A Study On The Meshless Method And Its Application In The Analysis Of Slope Engineering

Conventional numerical analysis methods such as the finite element method have been widely used in analysis of slopes and achieved great successes. However, the formation and existence of meshes accompanying the implementation of these methods have put limit to their applications. The meshless method, which is experiencing a rapid development, could work completely or partly without meshes, and has broad application prospects in large deformation analysis, elasto-plastic analysis, crack propagation simulation etc. Therefore, meshless method is becoming one of the most important development trendsof engineering calculation methods.Element Free Galerkin Method (EFGM) is one of the newly developed meshless methods and one of the focuses of numerical analysis research both at home and abroad. In EFGM, the numerical solution for a partial differential equation is done by using Moving Least Squares method to construct the shape function, deriving the control equation from the weak variation form of energy functional and imposing essential boundary conditions. Therefore only field and boundary nodal information is needed in the calculation, i.e. no element is needed. The Element Free Galerkin Method has its unique advantages in solving some of the mechanical problems compared with the finite element method, so it has the potential to become the important substitute for the traditional numerical analysis methods such as the finite element method.This paper introduces the research history and present development of meshless method in detail and analyzes different kinds of meshless methods systematically. Based on the Moving Least Squares method, this paper describes the basic principle of EFGM and the derivational process of EFGM control equation. Some important aspects of EFGM are also analyzed. The EFGM calculation program is developed using FORTRAN language. A typical cantilever beam example is calculated using the program. The feasibility and high precision of the program is verified by contrasting the calculation results and their corresponding exact solutions. The EFGM is used in analysis of slopes by developing EFGM calculation program, whose reasonable results show that this method is feasible in practice. With many times of calculation and analysis, this paper discusses some factors which may have effect on the calculation precision and gives some pertinent proposals in order to obtain better results. Finally, the paper summarizes the research work done. Further research work based on this paper is also presented.