多层地基上轴对称受荷刚性圆板问题  

Axisymmetric Loaded Rigid Circular Plate on Multi-layered Soil

作　　者：艾智勇[1] 梅阿敏[1] 

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

出　　处：《力学季刊》2008年第3期424-429,共6页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金项目(50578121)

摘　　要：利用刚性圆板表面各点位移相等,并结合刚性圆板与地基表面的位移相容条件与光滑接触条件,经由Hankel变换,推导出了刚性圆板与分层地基表面接触应力的对偶积分方程;求解该对偶积分方程,再由多层地基应力与位移的传递矩阵解,并经Hankel逆变换,得到了多层地基上轴对称受荷刚性圆板问题的解。编制了计算程序,并进行了数值分析与计算。计算结果表明:对均匀地基而言,实际工程的计算分析可只考虑4倍刚性圆板直径以内深度范围内的应力与位移;而地基的分层性对地基的位移和应力有着较大的影响,简单地将均匀地基的结论推广到分层和非均匀地基是不恰当的。Based on the equivalent settlements of rigid circular plate, the continuity and smooth contact conditions between subsoil surface and rigid circular plate, the dual integral equation of the interaction stresses between the rigid circular plate and multi-layered soil, was deduced after introducing Hankel transform. By resolving the dual integral equation, the solution of the rigid circular plate on multi-layered soil was obtained by using transfer matrix solutions for displacements and stresses of multi-layered soil and Hankel inverse transform. Numerical calculation and analysis were also carried out by computer program. The calculational result shows that for homogeneous soil, it is adequate to consider the displacements and stresses within the area of 4 times of the diameter of rigid plate, and it is unfit to extend the solution for the homogeneous soil into the multi-layered soil homogeneity have a considerable affects on the and the non-homogeneous soil, as the lamination and nondisplacements and stresses of the soils.

关 键 词：多层地基 传递矩阵法 刚性圆板 HANKEL变换 对偶积分方程 

分 类 号：TU433[建筑科学—岩土工程]