层状地基分析的超级有限层法  

Super Finite Layer Method for Layered Ground Analysis

作　　者：田管凤[1,2] 汤连生[1,3] 

机构地区：[1]中山大学地球科学系,广州510275 [2]中山大学应用力学与工程系,广州510275 [3]广东省地质过程与矿产资源探查重点实验室,广东广州510275

出　　处：《中山大学学报（自然科学版）》2013年第2期1-7,共7页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(40872205);全国高等学校博士学科专项科研基金资助项目(20120171110031);广东省自然科学基金资助项目(07003738);广东省科技计划资助项目(2008B030303009)

摘　　要：基于传统有限层法基本原理提出6参数一般有限层法。层元的位移模式采用5次完全多项式与双重级数相乘的形式;通过应用弹性体静力平衡条件对三维位移函数多项式系数之间的相关性进行分析简化,得到未知的独立位移参数6个,与层元的节面位移数目对应相等,保证了层元位移模式的完备性。通过超级有限层元与其内部小层元间的运算矩阵转换,进一步推导了6参数超级有限层法,满足了相邻小层元间高阶变形的协调性。通过算例分析表明,6参数一般有限层法仅适用多薄层地基;而超级有限层法可以适用于多种厚度的多层地基。Firstly, the 6-parameter common finite layer method is proposed based on the basic principle of conventional method. The displacement mode of a layer element is taken in the product form of five complete polynomial and double series. By applying the static equilibrium equations of elastic medium to the layer element, the correlation rules among three-dimensional displacement polynomial coefficients are discovered. Thus six unknown and independent displacement parameters can be obtained, whose number is the same as nodal surface displacement with the result that completeness requirement for the displace- ment mode can be ensured. Secondly, the 6-paramter super finite layer method has been deduced by transforming operational matrix between the super finite layer element and its interior small elements, in which the coordination of higher order deformations between adjacent small layer elements can be satis-fied. At last, it is concluded that the 6-parameter common finite layer method is suitable for thin layered ground, while the super finite layer method is for layered ground with various thickness.

关 键 词：超级有限层法 6参数一般有限层法 位移模式的完备性 高阶变形的协调性 

分 类 号：TU431[建筑科学—岩土工程]