层状地基与弹性薄板相互作用的边界元解  

A BEM for Interaction between Layered Foundations and an Elastic Thin Plate

作　　者：艾智勇[1,2] 蔡建邦 AI Zhiyong CAI Jianbang(Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China)

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：《湖南大学学报（自然科学版）》2017年第3期120-125,共6页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(50578121)~~

摘　　要：将无限大薄板的基本解作为薄板边界积分方程的核函数,对薄板的内部和边界进行离散,并假定薄板内部和边界上的节点与地基反力的分布情况,得到薄板的边界元方程组;同时基于层状地基的解析层元解,通过Guass-Legendre积分得到地基柔度矩阵;结合地基与薄板接触面上的位移协调条件,得到层状地基与薄板共同作用问题总的边界元法方程组;求解该方程组,得到层状地基与薄板共同作用问题的解答.基于本文理论,编制了相应的FORTRAN程序,通过与已有文献结果对比验证本文理论及程序的正确性,数值分析结果表明:方形基础薄板情况下,离板中心越近,垂直于坐标轴y(x)方向、距离相等的2条线段的竖向位移差越小,且该位移差随着板-土刚度比减小而减小;随着板长宽比的增大,板中心点与长边中点位移差变化不明显,而短边中心与边界角点的位移差也有相类似的规律.The kernel functions of the boundary integral equations for thin plate were determined by the fundamental solutions for an infinite thin plate. By the discretization of the plate interior and boundary as well as the assumption of the distribution states of plate nodes and foundation reaction forces, the BEM equations of the plate can be established. Meanwhile, based on the analytical layer element solutions for layered foundations, the flexibility matrix of the foundation was obtained by a two-dimensioned Guass- Legendre quadrature. Taking into account the compatible conditions of the displacements at the soils-plate interface, the global BEM equations for the interaction problem between the layered foundation and the thin plate were then established. The solutions for the problem were further obtained by solving the global BEM equations. The accuracy of the present method was verified by comparing existing solutions with the numerical results obtained from the corresponding FORTRAN program in this study. It is observed from numerical examples that when a square thin plate is placed on a foundation, the settlement difference between the two lines perpendicular to y or x coordinate decreases as they approach the center of the plate,and the difference decreases with the decrease of the plate-soil stiffness ratio. Furthermore, the settlement discrepancy between the plate center and the midpoint of the long side is unapparent with the increasing length-width ratio, and the similar variation trend can be found between the midpoint of the wide side and angular point.

关 键 词：边界元 层状地基 薄板 解析层元 

分 类 号：TU443[建筑科学—岩土工程]