Three-dimensional Element Free Galerkin Method Research Of Homogeneous Vertical Slope

Conventional numerical analysis methods such as the finite element method havebeen widely used in analysis of slopes and achieved great successes. However, theformation and existence of meshes accompanying the implementation of these methodshave put limit to their application. The meshes method, which is experiencing a rapiddevelopment, could work completely or partly without meshes, and has broadapplication prospects in large deformation analysis, elasto-plastic analysis, crackpropagation simulation etc. Therefore, meshless method is becoming one of the mostimportant development trends of engineering calculation methods.Element Free Method (EFM) is one of the newly developed meshless methods andone 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 LeastSquares method to construct the shape function, deriving the control equation from theweak variation form of energy functional and imposing essential boundary conditions.Therefor only field and boundary nodal information is needed in the calculation, noelement is needed. The Element Free Method has its unique advantages in solving someof the mechanical problems compared with the finite element method, so it has thepotential to become the important substitute for the traditional numberical analysismethods such as the finite element method.This paper introduces the research history and present development of meshlessmethod in detail and analyzes different kinds of meshless methods systematically.Baced on the Moving Least Squares method, this paper describes the basic principle ofEFGM and the derivational process of EFGM control equation. Some important aspectsof EFGM are also analyzed. On the other hand, the EFGM calculation program abouthomogeneous vertical slope in three-dimensional condition. The three-dimensionalhomogeneous vertical slope example is calculated using the program. Through theanalysis of height，modulus of elasticity, Poisson ratio affects the result, then I givesome advices.Through the analysis of calculation results, the article of three-dimensionalmeshless numerical analysis method can reflect the homogeneous vertical slopedisplacement and stress distribution, calculation accuracy is relatively high, itsoperation result is satisfying. In addition, further research work based on this paper is also presented.