NATURAL ELEMENT METHOD BASED ON LOCAL PETROV-GALERKIN PROCEDURE AND ITS OBJECT-ORIENTED DESIGN AND IMPLEMENTATION
基于局部Petrov-Galerkin过程的自然单元法及其面向对象的设计与实现

The local natural element method(LNEM) which can be used in the automatic analysis of geotechnical engineering problems is implemented for solving the elasticity problem. In LNEM,the whole interpolations are constructed with respect to the natural neighbour nodes and Voronoi tessellation of the given point,and a local weak form over the local Delaunay triangular sub-domain is used to obtain the discretized system of equilibrium equation. As a result,the numerical integration of the equilibrium equation can be analytically calculated at the center of the background triangular quadrature meshes. The design and management of the object about LNEM are also studied by abstracting the data and procedure of LNEM as auto-model building class,analysis class,control class,and other relevant classes and methods. Numerical results indicate that the theory and programs are accurate and effective.