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2019•Transportation research procediaOpen access

The Slope Stability Solution Using Meshless Local Petrov-Galerkin Method

Filip Gago, Juraj Mužík, Roman Bulko

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Abstract

The paper deals with use of the meshless method for slope stability analysis. There are many formulations of the meshless methods. The article presents the Meshless Local Petrov-Galerkin method (MLPG) – local weak formulation of the equilibrium equations. The main difference between meshless methods and the conventional finite element method (FEM) is that meshless shape functions are constructed using randomly scattered set of points without any relation between points. The shape function construction is the crucial part of the meshless numerical analysis. The numerical example of the slope stability was calculated using meshless computer code and compared with FEM and limit equilibrium (LEM) results.

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What this paper is about

The paper deals with use of the meshless method for slope stability analysis. There are many formulations of the meshless methods. The article presents the Meshless Local Petrov-Galerkin method (MLPG) – local weak formulation of the equilibrium equations. The main difference between meshless methods and the conventional finite element method (FEM) is that meshless shape functions are constructed using randomly scattered set of points without any relation between points. The shape function construction is the crucial part of the meshless numerical analysis. The numerical example of the slope stability was calculated using meshless computer code and compared with FEM and limit equilibrium (LEM) results.

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Available abstract

The paper deals with use of the meshless method for slope stability analysis. There are many formulations of the meshless methods. The article presents the Meshless Local Petrov-Galerkin method (MLPG) – local weak formulation of the equilibrium equations. The main difference between meshless methods and the conventional finite element method (FEM) is that meshless shape functions are constructed using randomly scattered set of points without any relation between points. The shape function construction is the crucial part of the meshless numerical analysis. The numerical example of the slope stability was calculated using meshless computer code and compared with FEM and limit equilibrium (LEM) results.

Key concepts: Regularized meshless method, Petrov–Galerkin method, Meshfree methods, Finite element method, Stability (learning theory), Singular boundary method, Mathematics, Galerkin method

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