层状地基与深置薄板静力相互作用解析研究  

Analytic study of the statics interaction between buried plate and multilayered subgrade

作　　者：王春玲[1] 张科宇[1] 郭莹[2] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055 [2]陕西科技大学机电工程学院,陕西西安710021

出　　处：《西安建筑科技大学学报（自然科学版）》2016年第2期234-239,共6页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：国家自然科学基金资助(51178387);陕西省自然科学基金资助(2014JM1033)

摘　　要：选用更具广泛性的层状横观各向同性弹性地基模型,分析研究深置于地基中的正交各向异性矩形薄板的弯曲解析解.基于直角坐标系下单层横观各向同性体的通解,借助傅里叶变换和矩阵传递法,获得荷载作用在土层内部的层状横观各向同性地基解;然后将正交各向异性薄板的弯曲控制方程,与基于获得的地基位移解建立的板与地基的变形协调方程相结合,得出深置于层状横观各向同性弹性地基中的正交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.不仅克服了数值法的弊端,取消了对地基反力的假设,而且考虑了地基的层状性和板与地基的异性性,得出了板的内力与地基反力更切实际的分布规律.同时通过算例分析验证了本文研究方法的可行性及地基深度、埋深比对地基和基础板相互作用的影响.In this paper,the bending solution of orthotropic anisotropic rectangular thin plate with four free edges on the transversely isotropic elastic multilayered subgrade is analyzed.Based on the general solution of transversely isotropic elastic single-layer subgrade under the rectangular coordinate system and by use of Fourier transformation,both the displacement and stress with undetermined coefficients can be calculated.Considering the boundary conditions and continual conditions of multilayered subgrade,the actual displacement and stress of transversely isotropic elastic multilayered subgrade under buried load can also be gained by using transferring matrix method.Combining the governing equation of bending of orthotropic anisotropic plate with deformation compatibility equation of the plate and foundation,and based on the static integral transform solution of displacement on the transversely isotropic elastic multilayered subgrade under arbitrary vertical load,the analytical bending solution of orthotropic anisotropic plate on the transversely isotropic elastic multilayered subgrade which has buried load is obtained.Then the analytical expression of foundation reaction force,deflection of the plate and the internal force of the plate are derived.Not only does this method excel the numerical method by excluding ground reaction force as the governing factor,it takes the foundation layer and its difference with plate into consideration,which better predicts the internal force distribution pattern and foundation reaction force distribution pattern respectively.In addition,the feasibility of the research methods is verified in this paper by analysis of some examples and with this method,the effect of foundation embedded depth and embedment ratio on foundation and plate can be analyzed as well.

关 键 词：横观各向同性 层状地基 深置基础 正交各向异性矩形薄板 弯曲 解析解 

分 类 号：TU470[建筑科学—结构工程]