• 한국지능시스템학회논문지
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• 제12권3호
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• pp.255-260
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• 2002

This paper describes a fuzzy-based system for analyzing the stress intensity factors (SIFs) of three-dimensional (3D) cracks. A geometry model, i.e. a solid containing one or several 3D cracks is defined. Several distributions of local node density are chosen, and then automatically superposed on one another over the geometry model by using the fuzzy knowledge processing. Nodes are generated by the bucketing method, and ten-coded quadratic tetrahedral solid elements are generated by the Delaunay triangulation techniques. The singular elements such that the mid-point nodes near crack front are shifted at the quarter-points, and these are automatically placed along the 3D crack front. The complete finite element(FE) model is generated, and a stress analysis is performed. The SIFs are calculated using the displacement extrapolation method. To demonstrate practical performances of the present system, semi-elliptical surface cracks in a inhomogeneous plate subjected to uniform tension are solved.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 봄 학술발표회 논문집
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• pp.110-118
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• 2001

In many areas of finite element analysis, elements with special properties are required to achieve maximal accuracy. As examples, we may mention infinite elements for the representation of spatial domain that extend to special and singular elements for modeling point and line singularities engendered by geomeric features such as reentrant corners and cracks. In this paper, we study on modified shape function representing singular properties and algorigthm for the pollution adaptive mesh generation. We will also show that the modified shape function reduces pollution error and local error.

• 대한기계학회논문집A
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• 제22권1호
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• pp.206-214
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• 1998

When a crack meets bimaterial interface stress singularity depends on the elastic constants of the adjacent materials. In the present study we are going to describe the finite element formulation for problems with a crack to be embedded in the stiffer material$({\mu}_2/{\mu}_1)$. The cubic isoparametric singular element, represented by adequately shifting the mid-side nodes adjacent to the crack tip is constructed to enclose the crack tip. An alternative method to obtain the optimal position of the mid-side nodes of cubic isoparametric elements is presented. In addition, a proper definition for the stress intensity factors of a crack normal to bimaterial interface is provided. It is based upon near a tip displacement solutions. Models for numerical analysis are two dimensional elastic bodies with a through crack under plain strain. The results obtained are compared with the previous solutions.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집A
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• pp.458-463
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• 2000

The mechanical structures generally have discontinuous parts such as the cracks, notches and holes owing to various reasons. In this paper, in order to analyze effectively these singularity problems using the finite element method, a mixed analysis method which an analytical solution and finite element solutions are simultaneously used is newly proposed. As the analytical solution is used in the singularity region and the finite element solutions are used in the remaining regions except this singular zone, this analysis method reasonably provides for the numerical solution of a singularity problem. Through various numerical examples, it is shown that the proposed analysis method is very convenient and gives comparatively accurate solution.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.551-556
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• 2004

We propose a 2D 'crack' element for the simulation of propagating crack with minimal remeshing. A regular finite element containing the crack tip is replaced with this novel crack element, while the elements which the crack has passed are split into two transition elements. Singular elements can easily be implemented into this crack element to represent the crack-tip singularity without enrichment. Both crack element and transition element proposed in our formulation are mapped from corresponding master elements which are commonly built using the moving least-square (MLS) approximation only in the natural coordinate. In numerical examples, the accuracy of stress intensity factor $K_I$ is demonstrated and the crack propagation in a plate is simulated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.281-292
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• 2009

The solution of the interface problem or Poisson problem with concave corner has singular perturbation at the interface corners or singular corners. The decoupled dual singular function method (DDSFM) which exploits the singular representations of the solutions was suggested in [3, 9] and estimated optimal accuracy in [10]. The convergence rates consist with theoretical results even for the problems with very strong singularity, with the efficiency depending on parameters used in the methods. Furthermore the errors in $L^2$ and $L^\infty$-spaces display some oscillation, in the cases with meshsize not small enough. In this paper, we present an answer to remove the oscillation via numerical experiments. We observe the effects of parameters in DDSFM, and show the consisting efficiency of the method over the strong singularity.

• 호남수학학술지
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• 제29권4호
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• pp.701-721
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• 2007

Recently, a new singular function(NSF) method was posed to get accurate numerical solution on quasi-uniform grids for two-dimensional Poisson and interface problems with domain singularities by the first author and his coworkers. Using the singular function representation of the solution, dual singular functions, and an extraction formula for stress intensity factors, the method poses a weak problem whose solution is in $H^2({\Omega})$ or $H^2({\Omega}_i)$. In this paper, we show that the singular functions, which are not in $H^2({\Omega})$, also satisfy the integration by parts and note that this fact suggests the possibility of different choice of the weak formulations. We show that the original choice of weak formulation of NSF method is critical.

• Journal of Electrochemical Science and Technology
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• 제8권3호
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• pp.244-249
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• 2017

This paper presents the results of an investigation into the isoamperic point of cyclic voltammograms, which is defined as the singular point where the voltammograms of various scan rates converge. The origin of the unique point is first considered from a theoretical perspective by formulating the voltammetric curves as a system of linear equations, the solution of which indicates that a trivial solution is only available at the potential at which the net current is zero during the reverse potential scan. In addition, by way of a mathematical formulation, it was also shown that the isoamperic point is dependent on the switching potential of the potential scanning. To validate these findings, theoretical and practical cyclic voltammmograms were studied using finite-element based digital simulations and 3-electrode cell experiments. The new understanding of the nature of the isoamperic point provides an opportunity to measure the charge transfer effects without the influence of the mass transfer effects when determining the thermodynamic and kinetic characteristics of a faradaic system.

• Structural Engineering and Mechanics
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• 제22권5호
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• pp.613-629
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• 2006

In this paper a recently developed scaled boundary finite element method (SBFEM) is applied to simulate stress concentration for two-dimensional structures. In addition, a simple and independent formulation for evaluating the coefficients, not only of the singular term but also higher order non-singular terms, of the stress fields near crack-tip is presented. The formulation is formed by comparing the displacement along the radial points ahead of the crack-tip with that of standard Williams' eigenfunction solution for the crack-tip. The validity of the formulation is examined by numerical examples with different geometries for a range of crack sizes. The results show good agreement with available solutions in literatures. Based on the results of the study, it is conformed that the proposed numerical method can be applied to simulate stress concentrations in both cracked and uncracked structure components more easily with relatively coarse and simple model than other computational methods.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.9-9
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• 2003

Let $\Omega$ be a bounded, open, and polygonal domain in $R^2$ with re-entrant corners. We consider the following Partial Differential Equations: $$(I-\nabla\nabla\cdot+\nabla^{\bot}\nabla\times)u\;=\;f\;in\;\Omega$$, $$n\cdotu\;0\;0\;on\;{\Gamma}_{N}$$, $${\nabla}{\times}u\;=\;0\;on\;{\Gamma}_{N}$$, $$\tau{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$, $$\nabla{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$ where the symbol $\nabla\cdot$ and $\nabla$ stand for the divergence and gradient operators, respectively; $f{\in}L^2(\Omega)^2$ is a given vector function, $\partial\Omega=\Gamma_{D}\cup\Gamma_{N}$ is the partition of the boundary of $\Omega$; nis the outward unit vector normal to the boundary and $\tau$represents the unit vector tangent to the boundary oriented counterclockwise. For simplicity, assume that both $\Gamma_{D}$ and $\Gamma_{N}$ are nonempty. Denote the curl operator in $R^2$ by $$\nabla\times\;=\;(-{\partial}_2,{\partial}_1$$ and its formal adjoint by $${\nabla}^{\bot}\;=\;({-{\partial}_1}^{{\partial}_2}$$ Consider a weak formulation(WF): Find $u\;\in\;V$ such that $$a(u,v):=(u,v)+(\nabla{\cdot}u,\nabla{\cdot}v)+(\nabla{\times}u,\nabla{\times}V)=(f,v),\;A\;v{\in}V$$. (2) We assume there is only one singular corner. There are many methods to deal with the domain singularities. We introduce them shortly and we suggest a new Finite Element Methods by using Singular representation for the solution.