横观各向同性弹性半空间地基上四边自由各向异性矩形薄板弯曲解析解  

Analytical Solution of Bending Anisotropic Rectangular Plates with Four Free Edges on the Transversely Isotropic Elastic Half-Space

作　　者：王春玲[1] 高典[1] 刘俊卿[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《力学季刊》2015年第1期95-104,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(51178387);陕西省自然科学基金(2014JM7015)

摘　　要：选用更具广泛性的横观各向同性弹性半空间地基模型,来分析四边自由各向异性矩形地基板的弯曲解析解.将异性薄板的弯曲控制方程,与基于横观各向同性弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后用三角级数法,得出横观各向同性弹性半空间地基上四边自由各向异性矩形薄板的弯曲解析解,包括地基反力、板的挠度及内力的解析表达式.该解析解克服了数值法的弊端,取消了对地基反力的假设,板的内力及地基反力求解更切实际.算例结果与文献结果吻合良好,证明本文方法的可行性.In this paper, the analytical solution of a bending anisotropic rectangular thin plate with four free edges on the transversely isotropic elastic half-space was derived. The governing equation of bending plate on the elastic foundation was combined with the deformation compatibility equation of the plate and foundation. The latter was based on static integral transform solution of the displacement on the transversely isotropic elastic half-space loaded with arbitrary vertical load. According to symmetrical decomposition, the analytical solution was obtained through triangular series method. The analytical expressions of the foundation reaction force, deflection and the internal force of the plate were derived. The proposed analytical solution overcomes the numerical limitations, and avoids the assumption of the Winkler foundation model or double parameter foundation model. The achieved internal force and plate foundation pressure are more reasonable in practical engineering. The results are consistent with the solution in open literatures, which proves the feasibility of the proposed method.

关 键 词：横观各向同性 半空间地基 各向异性 四边自由矩形薄板 弯曲 解析解 

分 类 号：TU311[建筑科学—结构工程] O342[理学—固体力学]