弹性半空间上中厚圆板弯曲的Fourier-Bessel级数解

本文对各向同性弹性半空间地基上中厚度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中厚度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,该级数解具有较快的收敛速度。

Fourier-Bessel Series Solution for General Bending of Moderately Thick Circular Plate on Elastic Half Space

The general bending of moderately thick circular plate on an elastic half-space was investigated.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 were ascertained by the boundary conditions of plate,the governing equations of plate,and continuous condition of plate ground.The problem of the interactions between plate and half space is changed to solve the numerical integral and algebraic equations.In the end,the numerical calculation was accomplished and indicates that the series are of quick convergence rate.