• 한국안전학회지
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• 제19권1호
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• pp.38-43
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• 2004

Many analysis methods, including finite element method, have been suggested and used for assessing the integrity of cracked structures. In the paper, in order to analyze arbitrary three dimensional cracks, the finite element alternating method is extended. The crack is modeled by the symmetric Galerkin boundary element method as a distribution of displacement discontinuities, which is formulated as singularity-reduced integral equations. And the finite element method is used to calculate the stress values for the uncracked body only. Applied the proposed method to several example problems for planner cracks in finite bodies, the accuracy and efficiency of the method were demonstrated.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2011년 춘계학술대회논문집
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• pp.311-317
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• 2011

The present paper deals with the continuous works of extending the multi-dimensional limiting process (MLP) for compressible flows, which has been quite successful in finite volume methods, into discontinuous Galerkin (DG) methods. From the series of the previous, it was observed that the MLP shows several superior characteristics, such as an efficient controlling of multi-dimensional oscillations and accurate capturing of both discontinuous and continuous flow features. Mathematically, fundamental mechanism of oscillation-control in multiple dimensions has been established by satisfaction of the maximum principle. The MLP limiting strategy is extended into DG framework, which takes advantage of higher-order reconstruction within compact stencil, to capture detailed flow structures very accurately. At the present, it is observed that the proposed approach yields outstanding performances in resolving non-compressive as well as compressive flaw features. In the presentation, further numerical analyses and results are going to be presented to validate that the newly developed DG-MLP methods provide quite desirable performances in controlling numerical oscillations as well as capturing key flow features.

• Journal of Mechanical Science and Technology
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• 제20권1호
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• pp.110-124
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• 2006

The multi scale wavelet-Galerkin method implemented in an adaptive manner has an advantage of obtaining accurate solutions with a substantially reduced number of interpolation points. The method is becoming popular, but its numerical efficiency still needs improvement. The objectives of this investigation are to present a new numerical scheme to improve the performance of the multi scale adaptive wavelet-Galerkin method and to give detailed implementation procedure. Specifically, the subdomain technique suitable for multiscale methods is developed and implemented. When the standard wavelet-Galerkin method is implemented without domain subdivision, the interaction between very long scale wavelets and very short scale wavelets leads to a poorly-sparse system matrix, which considerably worsens numerical efficiency for large-sized problems. The performance of the developed strategy is checked in terms of numerical costs such as the CPU time and memory size. Since the detailed implementation procedure including preprocessing and stiffness matrix construction is given, researchers having experiences in standard finite element implementation may be able to extend the multi scale method further or utilize some features of the multiscale method in their own applications.

• 한국수학사학회지
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• 제18권4호
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• pp.49-66
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• 2005

유한요소법(Finite Element Methods)은 지난 수십 년 동안 다양한 공학문제를 해석하는 주요 수치해석기법으로서, 지속적으로 연구$\cdot$개발되어 오늘에 이르고 있다. 그러나, 유한요소법은 계산을 위하여 요소망을 구성해야 하고 일부의 문제에 대하여서는 요소망을 재구성하는 등 특별한 처리기법과 계산의 소요가 필요하다. 이와같은 단점을 극복하기 위하여 무요소법(Meshfree Methods)이라 불리우는 일단의 수치해석 기법들이 고안되었다. 무요소법은 요소를 사용하지 않고 절점(node)만을 이용하여 함수를 근사하는 수치해석기법이다. 본 논문에서는 무요소법이 고안된 배경과 그 연산구조를 소개하고 무요소법의 대표적인 방법들인 Smoothed Particle Hydrodynamics(SPH)방법, 무요소 갤러킨 방법(Meshfree Galerkin Methods) 그리고 무요소 선점법(Meshfree Point Collocation Methods)의 기본 개념과 이들 수치해석기법의 방법론을 알아본다. 그리고 이들 방법의 장단점과 그 적용 예를 통하여 무요소 계산법의 유효함을 보인다.

• 한국콘텐츠학회논문지
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• 제11권1호
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• pp.404-410
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• 2011

1차원 개수로 부정류의 수치 해석을 위하여 Taylor-Galerkin 기법의 유한요소법을 St. Venant 방정식의 차분에 적용하였다. 단일 수로에서 수문의 닫힘에 의한 배수문제와 3개 이상 하도가 만나는 합류점을 포함하는 수지상(dendritic) 하천 네트워크에 적용하고 그 결과를 기존에 제시된 유한차분법, 유한요소법 등의 수치기법과 비교하였으며 매우 잘 일치함을 확인하였다. 본 연구에서 적용한 기법은 연속방정식과 운동량방정식을 순차적으로 해석해 나가기 때문에 적용이 간편하며, 최종적으로 삼대각 행렬과 합류점의 적합조건을 위한 최소한의 요소를 포함하기 때문에 삼대각 행렬의 연산 방법을 적용할 수 있어 계산 측면에서 빠르고 안정적이다. 또한, 행렬의 저장을 위한 메모리 측면에서 경제적이다.

• Structural Engineering and Mechanics
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• 제35권4호
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• pp.387-407
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• 2010

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.

• Computers and Concrete
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• 제23권4호
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• pp.235-243
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• 2019

The discontinuous Galerkin method (DGM) has become widely used as it possesses several qualities, such as a natural ability to dealing with discontinuities. DGM has its major success related to fluid mechanics. Its major importance is the ability to deal with discontinuities and still provide high order of approximation. That is an important advantage when simulating cracking propagation. No remeshing is necessary during the propagation, since the crack path follows the interface of elements. However, DGM comes with the drawback of an increased number of degrees of freedom when compared to the classical continuous finite element method. Thus, it seems a natural approach to combine them in the same simulation obtaining the advantages of both methods. This paper proposes the application of the combined continuous-discontinuous Galerkin method (CDGM) to crack propagation. An important engineering problem is the simulation of crack propagation in concrete structures. The problem is characterized by discontinuities that evolve throughout the domain. Crack propagation is simulated using CDGM. Discontinuous elements are placed in regions with discontinuities and continuous elements elsewhere. The cohesive zone model describes the fracture process zone where softening effects are expressed by cohesive zones in the interface of elements. Two numerical examples demonstrate the capacities of CDGM. In the first example, a plain concrete beam is submitted to a three-point bending test. Numerical results are compared to experimental data from the literature. The second example deals with a full-scale ground slab, comparing the CDGM results to numerical and experimental data from the literature.

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

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2009년 추계학술대회논문집
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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.

• 전산구조공학
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• 제6권4호
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• pp.83-88
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• 1993

시간변수에 대하여 불연속성을 주는 시간불연속 Galerkin 방법을 유한요소법으로 해석하였다. 이 방법은 미분방정식 관점에서 지금까지 요소간에 연속성을 준 일반적 유한요소법과 다르게 임의의 시간요소를 선택, 매 시간단계에서 요소경계에 불연속을 허락함으로서 해의 정확성을 높이고 무조건의 안정을 주는 상미분방정식의 해법인 것이다.