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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。
In order to analyze the analytical solution of bending of orthotropic rectangular plates on elastic half-space foundations, the bending control equations of rectangular orthotropic rectangular plates on elastic half-space foundation, which are described by three generalized displacement variables, The elastic half-space foundation is subjected to the static displacement integral solution under any vertical load combined with the deformation coordination equation of the foundation. Using triangular series method, the free orthotropic rectangular plate Under the analytical solution of bending under any vertical load, the analytic expressions of the reaction force of the foundation, the deflection of the plate and the internal force of the plate are obtained. The results show that this method overcomes the disadvantages of the numerical method, cancels the assumptions of the Winkler foundation model or the two-parameter foundation model, and obtains a more reasonable and accurate distribution rule of the internal force and the foundation reaction force.