自然单元法在岩土工程中应用两例

自然单元法(NEM)是较近出现的一种无网格方法，其形函数兼有无网格的特点和传统有限元的优点，是一种理想的适合岩土工程问题计算的新型数值方法。介绍了自然单元法的基本原理和特性，并讨论了其在岩土工程中的具体应用。将Goodman单元引入自然单元法以实现对不连续面的模拟，研究表明，在NEM中加入节理单元的总体原则和具体的实施细节与FEM中完全相同；而在一般的无网格方法中，则稍微复杂一点。为了实现对岩土工程中常见的无限域或半无限域问题的模拟，引入了无界单元；由于自然单元法的特性，自然单元法和无界元可实现无缝“耦合”。具体的数值算例验证了上述思路。

Natural element method and its application to geotechnical engineering

The natural element method (NEM) is a newly coming meshless method, of which the shape function possesses both the characteristics of the meshless methods and the advantages of traditional finite element method, so it’s a most promising numerical method for geotechnical problems. The basic theory and the characteristics of NEM are addressed; and then some detailed application examples in geotechnical engineering are discussed. The Goodman element is introduced into the NEM to model the discontinuity; the general principle and detailed implementation are identical to those in FEM. How to model the infinite or semi-infinite problems using NEM, is discussed too. The coupling of NEM and FEM or IEM is seamless, because the NEM shape function satisfies the property of linear interpolation between adjacent boundary nodes. So the solving ability is enhanced by the coupling. Numerical examples show the rationality of scheme presented above.