自然元与无限元耦合方法在岩土工程粘弹性分析中的应用

COUPLING METHOD OF NATURAL AND INFINITE ELEMENT FOR VISCO-ELASTICAL ANALYSIS IN GEOTECHNICAL ENGINEERING

自然单元法是一种新的偏微分方程数值解法,由于其位移插值函数采用无网格的方式构造且形函数满足插值性质,从而克服传统有限元方法对单元网格信息的依赖,大大简化数值计算的前处理过程,同时又能像有限元那样准确施加边界条件,在岩土工程中具有广阔的应用前景;介绍了自然元与无限元的基本原理,针对在处理岩土工程无限域或半无限域问题时需要人为确定边界条件而带来计算误差的问题,引入无限元模拟无穷远处边界条件,与自然元相结合形成耦合分析方法;并根据粘弹性理论,采用Laplace插值,编制了基于自然元与无限元耦合方法的二维粘弹性分析程序,通过算例验证了算法的正确性,结果也表明相对于纯自然单元法,耦合方法能够显著提高分析结果的精度,在此基础上拓展了自然单元法在岩土工程中的应用范围。

The natural element method(NEM)has advantages of both FEM and meshless method and is a promising numerical method for complex geotechnical engineering.The basic theory of NEM and infinite element method(IEM)was introduced.In order to overcome the defect that the errors are inevitably caused by selecting a certain finite region and setting the boundary conditions subjectively when treating infinite or half infinite domain problem in geotechnical engineering using NEM,the IEM was applied to simulate the boundary conditions at infinitely distant place,thus the coupling analysis method of NEM and IEM was provided.Combining with visco-elastical theory,the 2D visco-elastical analysis program based on the coupling method of NEM and IEM with Laplace interpolation was presented.Through an example,the correctness of the computation method was proved.The results show that compared with single NEM,the coupling method greatly improves the calculation precision,and extends the application scope of NEM in geotechnical engineering.