Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

Hybrid of Natural Element Method (NEM) with Genetic Algorithm (GA) to find critical slip surface

Abstract: One of the most important issues in geotechnical engineering is the slope stability analysis for determination of the factor of safety and the probable slip surface. Finite Element Method (FEM) is well suited for numerical study of advanced geotechnical problems. However, mesh requirements of FEM creates some difficulties for solution processing in certain problems. Recently, motivated by these limitations, several new Meshfree methods such as Natural Element Method (NEM) have been used to analyze engineering problems. This paper presents advantages of using NEM in 2D slope stability analysis and Genetic Algorithm (GA) optimization to determine the probable slip surface and the related factor of safety. The stress field is produced under plane strain condition using natural element formulation to simulate material behavior analysis utilized in conjunction with a conventional limit equilibrium method. In order to justify the preciseness and convergence of the proposed method, two kinds of examples, homogenous and non-homogenous, are conducted and results are compared with FEM and conventional limit equilibrium methods. The results show the robustness of the NEM in slope stability analysis.

A New and Simple Meshless LBIE-RBF Numerical Scheme in Linear Elasticity

Abstract: A new meshless Local Boundary Integral Equation (LBIE) method for solving two-dimensional elastostatic problems is proposed. Randomly distributed points without any connectivity requirement cover the analyzed domain and Local Radial Basis Functions (LRBFs) are employed for the meshless interpolation of displacements. For each point a circular support domain is centered and a local integral representation for displacements is considered. At the local circular boundaries tractions are eliminated with the aid of companion solution, while at the intersections between the local domains and the global boundary displacements and tractions are treated as independent variables avoiding thus derivatives of LRBFs. Stresses are evaluated with high accuracy and without derivatives of LRBFs via a LBIE valid for stresses. All the integrations are performed quickly and economically and in a way that renders the extension of the method to three-dimensional problems straightforward. Six representative numerical examples that demonstrate the accuracy of the proposed methodology are provided.

Moving Kriging Interpolation-based Meshfree Method for Dynamic Analysis of Structures

Abstract: A novel meshfree model based on the standard element-free Galerkin method incorporated moving Kriging interpolation (MK) is developed for free and forced vibration analysis of 2D structures. Instead of employing moving least square approximation (MLS), shape functions here are constructed by the MK method. Due to the satisfaction of the Kronecker delta function, the essential boundary conditions are thus imposed directly as the finite element method and no special techniques are required. Elastodynamic equations are transformed into a standard weak formulation and then discretized into a meshfree time-dependent equation solved by the standard Newmark time integration method. Some numerical examples of stuctural problems in 2D are attempted, and it is found that the method is adequately accurate and stable for dynamic problems. c 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim The analysis of structural dynamics problems is of great importance in structural mechanics and computational mechanics. The dynamic solutions need more efforts in modeling than the static ones because of acting of many different conditions of complicated external loadings. The present work proposes a meshfree model which is based on an incoporation between standard element-free Galerkin (EFG) method [1] and moving Kriging (MK) interpolation [2–4] for dynamic analysis of structures. The MK technique possesses Kronecker’s delta function property and hence it has great advantages in imposing essential boundary conditions without any special techniques over the moving least square approximation method.

Conforming local meshfree method

Abstract: This work is motivated by the current numerical limitation in multiscale simulation of ductile fracture processes at scale down to the microstructure size and aims to overcome the difficulties in 3D complicated mesh generation and locally extremely large strain analysis (local mesh distortion). The proposed 'conforming local meshfree approximation' directly and exactly satisfies displacement compatibility on a non-conforming assembly mesh. Local meshfree nodes, which can be freely placed and move on a finite element mesh, describe local large deformation. The improved accuracy on non-conforming mesh, the exactness in geometry representation on a structured mesh, and the good tolerance to mesh distortion are demonstrated by numerical examples.