its surface consists of two integrals. Except for the coefficients before these integrals, the first one is a single layer potential and the second one is a double layer potential in case the exerted pressure is the contacting pressure between the part of the surface of the half-space and the bottom of an inverted thin elastic shallow shell with positive Gaussian curvature. By using the formulae of finite jumps for double layer potential's function value and for single layer potential's normal derivative value when passing across the contacting surface, we obtain the inverse formula of the Boussinesq's integral in partial differential form which enables us to solve the governing equations of thin elastic shallow shell on elastic half-space much like that of the common thin elastic shallow governing equations without encountering the unsurmountable mathematical difficulty of solving system of three partial differential-integral equations analytically. The example of an elliptic paraboloid thin elastic shallow shell under dynamic vertical load on elastic half-space is given to illustrate our method.
出处
《地震研究》
CSCD
北大核心
1990年第4期435-442,共8页
Journal of Seismological Research
基金
云南省科委应用基础理论研究基金
关键词
地震力
弹性
半空间
位势
Elastic half space
Potential theory
