• 한국전산구조공학회논문집
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• 제15권1호
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• pp.85-94
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• 2002

본 연구에서는 Bubble Mesh 기법을 이용한 적응적 최적 절점생성기법을 제안하고 이를 Element-free Galerkin 방법에 적용하였다. 무요소방법에서 제안된 일반적인 적응적 절점배치방법의 경우 적분격자를 이용하기 때문에 그 절점의 분포가 평가된 오차를 정확히 반영하지 못하고 불균등한 세분화로 인해 주변 절점분포와 급격한 절점밀도의 차이를 보이게 되어 추가적인 해석오차를 유발한다. 본 연구에서는 평가된 오차의 분포와 적분격자를 따라 구성된 불균등한 초기절점배치를 최적삼각격자 구성기법인 Bubble Mesh 기법을 이용하여 최적화 시키는 적응적 절점구성기법을 제안하였다. 절점의 불균등한 배치에 따른 추가적인 오차의 발생현상을 보이기 위해 1차원 문제를 해석하였고 본 연구에서 제안된 Bubble Mesh 기법을 이용한 적응적 무요소해석법의 적용성을 보이기 위해 2차원 문제를 해석하였다.

• 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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.507-512
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• 2007

A new type of extended element-free Galerkin method (XFEM) is proposed on this paper. The blending region which was inevitable in the extended finite element method and the extended meshfree method is removed in this method. For this end, two different techniques are developed. The first one is the modification of the domain of influence so that the crack tip is always placed on the edge of a domain of influence. The second method is the use of the Lagrange multiplier. The crack is virtually extended beyond the actual crack tip. The virtual extension was forced close by the Lagrange multiplier. The first method can be applied to two dimensional problems only Lagrange multiplier method can be used in both two and three dimensions.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2005년도 춘계학술대회 논문집
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• pp.43-46
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• 2005

Micro molding technology is a promising mass production technology for polymer based microstructures. Mass production technologies such as the micro injection/compression molding, hot embossing, and micro reaction molding are already in use. In the present study, we have developed a numerical analysis system to simulate three-dimensional non-isothermal cavity filling for hot embossing, with a special emphasis on the free surface capturing. Precise free surface capturing has been successfully accomplished with the level set method, which is solved by means of the Runge-Kutta discontinuous Galerkin (RKDG) method. The RKDG method turns out to be excellent from the viewpoint of both numerical stability and accuracy of volume conservation. The Stokes equations are solved by the stabilized finite element method using the equal order tri-linear interpolation function. To prevent possible numerical oscillation in temperature Held we employ the streamline upwind Petrov-Galerkin (SUPG) method. With the developed code we investigated the detailed change of free surface shape in time during the mold filling. In the filling simulation of a simple rectangular cavity with repeating protruded parts, we find out that filling patterns are significantly influenced by the geometric characteristics such as the thickness of base plate and the aspect ratio and pitch of repeating microstructures. The numerical analysis system enables us to understand the basic flow and material deformation taking place during the cavity filling stage in microstructure fabrications.

• 대한기계학회논문집A
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• 제24권10호
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• pp.2469-2476
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• 2000

The meshing of the domain has long been the major bottleneck in performing the finite element analysis. Research efforts which are so-called meshfree methods have recently been directed towards eliminating or at least easing the requirement for meshing of the domain. In this paper, a new meshfree method for solving nonlinear boundary value problem, based on the bubble packing technique and Delaunay triangle is proposed. The method can be efficiently implemented to the problems with singularity by using formly distributed nodes.

• 물과 미래
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• 제14권2호
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• pp.53-62
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• 1981

댐이나 제방과 같이 흙으로 축조된 수리구조물에 있어서, 자유지하수면의 최상부 침투선을 해석하였다. 자유지하수면에 작용하는 압력은 대기압이고, 침투선은 유선이라는 원리에 의하여 연구를 수행하였다. 미지의 침투선을 해석하기 위하여 Galerkin 원리에 기초를 둔 유한요소법에 의하여 다공체속을 흐르는 정류상태의 침투수를 해석하여 실험치와 이론치를 비교하였고 그 결과 이론치와 실험치가 거의 일치함을 알았다. 결론적으로 침투선해석에 있어서 유한요소법이 실험적인 방법보다 더 실용적이라는 것을 알았다.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.165-181
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• 2004

Based on Landau-type transformation, a Stefan problem with non-linear free boundary condition is transformed into a system consisting of parabolic equation and the ordinary differential equations. Semidiscrete approximations are constructed. Optimal orders of convergence of semidiscrete approximation in $L_2$, $H^1$ and $H^2$ normed spaces are derived.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.223-235
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• 2006

By applying the Landau-type transformation, we transform a Stefan problem with nonlinear free boundary condition into a system consisting of a parabolic equation and the ordinary differential equations. Fully discrete finite element method is developed to approximate the solution of a system of a parabolic equation and the ordinary differential equations. We derive optimal orders of convergence of fully discrete approximations in $L_2,\;H^1$ and $H^2$ normed spaces.

• 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.

• Steel and Composite Structures
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• 제32권3호
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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.