弹性地基板的分析简化模型

将弹性半空间地基受任意竖向荷载作用下的静力位移积分变换解与弹性半空间地基上四边自由矩形板受任意竖向荷载作用的弯曲解析解相结合，建立了求解板下地基位移的方法。对一些算例进行大量数值计算分析，得出弹性半空间地基上四边自由矩形板板下地基水平位移和竖向位移的分布规律；并基于该位移分布规律，提出地基位移沿深度按一定的函数关系变化的假设，考虑板下地基水平位移，利用板地基系统的总势能最小原理，通过复杂的变分运算，得出弹性地基板的简化模型。在不考虑板下地基水平位移时，该模型退化成双参数地基模型，并给出了求解其上四边自由矩形板的近似边界条件。

Refined model for analysis of plates on elastic foundations

Combined the integral representations for displacements of semi-infinite elastic foundation subjected to arbitrary vertical dead load with the bending analytic solution of an elastic rectangle plate with four free edges rested on semi-infinite elastic foundation to develop an efficient calculating technique used to resolve the foundation displacements. Based on carrying on a great quantity of numerical calculation analysis of some instances, the displacement distributed regularities are given for the foundation beneath the plate with four free edges rested on semi-infinite elastic foundation along the foundation depth. Based on the distributed disciplinarians of foundations’ horizontal displacement and vertical displacement, proposed the assumptions that the foundations’ displacements change according to the specified functional relation along the depth. Considered horizontal displacement of the foundation beneath the plate, utilized the plate and foundation system’s principle of minimum potential energy, operated by means of the variational principles, and gave out the refined model for plates on elastic foundations. This model is reduced to double-parameter model under not considering the foundations’ horizontal displacement beneath the plate. The approximate boundary conditions of plates on this refined model of foundations are given.