New algorithm of coupling element-free Galerkin with finite element method

2005 ◽  
Vol 26 (8) ◽  
pp. 982-988
Author(s):  
Zhao Guang-ming ◽  
Song Shun-cheng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Coupling Element ◽  
Element Free Galerkin ◽  
Element Free ◽  
Element Method

Experimental and numerical comparisons between finite element method, element-free Galerkin method, and extended finite element method predicted stress intensity factor and energy release rate of cortical bone considering anisotropic bone modelling

2019 ◽  
Vol 233 (8) ◽  
pp. 823-838 ◽  
Author(s):  
Ajay Kumar ◽  
Pankaj Shitole ◽  
Rajesh Ghosh ◽  
Rajeev Kumar ◽  
Arpan Gupta
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Galerkin Method ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Element Method

Stress intensity factor and energy release rate are important parameters to understand the fracture behaviour of bone. The objective of this study is to predict stress intensity factor and energy release rate using finite element method, element-free Galerkin method, and extended finite element method and compare these results with the experimentally determined values. For experimental purpose, 20 longitudinally and transversely fractured single-edge notched bend specimens were prepared and tested according to ASTM standard. All specimens were tested using the universal testing machine. For numerical simulations (finite element method, element-free Galerkin method, and extended finite element method), two-dimensional model of cortical bone was developed by assuming plane strain condition. Material properties of the cortical bone were considered as anisotropic and homogeneous. The values obtained through finite element method, element-free Galerkin method, and extended finite element method are well corroborated to experimentally determined values and earlier published data. However, element-free Galerkin method and extended finite element method predict more accurate results as compared to finite element method. In the case of the transversely fractured specimen, the values of stress intensity factor and energy release rate were found to be higher as compared to the longitudinally fractured specimen, which shows consistency with earlier published data. This study also indicates element-free Galerkin method and extended finite element method predicted stress intensity factor and energy release rate results are more close to experimental results as compared to finite element method, and therefore, these methods can be used in the different field of biomechanics, particularly to predict bone fracture.

Application in Die Forging Simulation Coupling Finite Element and Element-Free Galerkin Method

2011 ◽  
Vol 474-476 ◽  
pp. 1111-1115
Author(s):  
Di Li ◽  
Wen Qian Kang ◽  
Peng Wei Guo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Efficiency ◽  
Fe Method ◽  
Element Free Galerkin ◽  
Die Forging ◽  
Coupling Algorithm ◽  
Element Free ◽  
Element Method

The finite element method has been extensively used to predict forming difficulties of die forging problems. However, the analysis for die forging problems with finite element method can lose considerable accuracy due to severely distortional meshes. Based on the equality of elements, an automatically coupling algorithm has been proposed to analyze die forging problems, which converts the FE analysis into the EFG computation to preserve the accuracy in the region where meshes have been severely distorted and still employs the FE method to ensure high computational efficiency in the region where the quality of the FE meshes is acceptable. Numerical example shows that the present algorithms exploit the respective advantages of both the FE method whose computational efficiency is high and the EFG method which can throws out mesh distortions.

scholarly journals An element-free Galerkin method for electromechanical coupled analysis in piezoelectric materials with cracks

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769373
Author(s):  
Xiao Lin Li ◽  
Li Ming Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Piezoelectric Materials ◽  
New Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Electromechanical Coupled ◽  
Element Method

We present an element-free Galerkin method for electromechanical coupled fracture analysis in piezoelectric materials. Singularity terms were introduced into the approximation function of the new method to describe the displacement and electric fields near the crack. The new method requires a smaller domain to describe the crack-tip singular field compared with the finite element method. Then, we computed the J-integrals of piezoelectric materials and investigated the effects of crack length on the computational precision. Numerical examples were used to highlight the accuracy of the new method compared with the analytical solutions and finite element method.

Element-Free Galerkin Method of Cold Forging Steel Ball

2014 ◽  
Vol 1004-1005 ◽  
pp. 1046-1049
Author(s):  
Ye Yuan ◽  
Hong Bin Liu ◽  
Hai Tao Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Steel Ball ◽  
Cold Forging ◽  
Element Free Galerkin Method ◽  
Forming Process ◽  
Element Free Galerkin ◽  
Element Free ◽  
Element Method

The fundamental principle of three dimensional Element-free Galerkin has been briefly investigated in this paper, and built forming mode of steel ball cold forging, Element-free Galerkin method successfully applied to the simulation analysis of steel ball cold forging forming process in the LS-DYNA simulation software. In comparison to Finite Element Method and experiment data, Proved Element-free Galerkin method was feasible in metal plastic forming process, and in the large deformation simulation was more accurate than the finite element method, Element-free Galerkin method has more obvious advantages after altering the impact factors.

scholarly journals An enforced essential boundary condition by penalty method in the element-free Galerkin (EFG) methods

2009 ◽  
Vol 31 (2) ◽  
pp. 122-132 ◽  
Author(s):  
Nguyen Hoai Son
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Penalty Method ◽  
Weight Functions ◽  
Two Dimensional ◽  
Monomial Basis ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free ◽  
Element Method

A meshless approach to the analysis of two-dimensional elasticity problems by the Element-Free Galerkin (EFG) method is presented. This method is based on moving least squares approximant (MLS). The unknown function of displacement \(u(x)\) is approximated by moving least square approximants \(u^h (x)\). These approximants are constructed by using a weight function, a monomial basis function and a set of nonconstant coefficients. A subdivision similar to finite element method is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Penalty Method. The results are obtained for a two-dimensional problem using different EFG weight functions and compared with the results of finite element method and exact methods.

A Coupled Finite Element-Element Free Galerkin Method for Liquefiable Soil-Structure Interaction Analysis Under Earthquake Loading

2009 ◽  
Author(s):  
Xiaowei Tang ◽  
Ying Jie ◽  
Maotian Luan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Soil Structure ◽  
Soil Structure Interaction ◽  
Element Free Galerkin Method ◽  
Structure Interaction ◽  
Element Free Galerkin ◽  
Liquefiable Soil ◽  
Element Free

This study presents a numerical method for the seismic behavior assessment of liquefiable soil-structure interaction. In the method, the element-free Galerkin method (EFGM) is applied to simulate the behavior of the liquefiable sandy soil which will take place large permanent deformation under earthquake loading. The finite element method (FEM) is used to describe the behavior of the structure. Then, the EFGM and FEM are related by contact elements. The cyclic elasto-plastic constitutive model and updated Lagrangian large-deformation formulation are jointly adopted to establish the governing equations in order to take account for both physical and geometrical nonlinearities. The shape function is established by moving least squares method while hexahedral background cells are used. The essential boundary conditions are treated with the help of the penalty method. The coupled method can avoid the volumetric locking in the numerical computations using finite element method when non-uniform deformations happen. In order to assess the effectiveness and accuracy of the current procedure, numerical simulation of caisson-type quay wall subjected to earthquake motion is conducted.

AN ENHANCEMENT OF FINITE ELEMENT METHOD WITH MOVING KRIGING SHAPE FUNCTIONS

2005 ◽  
Vol 02 (04) ◽  
pp. 451-475 ◽  
Author(s):  
K. PLENGKHOM ◽  
W. KANOK-NUKULCHAI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Field Variable ◽  
Kriging Interpolation ◽  
Shape Functions ◽  
Specific Domain ◽  
Finite Set ◽  
Global Smoothness ◽  
Element Free ◽  
Element Method

This paper presents an enhancement of the finite element method (FEM) by adopting the moving Kriging (MK) interpolation as a substitute for the traditional hat functions. The MK shape functions can be referred as element-free because their construction is not tied to the element geometry. Kriging interpolation is a geostatistical technique for spatial interpolation. The basic idea of Kriging is that any unknown point can be interpolated from known scatter points in a specific domain. Using the moving Kriging interpolation, shape functions can be generated over any finite set of nodes. This leads to an idea to extend the influence of a node beyond the layer of surrounding elements to enhance the global smoothness of the field variable and its derivatives. The present paper thus proposes a concept of layered domain of influence. Hence, characteristic arrays of an element, such as the element stiffness, have contributions from all visible nodes that include a set of satellite nodes unattached to the element. The validation of the method was confirmed through numerical tests of one and two-dimensional problems. The results show remarkable accuracy and global smoothness. Existing general-purposed FE programs can be easily modified to accommodate this new element concept; thus, the method has a higher chance to be accepted in practice.

A Coupled Finite Element and Element-Free Galerkin Method for Rigid Plastic Problems

2010 ◽  
Vol 450 ◽  
pp. 490-493
Author(s):  
Di Li ◽  
Wen Qian Kang ◽  
Peng Wei Guo
Keyword(s):  
Finite Element ◽  
Interface Element ◽  
Fe Method ◽  
Rigid Plastic ◽  
Element Free Galerkin ◽  
Plastic Forming ◽  
Forming Analysis ◽  
Coupling Algorithm ◽  
Element Free ◽  
Element Method

The analysis for rigid plastic forming problems with finite element method can lose considerable accuracy due to severely distortional meshes. By measuring the mesh equality of elements, a coupling algorithm for rigid plastic problems have been proposed based on the interface element method, which converts the FE analysis into the EFG computation to preserve the accuracy in the region where meshes have been severely distorted. Numerical example shows that the present algorithms exploit the respective advantages of both the FE method whose computational efficiency is high and the EFG method which can throws out mesh distortions and be suitable for rigid plastic forming analysis.

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