Coupled interpolating element-free Galerkin scaled boundary method and finite element method for crack problems

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.

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

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.474-476.1111 ◽

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.

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

Advances in Mechanical Engineering ◽

10.1177/1687814017693733 ◽

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.

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Element-Free Galerkin Method of Cold Forging Steel Ball

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1004-1005.1046 ◽

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.

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

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/31/2/5489 ◽

2009 ◽

Vol 31 (2) ◽

pp. 122-132 ◽

Cited By ~ 2

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.

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Wavelet Finite Element Method Analysis of Bending Plate Based on Hermite Interpolation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.389.267 ◽

2013 ◽

Vol 389 ◽

pp. 267-272 ◽

Cited By ~ 1

Author(s):

Peng Shen ◽

Yu Min He ◽

Zhi Shan Duan ◽

Zhong Bin Wei ◽

Pan Gao

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Thin Plate ◽

Hermite Interpolation ◽

Energy Functional ◽

Field Function ◽

Wavelet Finite Element Method ◽

Wavelet Finite Element ◽

Crack Problems ◽

Element Method

In this paper, a new kind of finite element method (FEM) is proposed, which use the two-dimensional Hermite interpolation scaling function constructed by tensor product as the basis interpolation function of field function, and then combine with the energy functional with related mechanics and variational principle, the wavelet finite element equations for solving elastic thin plate unit that constructed in this paper are derived. Then the bending problem of thin plate is solved very quickly and availably through the matlab program. The numerical example in this paper indicates the correctness and validity of this method, and has high calculation precision and convergence speed. Moreover, it also provides a reliable method to solve the free vibration problem of thin plate and the pipe crack problems.

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