Meshless Local Petrov-Galerkin Method And Application Of It To The Slope Stability Evaluation

Meshless method is a new numerical method developed in the recent years. More and more attention paid to the method. Problem domain is not required to mesh and only need to discrete as a series of nodes with boundary condition. The meshless local PetrovGalerkin method(MLPG) is a true meshless method, and no mesh and global background mesh. In this paper, the MLPG is applied to elasticity, hyperelasticity, and elastoplasticity problems. In addition, a geotechnical elastoplasticity MLPG method is applied to the soil slope problem, and the effectiveness is affirmed by practical engineering cases. In this respect, the main results are as follows:(1) At the beginning of the dissertation, a modified MLPG method is employed, in which reasonable weight function is selected to simplify the integration of internal integral domain for stiffness matrices of system equation. The step raises the computational efficiency. In view of the feature of only two lines in the overall stiffness matrices and force vector of nodes be related to every node, a direct interpolation method is used to impose the essential boundary condition that is convenient for imposition of complicated boundary condition. A numerical example shows the effectiveness of the method.(2) The feature of approximation functions of moving least squares, radial point interpolation method, and reproducing kernel particle method are discussed. Initialization of shape function is determined for two dimensional problems. In addition, the main major factors affecting accuracy of shape function of are discussed. The accuracy and astringency of interpolation are discussed based on MLS and RPIM methods that provide reference for constructing shape function.(3) Computational scheme of MLPG method depending on initial configuration is proposed. Based on the constitutive relation of hyperelastic material, examples are discussed by Newton-Raphson iterative method. The comparison between computed results and analytic solutions shows better stability for large deformation.(4) Based on MLPG method and elastic-plastic mechanics theory, incremental elasticplastic MLPG equations are derived. Two dimensional computation programs are given. Practicability of elastic-plastic MLPG method is verified by cases. In addition, the main factors affecting computational accuracy are discussed and the method is applied to geotechnical engineer materials. The comparison of different yield criteria indicates that it is feasible to apply the method to solving heterogeneous materials.(5) The MLPG model based on strength reduction method is established for plane strain problem of soil slope. The stability factor of soil slope under the effect of gravity is calculated and identical with result of finite element method.The two dimensional model of meshless slope model is build based on engineering geology condition and rock and soil parameters and the stability of slope is evaluated. The comparison results of meshless slope model and finite element result computed by other author shows that it is feasible to apply to practical engineering.