广义Gibson地基上无限大薄板轴对称问题求解  

Solutions for axisymmetric problems of infinite elastic thin plate on generalized Gibson subgrade

作　　者：杜秦文[1] 朱向荣[1] 葛锐 王秉纲[1] 

机构地区：[1]长安大学特殊地区公路工程教育部重点实验室 [2]西安市市政设计研究院,西安710068

出　　处：《哈尔滨工业大学学报》2007年第6期984-988,共5页Journal of Harbin Institute of Technology

基　　金：长安大学科技发展基金重点项目(06Z05)

摘　　要：Gibson地基是指一种土体不可压缩,剪切模量随深度线性变化的非均质线弹性地基,如果地基表面处剪切模量不为零,被称为广义Gibson地基.利用Hankel变换,推导了广义Gibson地基上无限大薄板在一般轴对称荷载作用下,板和地基土体的应力位移的积分形式解,采用数值方法,讨论了地基的非均质性对板内弯矩的影响,结果显示:1.在最大弯矩区域内,相对于均质弹性地基上的板,Mr和Mθ的值都减小;2.地基非均质性影响板内弯矩的分布,对Mr的影响更大,局部区域内,弯矩的方向可能与均质弹性情况下相反,绝对值更大.获得的解可以退化到均质弹性情况下的解.Gibson subgrade is a kind of incompressible subgrade whose shear modulus varies linearly with depth. If the shear modulus is not zero on the surface of the subgrade, it is called generalized Gibson subgrade. This paper presents analytical solutions for stress and displacement of semi - infinite generalized Gibson subgrade soil subject to an axisymmetric surface load Based on these, analytical solutions for moments and displacements of an infinite elastic thin plate on the kind of non - homogenous elastic subgrade are deduced. It is shown that： the value of moments is smaller than it on homogeneous subgrade in area near the maximal moments; and non - homogeneity of subgrade influences the distributing of moments. Compared to it on homogeneous subgrade, directions of moment is inverse in local area, and the absolute value of it is greater in reverse. Hankel integral transforms method is used in the analysis.

关 键 词：GIBSON地基 非均质 薄板 轴对称 HANKEL变换 

分 类 号：U411[交通运输工程—道路与铁道工程]