弹性半空间上圆板的弯曲分析

The analysis series to general bending of circular plates on elastic half-space

对各向同性弹性半空间地基上薄圆板一般弯曲问题进行了系统的分析。板的挠度、荷载、地基反力及板下地基表面的沉降均被展开为二重Fourier-Bessel级数,这些级数中的待定系数,由板的边界条件、板的控制方程及板—地基的相容条件加以确定,从而将弹性半空间地基与薄圆板的相互作用问题转化为数值积分和代数方程组的求解问题。数值计算表明,该级数解答具有较快的收敛速度。

General bending of thin circular plates on an elastic half-space is investigated in this paper. The deflection of plate, the load, the reactive force of soil ground, and the settlement of half-space＇s surface under the plate are all expanded to the double Fourier-Bessel series. The unknown coefficients in those series are ascertained by the boundary conditions of plate, the governing equation of plate, and the continuous condition of plate-ground. The problems of interactions between plate and half-space are changed to the problems of numerical integral and algebraic equations. In the end, the numerical calculi are accomplished and the results indicate that the series are of quick convergence rate.