层状地基与弹性薄板相互作用的边界元解

发布时间：2018-07-24 17:19

【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.
[Abstract]:Taking the basic solution of infinite thin plate as the kernel function of the boundary integral equation of thin plate, the interior and boundary of thin plate are discretized, and the distribution of reaction force between node and foundation is assumed, and the boundary element equations of thin plate are obtained. At the same time, based on the analytic layer element solution of layered foundation, the flexibility matrix of foundation is obtained by Guass-Legendre integral, and the general boundary element method equations of the interaction between layered foundation and thin plate are obtained by combining the displacement coordination condition on the interface between foundation and thin plate. The solution to the problem of the interaction between layered foundation and thin plate is obtained by solving the equations. Based on the theory of this paper, the corresponding FORTRAN program is compiled, and the correctness of the theory and program is verified by comparing the results with the existing literatures. The numerical results show that the closer the center of the plate is to the thin plate with square foundation, the closer it is to the center of the plate. Perpendicular to the axis y (x) direction, the vertical displacement difference of the two line segments with equal distance is smaller, and the displacement difference decreases with the decrease of the slab-soil stiffness ratio, and the displacement difference between the center point of the plate and the midpoint of the long side does not change obviously with the increase of the ratio of length to width of the plate. The displacement difference between the center of the short side and the corner of the boundary is similar.
【作者单位】：同济大学地下建筑与工程系;同济大学岩土及地下工程教育部重点实验室;
【基金】：国家自然科学基金资助项目(50578121)~~
【分类号】：TU470

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