多层地基轴对称弹性空间问题的解析层元解  

Analytical layer element solution of axisymmetrically elastic problem for multilayered soils

作　　者：艾智勇[1] 董洲[2] 成怡冲[2] 

机构地区：[1]同济大学地下建筑与工程系,上海200092 [2]同济大学岩土及地下工程教育部重点实验室,上海200092

出　　处：《建筑结构学报》2012年第4期150-153,共4页Journal of Building Structures

基　　金：国家自然科学基金项目(50578121)

摘　　要：从轴对称弹性空间问题的基本控制方程出发,推导出Hankel积分变换域内单层地基的精确刚度矩阵,即解析层元,然后按有限层法组装成多层地基的总体刚度矩阵。通过求解由总体刚度矩阵形成的方程组,得到该问题在Hankel积分变换域内的解,再通过Hankel积分逆变换,得到轴对称荷载作用下多层地基的精确解。编制了相应程序进行计算,通过与已有文献的结果及有限元计算结果比较,证明了所提方法的正确性;通过多层地基模型与均匀地基模型的比较,揭示了两者的差异。天然地基往往呈层状分布,各层土的物理性质差别较大,故与通常采用的均匀地基模型相比,成层地基模型更能真实地分析天然地基在轴对称荷载作用下的位移。Starting from the governing equations of axisymmetrical problem of elastic body,this paper deduced the stiffness matrix of single-layered soil in Hankel integral transformation domain,i.e.the analytical layer element.Then the global stiffness matrix of multilayered soils was assembled by finite layer method.The solution in Hankel integral transformation domain was obtained by solving the algebraic equations of the global stiffness matrix.And the exact solution of multilayered soils under the axisymmetrical loading was obtained through the inversion of Hankel integral transformation.Numerical calculation was carried out by a computer program.The correctness of the proposed method was proved by comparing with the existing results and the results by finite element method;the difference between homogeneous foundation model and layered foundation model was revealed by comparing the calculated results.The distribution of natural foundation is often layered.The differences in physical property are great among different layers.Thus layered foundation model can realize a more realistic analysis of the displacement of the natural foundation under axisymmetrical loading compared with the commonly used homogeneous foundation model.

关 键 词：多层地基 轴对称问题 Hankel积分变换 解析层元 

分 类 号：TU433[建筑科学—岩土工程]