• Advances in environmental research
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• v.8 no.1
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• pp.1-21
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• 2019

In the present study, analysis of contaminant transport through one dimensional unsaturated stratified media using element free Galerkin method has been presented. Element free Galerkin method is a meshfree method. A FORTRAN code has been developed for the same. The developed model is compared with the results available in the literature and are found in good agreement. Further a parametric study has been conducted to examine the effects of various parameters like velocity, dispersivity, retardation factor and effect of saturation on the contaminant flow. The results presented conclude that transport of contaminant is retarded in unsaturated zone in comparison with the saturated zone.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.1001-1006
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• 2004

본 연구에서는 요소를 사용하지 않고 절점들만을 이용하여 해석이 가능한 수치기법인 무요소절점법(element-free Galerkin method)의 개념을 선형파의 회절 및 방사문제에 적용하는 방법에 대해 연구하였다. 파동장에 놓인 부유식 구조물에 의한 연직 2차원 경계치 문제를 해석 대상으로 하였고, 파랑과 구조물의 상호작용을 해석함에 있어 구조물에 작용하는 동유체력과 이로 인한 구조물의 동적응답을 계산하기 위해서 무요소절점법을 이용하였다. 무요소절점법의 수식화과정을 체계적으로 정리하였으며, 무요소절점법의 타당성 및 적용성을 입증하기 위해서 직사자형 부유체에 내한 수치해석을 실시하여 타 논문의 결과와 비교하였다. 또한 해의 정확도에 직접적으로 영향을 미치는 절점간격과 파수와의 관계에 대한 기준 설정을 위한 수치실험도 수행하였다.

• Structural Engineering and Mechanics
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• v.21 no.3
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• pp.315-332
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• 2005

The Element-free Galerkin Method has become a very popular tool for the simulation of mechanical problems with moving boundaries. The internally applied Moving Least Squares interpolation uses in general Gaussian or cubic weighting functions and has compact support. Due to the approximative character of this interpolation the obtained shape functions do not fulfill the interpolation conditions, which causes additional numerical effort for the application of the boundary conditions. In this paper a new weighting function is presented, which was designed for meshless shape functions to fulfill these essential conditions with very high accuracy without any additional effort. Furthermore this interpolation gives much more stable results for varying size of the influence radius and for strongly distorted nodal arrangements than existing weighting function types.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.452-459
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• 1999

In this study, error estimates using the stress projecting scheme and adaptive nodal generation procedure in the element-free Galerkin(EFG) method are proposed. The essence of proposed error estimates is to use the difference between the values of the projected stress and these given directly by the EFG solution. The stress projection can be obtained simply by taking product of shape function based on a different domain of influence with the stresses at nodes. An adaptive procedure based on error estimates is discussed in this paper. By use of background integration cell, adding node scheme at high error norm area is proposed. To demonstrate the performance of proposed scheme, the convergence behavior is investigated for several examples

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.315-322
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• 2000

In this study, an algorithm analyzing dynamic mutiple-crack propagation problem by Meshfree Method is proposed. A short description of Meshfree Method especially, Element-free Galerkin (EFG) method is presented and the elastodynamic fracture theory is summarized. A numerical implementation algorithm for dynamic analysis by Meshfree Method is discussed and an algorithm for mutlple-crack dynamic propagation is also presented. A couple of numerical examples of dynamic crack propagation problem illustrate the performance of the proposed technique. The accuracy of the algorithm is studied in the first example by being compared with experimental results, and the applicability and efficiency of the developed algorithm is studied in the second example.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.4
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• pp.691-700
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• 1999

본 연구에서는 요소를 사용하지 않는 새로운 해석방법인 EFG(Element-Free Galerkin)법을 사용하여 복수의 초기균열을 지닌 강재가 반복피로하중을 받는 경우 균열들이 점진적으로 성장하여 부재가 파단에 이르는 과정을 해석적으로 규명하였다. 이를 위하여 본 연구에서는 일반적인 피로균열성장법칙을 EFG법을 이용한 균열해석 알고리즘에 적용하여 복수의 균열들이 각각의 응력상태에 따라 차별적으로 성장해 나가는 과정을 해석할 수 있는 알고리즘을 도입하고 이를 바탕으로 다양한 하중상태하에서 복수의 균열들의 성장경로를 추정함과 동시에 이에 따른 잔존수명을 산정할 수 있는 기법을 제시하였다. 본 연구에서 제안된 해석방법을 피로균열 발생빈도가 큰 몇가지의 강부재 형태에 적용해 본 결과 다수균열 함유 부재의 피로균열 성장거동과 균열들의 피로수명을 성공적으로 예측할 수 있었다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.1
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• pp.47-56
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• 1999

최근 요소망의 구성없이 공학적인 문제의 해석이 가능한 무요소법이 많은 학자들에 의하여 제안되고 이에 관한 집중적인 연구가 이루어지고 있다. 본 연구에서는 갤러킨 정식화에 의한 무요소법을 고체역학적인 문제에 적용하여 이의 특성을 규명하고자 하였다. 특히 일반적으로 사용되고 있는 몇가지 가중 함수를 선정하여 이들이 해석결과에 미치는 특성과 절점 배치방법 및 가중 함수의 영향 영역 변화에 따른 해의 정확도 등을 서로 비교하고 검토하였다. 연구결과로 가중 함수의 형태와 영향 영역의 크기, 기정 함수의 차수와 절점 배치방법 등은 서로 상관관계를 갖고 해의 정확도에 크게 영향을 미침을 확인할 수 있었고 이의 적절한 선정은 무요소해석의 중요한 요건임을 알 수 있었다.

• Steel and Composite Structures
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• v.32 no.3
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• pp.293-304
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• 2019

In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.223-227
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• 2009

In the present study, a least square weighted residual method and Taylor-Galerkin method were formulated and tested for the discretization of the two hyperbolic type equations of level set method; advection and reinitialization equations. The two approaches were compared by solving a time reversed vortex flow and three-dimensional broken dam flow by employing a four-step splitting finite element method for the solution of the incompressible Navier-Stokes equations. From the numerical experiments, it was shown that the least square method is more accurate and conservative than Taylor-Galerkin method and both methods are approximately first order accurate when both advection and reinitialization phase are involved in the evolution of free surface.

• Steel and Composite Structures
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• v.37 no.5
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• pp.551-569
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• 2020

Vibration of vertically aligned-monolayered-nonuniform nanorods consist of functionally graded materials with elastic supports has not been investigated yet. To fill this gap, the problem is examined using the elasticity theories of Eringen and Gurtin-Murdoch. The geometrical and mechanical properties of the surface layer and the bulk are allowed to vary arbitrarily across the length. The nonlocal-surface energy-based governing equations are established using differential-type and integro-type formulations, and solved by employing the Galerkin method by exploiting admissible modes approach and element-free Galerkin (EFG). Through various comparison studies, the effectiveness of the EFG in capturing both nonlocal-differential/integro-based frequencies is proved. A constructive parametric study is also conducted, and the roles of nanorods' diameter, length, stiffness of both inter-rod's elastic layer and elastic supports, power-law index of both constituent materials and geometry, nonlocal and surface effects on the dominant frequencies are revealed.