An Element-Free Galerkin Coupled with Improved Infinite Element Method for Exterior Acoustic Problem

2019 ◽  
Vol 27 (02) ◽  
pp. 1850021 ◽  
Author(s):  
Shaowei Wu ◽  
Yang Xiang ◽  
Jiachi Yao ◽  
Shuai Wang
Keyword(s):  
Acoustic Pressure ◽  
Shape Function ◽  
Acoustic Radiation ◽  
Variable Order ◽  
Infinite Domain ◽  
Element Free Galerkin ◽  
Infinite Element Method ◽  
Element Free ◽  
Function Construction ◽  
Element Method

It is known that the variable-order infinite acoustic wave envelope element (WEE) must be coupled with finite element method (FEM) by element matching for computing acoustic field radiated from radiators with complex geometric shapes. Therefore, the WEEs have to be reconstructed when the finite elements are refined or changed. To overcome the shortcoming, the element-free Galerkin (EFG) coupled with improved WEE (IWEE) method is presented to compute acoustic problems in the infinite domain. The continuity and compatibility of the acoustic pressure are maintained by IWEE that is composed of a standard WEE and a fictitious finite mesh. A key feature of the method is the introduction of the EFG method which is employed to eliminate the element matching and improve the accuracy of predicted acoustic pressure. The factors that affect the performance of the method are investigated by numerical examples, which include shape function construction, the weight function and the size of the influence domain. The numerical results show that the present method provides more accurate results compared to the coupled FEM-WEE method. The experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain.

scholarly journals Limit analysis of microstructures based on homogenization theory and the element-free Galerkin method

2020 ◽  
Vol 42 (4) ◽  
pp. 415-426
Author(s):  
Canh V. Le ◽  
Phuc L. H. Ho
Keyword(s):  
Optimization Problem ◽  
Shape Function ◽  
Limit State ◽  
Great Accuracy ◽  
Homogenization Theory ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Second Order Cone ◽  
Numerical Formulation ◽  
Element Free

This paper presents a novel numerical formulation of computational homogenization analysis of materials at limit state. The fluctuating displacement field are approximated using the Element-Free Galerkin (EFG) meshless method. The estimated yield surface of materials can be determined by handling the multiscale (macro-micro) transition. Taking advantage of high-order EFG shape function and the second-order cone programming, the resulting optimization problem can be solved rapidly with the great accuracy. Several benchmark examples will be investigated to demonstrate the computational efficiency of proposed method.

Study on Numerical Methods for Acoustic Radiation of Open Structure

2010 ◽  
Vol 439-440 ◽  
pp. 692-697
Author(s):  
Li Jun Li ◽  
Xian Yue Gang ◽  
Hong Yan Li ◽  
Shan Chai ◽  
Ying Zi Xu
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Boundary Element ◽  
Acoustic Radiation ◽  
Coupling Method ◽  
Open Structure ◽  
Acoustic Coupling ◽  
Infinite Element Method ◽  
Direct Boundary Element Method ◽  
Element Method

For acoustic radiation of open thin-walled structure, it was difficult to analyze directly by analytical method. The problem could be solved by several numerical methods. This paper had studied the basic theory of the numerical methods as FEM (Finite Element Method), BEM (Boundary Element Method) and IFEM (Infinite Element Method), and the numerical methods to solve open structure radiation problem. Under the premise of structure-acoustic coupling, this paper analyzed the theory and flow of the methods on acoustic radiation of open structure, including IBEM (Indirect Boundary Element Method), DBEM (Direct Boundary Element Method) coupling method of interior field and exterior field, FEM and BEM coupling method, FEM and IFEM coupling method. This paper took the open structure as practical example, and applied the several methods to analyze it, and analyzed and compared the several results to get relevant conclusions.

THE INTERPOLATING ELEMENT-FREE GALERKIN (IEFG) METHOD FOR TWO-DIMENSIONAL ELASTICITY PROBLEMS

2011 ◽  
Vol 03 (04) ◽  
pp. 735-758 ◽  
Author(s):  
HONGPING REN ◽  
YUMIN CHENG
Keyword(s):  
Least Squares ◽  
Shape Function ◽  
Weak Form ◽  
New Method ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Element Free Galerkin ◽  
Elasticity Problems ◽  
Mls Approximation ◽  
Element Free

In this paper, a new method for deriving the moving least-squares (MLS) approximation is presented, and the interpolating moving least-squares (IMLS) method proposed by Lancaster is improved. Compared with the IMLS method proposed by Lancaster, a simpler formula of the shape function is given in the improved IMLS method in this paper so that the new method has higher computing efficiency. Combining the shape function constructed by the improved IMLS method with Galerkin weak form of the elasticity problems, the interpolating element-free Galerkin (IEFG) method for the two-dimensional elasticity problems is presented, and the corresponding formulae are obtained. In the IEFG method, the boundary conditions can be applied directly which makes the computing efficiency higher than the conventional EFG method. Some numerical examples are presented to demonstrate the validity of the 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.

The Improved Interpolating Complex Variable Element Free Galerkin Method for Two-Dimensional Potential Problems

2019 ◽  
Vol 11 (10) ◽  
pp. 1950104 ◽  
Author(s):  
Yajie Deng ◽  
Xiaoqiao He ◽  
Ying Dai
Keyword(s):  
Complex Variable ◽  
Basis Function ◽  
Potential Problem ◽  
Shape Function ◽  
Weak Form ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Variable Element ◽  
Potential Problems ◽  
Element Free

In this paper, the improved interpolating complex variable moving least squares (IICVMLS) method is applied, in which the complete basis function is introduced and combined with the singular weight function to achieve the orthometric basis function. Then, the interpolating shape function is achieved to construct the interpolating trial function. Incorporating the IICVMLS method and the Galerkin integral weak form, an improved interpolating complex variable element free Galerkin (IICVEFG) method is proposed to solve the 2D potential problem. Because the essential boundary conditions can be straightaway imposed in the above method, the expressions of final dispersed matrices are more concise in contrast to the non-interpolating complex variable meshless methods. Through analyzing four specific potential problems, the IICVEFG method is validated with greater computing precision and efficiency.

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