弹性半空间地基上正交异性矩形中厚板的弯曲

Bending of orthotropic rectangular middle thick plate on elastic half-space foundation

为了分析弹性半空间地基上正交异性矩形中厚板的弯曲解析解,将3个广义位移变量描述的弹性半空间地基上四边自由正交各向异性矩形中厚板的弯曲控制方程,与基于弹性半空间地基受任意竖向荷载作用下的静力位移积分解建立的板与地基变形协调方程相结合,用三角级数法,得出弹性半空间地基上四边自由正交异性矩形中厚板受任意竖向荷载作用下的弯曲解析解,即得出了地基反力、板的挠度及板的内力的解析表达式。研究结果表明,该方法克服了数值法的弊端,取消了Winkler地基模型或双参数地基模型的假设,从而得到板的内力及地基反力更合理、更精确的分布规律。

The bending equation of orthotropic rectangular middle thick plate with four free edges was combined with the equation of deformation compliance of the plate and the foundation based on the integral solution of the elastic half-space foundation loaded with arbitrary vertical lead force.An analytical solution was gained to the problem of the bending of the orthotropic rectangular middle thick plate with four free edges on the semi-infinite elastic foundation by using the trigonometric series,the analytical representations of the reactive force of the ground,the deflection and the inner force of the plate were obtained.The results show that the method not only overcomes some defects involved in traditional numerical methods,but also avoids the assumption of Winkler foundation model or two-parameter foundation model.The distributions law of the inner forces in the plate and the contact pressure are more reasonable and accurate.1 tab,4 figs,11 refs.