THE NONLINEAR ELASTIC–PLASTIC ANALYSIS OF JOINTED ROCK MASS USING ELEMENT FREE GALERKIN METHOD

2009 ◽  
Vol 06 (03) ◽  
pp. 413-424 ◽  
Author(s):  
N. HATAF ◽  
M. HAJIAZIZI ◽  
A. GHAHRAMANI
Keyword(s):  
Rock Mass ◽  
Galerkin Method ◽  
Jointed Rock ◽  
Jointed Rock Mass ◽  
Plastic Behavior ◽  
Element Free Galerkin Method ◽  
Elastic Plastic ◽  
Element Free Galerkin ◽  
Mesh Free ◽  
Element Free

In this paper the application of mesh-free (Element Free Galerkin) method in analyzing the nonlinear and elastic-plastic behavior of jointed rock mass is presented. The domain is represented by a set of arbitrary distributed nodes and the essential boundary conditions are enforced using penalty method. The Patton's failure criterion was used for behavior of joint failure. Few examples, showing the effectiveness of the method in predicting the elastic-plastic behavior of jointed rocks are presented and the results are compared well with finite difference method.

scholarly journals Behavior of beam on elastic foundation using element free Galerkin method

2021 ◽  
Vol 12 (4) ◽  
pp. 14-22
Author(s):  
H.T.T. Lan
Keyword(s):  
Galerkin Method ◽  
Elastic Foundation ◽  
Least Square ◽  
Element Free Galerkin Method ◽  
Moving Least Square ◽  
Beam On Elastic Foundation ◽  
Element Free Galerkin ◽  
Mesh Free ◽  
System Equations ◽  
Element Free

One of mesh free methods, element free Galerkin method, is presented to analyze the finite beam on elastic foundation. The shape functions are constructed by using the moving least square interpolation based on a set of nodes that are arbitrarily distributed in specified domain. Discrete system equations are derived from the variation form of system equations. Numerical examples of finite beam on elastic foundation are given by establishing Matlab code. The results of this paper demonstrate the effectiveness of the proposed method with small errors compared to analytical solutions. Keywords: mesh free method, element free Galerkin method, moving least square, finite beam, elastic foundation.

PSEUDO-ELASTIC ANALYSIS OF ELASTIC–PLASTIC CRACK TIP FIELDS USING ELEMENT-FREE GALERKIN METHOD

2008 ◽  
Vol 05 (01) ◽  
pp. 91-117 ◽  
Author(s):  
RAJU SETHURAMAN ◽  
CH. SRIDHAR REDDY
Keyword(s):  
Galerkin Method ◽  
Crack Tip ◽  
Stress Fields ◽  
Elastic Analysis ◽  
Element Free Galerkin Method ◽  
Material Parameters ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Element Free Galerkin ◽  
Element Free

A methodology for the characterization of asymptotic elastoplastic crack tip stress fields is presented by coupling the pseudo-elastic analysis with the element-free Galerkin method (EFGM). An iterative linear elastic analysis using EFGM is carried out for the determination of elastic–plastic crack tip stress fields by treating material parameters as spatial field variables. Effective material parameters are used to describe the constitutive behavior of the continuum and are defined by using the Hencky's total deformation theory of plasticity. The effective material parameters are updated in an iterative manner based on strain controlled projection method using experimental uniaxial tension test curve. The effectiveness of the method is illustrated by predicting the stress fields near the crack tip region of a square plate subjected to asymptotic linear elastic displacement field on the outer boundary of the plate. Different geometries subjected to mode-I and mode-II loadings are considered for the present study. The material model considered in these problems is Ramberg–Osgood model with different hardening exponent values. The predictions of the asymptotic elastic–plastic stress fields near the crack tip are compared with the results of nonlinear finite element analysis and also with the HRR singular stress fields and found to be in good agreement. J-integral values which characterize the amplitude of HRR stress field are also evaluated for the considered geometries and are found to close matching with the EPRI estimation scheme.

Application of an Element-free Galerkin Method to Water Wave Propagation Problems

2014 ◽  
Vol 60 (1-4) ◽  
pp. 87-105 ◽  
Author(s):  
Ryszard Staroszczyk
Keyword(s):  
Wave Propagation ◽  
Galerkin Method ◽  
Present Model ◽  
Free Surface Elevation ◽  
Element Free Galerkin Method ◽  
Plane Flow ◽  
Element Free Galerkin ◽  
Proposed Model ◽  
Sloping Bed ◽  
Element Free

Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

Implementing of Displacement Boundary Conditions of Element-Free Galerkin Method and its Applications Used in Fracture Mechanics

2012 ◽  
Vol 629 ◽  
pp. 606-610
Author(s):  
Gang Cheng ◽  
Wei Dong Wang ◽  
Dun Fu Zhang
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Transformation Method ◽  
Computational Method ◽  
Reproducing Kernel Particle Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

The main draw back of the Moving Least Squares (MLS) approximate used in element free Galerkin method (EFGM) is its lack the property of the delta function. To alleviate difficulties in the treatment of essential boundary conditions in EFGM, the local transformation method and the boundary singular weight method, which are used in the reproducing kernel particle method, is combined with the element free Galerkin method. The computational method is given to analyze the stress intensity factors and the numerical simulation of crack propagation of two-dimentional problems of the elastic fracture analysis. The application examples reveal the effectiveness and feasibility of the present methods.

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