半空间地基与正交异性矩形中厚板相互作用解析解

Analytic Solution of Interaction Between Half-Space Foundation and Orthotropic Rectangular Middle Thick Plate

将3个广义位移变量描述的正交各向异性矩形中厚板的控制方程,与基于弹性半空间地基受任意竖向荷载作用的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的解析解.用该方法对算例进行计算,并将其数值结果与文献结果进行对比,发现吻合良好,说明了该方法的有效性.

To gain the analytic solution of interaction between half-space and orthotropic rectangular middle thick plate, two equations were combined. One is the displacement control equation of orthotropic rectangular middle thick plate and the other is the plate-ground deformation compliance equation based on the integral solution of the elastic half-space loaded with arbitrary vertical force. Using the method of trigonometric series, the analytical solution was obtained to describe the characteristics of the orthotropic rectangular middle thick plate with four free edges on the elastic half-space, including the reactive force of the ground, the deflection and the inner force of the plate, etc. Some computational examples were presented. The results fit well with those appeared in literatures. The method proposed in this paper would be of important practical applications.