• 한국지하수토양환경학회:학술대회논문집
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• 한국지하수토양환경학회 2001년도 총회 및 춘계학술발표회
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• pp.77-80
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• 2001

The element-free Galerkin (EFG) method is one of meshless methods, which is an efficient method of modeling problems of fluid or solid mechanics with complex boundary shapes and large changes in boundary conditions. This paper discusses the theory of the EFG method and its applications to modeling of groundwater flow. In the EFG method, shape functions are constructed based on the moving least square (MLS) approximation, which requires only set of nodes. The EFG method can eliminate time-consuming mesh generation procedure with irregular shaped boundaries because it does not require any elements. The coupled EFG-FEM technique was introduced to treat Dirichlet boundary conditions. A computer code EFGG was developed and tested for the problems of steady-state and transient groundwater flow in homogeneous or heterogeneous aquifers. The accuracy of solutions by the EFG method was similar to that by the FEM. The EFG method has the advantages in convenient node generation and flexible boundary condition implementation.

• Interaction and multiscale mechanics
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• 제3권2호
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• pp.123-143
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• 2010

The essential idea of the element-free Galerkin method (EFG) is that moving least-squares (MLS) approximation are used for the trial and test functions with the variational principle (weak form). By using the weighted orthogonal basis function to construct the MLS interpolants, we derive the formulae for an improved element-free Galerkin (IEFG) method for solving three-dimensional problems in linear elasticity. There are fewer coefficients in improved moving least-squares (IMLS) approximation than in MLS approximation. Also fewer nodes are selected in the entire domain with the IEFG method than is the case with the conventional EFG method. In this paper, we selected a few example problems to demonstrate the applicability of the method.

• 한국전산구조공학회논문집
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• 제13권4호
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• pp.485-500
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• 2000

본 논문에서는 element-free Galerkin(EFG) 방법에 기반한 적응적 정적균열진전해석기법을 제시하였다. 균열진전 매단계마다 적응적해석을 수행함으로써 전체 해석의 일관성과 정밀성을 동시에 확보할 수 있었다. 균열진전과정에 있어서의 적응적해석은 산정된 오차지표에 따라 적분을 위한 격자구조에 따라 절점을 추가하고 소거하는 과정을 통해 구현되었다. 이 때 사용된 오차지표는 원 EFG해석결과 얻어진 응력과 절점응력을 다시 투영한 응력의 차에 의해 얻어졌다. 제안된 해석기법의 타당성과 효용성을 수치예제에 의해 검증하였다. 그 결과 제안된 해석기법이 균열진전해석시 효율적으로 적용될 수 있음을 보였다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 봄 학술발표회 논문집
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• pp.76-83
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• 2001

In this study, a new method coupling of Element-Free Galerkin(EFG) method and Infinite Elements(IE) method is presented for extending application of the EFG method to engineering problems in unbounded domain. EFG method and IE method are briefly reviewed, and then the coupling procedure of the two methods is proposed. Numerical Algorithm by way of EFG-lE coupling technique is also developed. Numerical results illustrate the performance of the proposed technique. The accuracy of numerical solutions by the developed algorithm is guaranteed in comparing those of the other methods.

• Wind and Structures
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• 제31권1호
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• pp.75-84
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• 2020

The aerostatic stability analysis of a long-span suspension bridge by the Element-free Galerkin (EFG) method is presented in this paper. Nonlinear effects due to wind structure interactions should be taken into account in determining the aerostatic behavior of long-span suspension bridges. The EFG method is applied to investigate torsional divergence of suspension bridges, based on both the three components of wind loads and nonlinearities of structural geometric. Since EFG methods, which are based on moving least-square (MLS) interpolation, require only nodal data, the description of the geometry of bridge structure and boundaries consist of defining a set of nodes. A numerical example involving the three-dimensional EFG model of a suspension bridge with a span length of 888m is presented to illustrate the performance and potential of this method. The results indicate that presented method can effectively be applied for modeling suspension bridge structure and the computed results obtained using present modeling strategy for nonlinear suspension bridge structure under wind flow are encouragingly acceptable.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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• pp.279-287
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• 2003

This paper deals with a comparative study on coupling of Element-free Galerkin(EFG) method and Infinite Element(IE) by IE's shape function. In this study, mapped infinite elements(mapped IE) and decay function infinite elements(decay IE) are coupled with the EFG method. A coupling procedure of EFG-Mapped IE is much easier to be integrated than a coupled EFG-Decay IE. A coupled EFG-IE method used well-defined functions to preserve the continuity and linear consistency on the interface of the EFG region and IE region. Several benchmark problems are solved to verify the effectiveness and accuracy of the coupling algorithms by IE's shape function. The numerical results show that the developed algorithms work well for the elastic problems with infinite boundaries.

• 한국전산구조공학회논문집
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• 제14권3호
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• pp.381-390
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• 2001

본 연구에서는 균열의 특이성과 불연속성을 Element-Free Galerkin(EFG) 법에 반영하기 위해 특이기저함수를 포함하는 확장항을 기존의 EFG 근사함수에 추가하고 균열면을 가로지르는 형상함수 구성시 불연속함수를 적용한 향상된 EFG 균열해석기법을 제안하였다. 기존의 EFG법이 균열선단주변의 특이응력장을 표현하기 위해 상당한 절점추가를 필요로 하지만 본 연구에서 제안한 기법은 절점의 추가나 해석모형의 수정이 필요 없다. 또한, 기존의 확장근사함수를 사용하는 EFG법이 계방정식의 크기를 상당히 증가시키는데 반해, 개선된 EFG 균열해석기법은 확장근사함수를 적용범위를 국소영역으로 제한하여 계방정식의 크기증가를 최소화하고서도 정도 높은 수치해를 얻었다. 수치예제는 제안된 기법의 향상된 면모와 효율성을 검증하여 준다.

• Structural Engineering and Mechanics
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• 제10권6호
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• pp.635-650
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• 2000

In this paper, the adaptive nodal generation procedure based on the estimated local and global error in the element-free Galerkin (EFG) method is proposed. To investigate the possibility of h-type adaptivity of EFG method, a simple nodal refinement scheme is used. By adding new node along the background cell that is used in numerical integration, both of the local and global errors can be controlled adaptively. These errors are estimated by calculating the difference between the values of the projected stresses and original EFG stresses. The ultimate goal of this study is to develop the reliable nodal generator based on the local and global errors that is estimated posteriori. To evaluate the performance of proposed adaptive procedure, the convergence behavior is investigated for several examples.

• 한국전산구조공학회논문집
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• 제12권3호
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• pp.485-494
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• 1999

본 연구에서는 요소를 사용하지 않고 절점들만을 이용하여 해석이 가능한 새로운 수치해석기법인 EFG(Element-Free Galerkin)법을 사용하여 임의의 균열의 성장과정을 해석할 수 있는 효율적인 알고리즘을 개발하고, 이를 바탕으로 균열의 성장방향과 경로를 정확히 추정하여 일련의 균열진전해석을 수행할 수 있는 프로그램을 개발하였다. 균열해석에 있어서는 균열선단의 특이성과 균열면의 분연속성을 수치적으로 반영할 수 있는 기법을 도입하여 균열을 모형화하였으며, 선형탄성파괴역학이론에 근거하여 균열해석과정을 정식화하였다. 또한, EFG 형상함수가 kronecker delta 조건을 만족시키지 못함으로써 발생하는 필수경계조건의 처리문제를 penalty법을 이용하여 해결하였다. 개발된 균열진전해석 알고리즘을 정지상태와 성장하는 상태에 있는 모드 Ⅰ, 모드 Ⅱ 및 혼합모드상태의 대표적인 균열문제들에 적용하여 응력확대계수와 균열성장방향 및 균열의 성장경로를 추정하고 이를 이론적·실험적 결과들과 비교함으로써 그 정확성과 효율성을 검증하였다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.615-622
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• 2002

In this paper, the modification of double projection method for the adaptive analysis of Element-free Galerkin(EFG) method were proposed. As results of the double projection method, the smoothed error profile that is adequate for adaptive analysis was obtained by re-projection of error that means the differences of EFG stress and projected stress. However, it was found that the efficiency of double projection method is degraded as increase of the numerical integration order. Since, the iterative refinement to single step error estimation made the same effect as increasing of integration order, the application of the iterative refinement base on double projection method could be produced the inadequately refined analysis model. To overcome this defect, a modified scheme of double projection were proposed. In the numerical example, the results did not show degradation of double projection effect in iterative refinement and the efficiency of proposed scheme were proved.