• Coupled systems mechanics
• /
• 제4권4호
• /
• pp.365-383
• /
• 2015

Strip footing is an important type of shallow foundations and is commonly used beneath the walls. Analysis of shallow foundation involves the determination of stresses and deformations. Element free Galerkin method, one of the important mesh free methods, is used for the determination of stresses and deformations. Element free Galerkin method is an efficient and accurate method as compared to finite element method. The Element Free Galerkin method uses only a set of nodes and a description of model boundary is required to generate the discrete equation. Strip footing of width 2 m subjected to a loading intensity of 200 kPa is studied. The results obtained are agreeing with the values obtained using analytical solutions available in the literature. Parametric study is done and the effect of modulus of deformation, Poisson's ratio and scaling parameter on deformation and stresses are determined.

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

• 전산구조공학
• /
• 제11권3호
• /
• pp.44-54
• /
• 1998

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2008년도 추계학술대회B
• /
• pp.2558-2561
• /
• 2008

In the present study, a parallel Taylor-Galerkin/level set based two-phase flow code was developed using finite element discretization and domain decomposition method based on MPI (Message Passing Interface). The proposed method can be utilized for the analysis of a large scale free surface problem in a complex geometry due to the feature of FEM and domain decomposition method. Four-step fractional step method was used for the solution of the incompressible Navier-Stokes equations and Taylor-Galerkin method was adopted for the discretization of hyperbolic type redistancing and advection equations. A Parallel ILU(0) type preconditioner was chosen to accelerate the convergence of a conjugate gradient type iterative solvers. From the present parallel numerical experiments, it has been shown that the proposed method is applicable to the simulation of large scale free surface flows.

• 한국전산구조공학회논문집
• /
• 제14권4호
• /
• pp.525-535
• /
• 2001

본 연구에서는 무요소법의 일종인 element-free Galerkin 방법(EFGM)을 이용한 새로운 적응적 해석법을 제안하였다. 이 방법의 핵심은 Delaunay 삼각화에 기초를 둔 적분 격자를 기초로 수치적분과 적응적인 절점의 추가 및 소거를 수행하는 것이다. 이러한 적응적 해석법은 적분격자의 분할이나 이를 위한 추가적인 정보에 대한 관리가 필요 없이 간편하게 적응적 해석을 수행할 수 있다. 또한 균열의 진전과 같은 다단계 적응적 해석에 있어서도 매 해석단계별로 평가된 오차에 기초를 둔 최적 해석모델이 Delaunay 삼각화에 의해 구성되도록 하였다. 이러한 특성은 요소의 구성으로부터 자유로운 무요소법의 장점을 최대한 활용하여 해석모델의 구축을 보다 원활하게 수행할 수 있다. 적응적 해석에 기초가 되는 해석 후 오차평가는 계산된 응력과 투영응력과의 차이를 오차로 추정하는 투영응력법을 이용하였다. 균열진전을 포함하는 2차원예제의 해석을 수행한 결과 제안된 해석법의 타당성과 적용성을 입증할 수 있었다.

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

• Journal of Mechanical Science and Technology
• /
• 제17권1호
• /
• pp.64-76
• /
• 2003

In this work, a new penalty formulation is proposed for the analysis of Mindlin-Reissner plates by using the element-free Galerkin method. A penalized weak form for the Mindlin-Reissner Plates is constructed through the exterior penalty method to enforce the essential boundary conditions of rotations as well as transverse displacements. In the numerical examples, some typical problems of Mindlin-Reissner plates are analyzed, and parametric studies on the order of integration and the size of influence domain are also carried out. The effect of the types of background cells on the accuracy of numerical solutions is observed and a proper type of background cell for obtaining optimal accuracy is suggested. Further, optimal order of integration and basis order of Moving Least Squares approximation are suggested to efficiently handle the irregularly distributed nodes through the triangular type of background cells. From the numerical tests, it is identified that unlike the finite element method, the proposed element-free Galerkin method with penalty technique gives highly accurate solution without shear locking in dealing with Mindlin-Reissner plates.

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

• Coupled systems mechanics
• /
• 제5권3호
• /
• pp.203-221
• /
• 2016

The present study deals with the numerical modelling for the one dimensional contaminant transport through saturated homogeneous and stratified porous media using meshfree method. A numerical algorithm based on element free Galerkin method is developed. A one dimensional form of the advectivediffusive transport equation for homogeneous and stratified soil is considered for the analysis using irregular nodes. A Fortran program is developed to obtain numerical solution and the results are validated with the available results in the literature. A detailed parametric study is conducted to examine the effect of certain key parameters. Effect of change of dispersion, velocity, porosity, distribution coefficient and thickness of layer is studied on the concentration of the contaminant.

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