• Structural Engineering and Mechanics
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• v.59 no.5
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• pp.901-920
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• 2016

MeshFree methods have become popular owing to the ease with which high stress gradients can be identified and node density distribution can be reformulated to accomplish faster convergence. This paper presents a strategy for nodal density refinement with strain energy as basis in Element-Free Galerkin MeshFree technique. Two popular flat plate problems are considered for the demonstration of the proposed strategies. Issue of integration errors introduced during nodal density refinement have been addressed by suggesting integration cell refinement. High stress effects around two symmetrical semi-circular notches under in-plane axial load have been addressed in the first problem. The second considers crack propagation under mode I and mode II fracture loading by the way of introducing high stress intensity through line crack. The computational efficacy of the adaptive refinement strategies proposed has been highlighted.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.11-18
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• 2001

In this paper, a new algorithm of coupling Element-Free Galerkin Method(EFGM) and Boundary Element Method(BEM) using the variational formulation is presented. A global variational coupling formulation of EFGM-BEM is achieved by combining the variational form on each subregion. In the formulation, Lagrange multiplier method is introduced to satisfy the compatibility conditions between EFGM subregion and BEM subregion. Some numerical examples are studied to verify accuracy and efficiency of the proposed method, in which numerical performance of the method is compared with that of conventional method such as EFGM-BEM direct coupling method, EFGM and BEM. The proposed method incorporating the merits of EFGM and BEM is expected to be applied to special engineering problems such as the crack propogation problems in very large domain, and underground structures with joints.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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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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• v.22 no.1_2
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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.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2005.05a
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.10 s.181
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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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.

• Water for future
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• v.14 no.2
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• pp.53-62
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• 1981

In the Hydraulic Structure, Such as dam body or levee of river that is constructed with soil, We analyzed a top line of free ground water table. This study is based on the logical reason that the pressure on the free surface is atmospheric and the seepage line is a stream line. In order to research for the unknown seepage line. We analyzed seepage water of steady flow through parous media by Finite Element method based on Galerkin Principle, and compared the comluted value with experimental value. The results show that the computed value was nearly equal to the experimental value. Finally, it noticed that finite Element method was more practical than Experimental Method for Seepage line analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.371-378
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• 2000

In this study an adaptive node generation procedure in the Element-free Galerkin (EFG) method using bubble-meshing technique is proposed. Based on the error function that obtained by projected error estimation method, the initial node arrangement is defined along the background cell that is used in the numerical integration. To obtain the smooth nodal configuration, the nodal configuration are regenerated by bubble-meshing technique. This bubble meshing technique was originally developed to generate a set of well-shaped triangles and tetrahedra. Its basic idea is packing circles or spheres, called bubble, into the specified area or space naturally using some dynamic equations with attracting and repelling force. To demonstrate the performance of proposed scheme, the convergence behaviors are investigated for several problems.