• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.308-313
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• 2009

본 논문은 확장된 이동최소제곱 유한차분법을 이용하여 1차원 Stefan 문제를 해석할 수 있는 수치기법이 제시한다. 이동하는 경계의 자유로운 묘사를 위해 요소망이나 그리드 없이 절점만을 사용하는 이동최소제곱 유한차분법을 사용하였으며, 계면경계의 특이성을 모형화하기 위해 Taylor 다항식에 쐐기함수를 도입했다. 지배방정식은 안정성이 높은 음해법(implicit method)을 이용하여 차분하였다. 미분의 특이성을 갖는 이동경계를 포함한 반무한 융해문제의 수치해석을 통해 확장된 이동최소제곱 유한차분법이 높은 정확성과 효율성을 갖는 것을 보였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.779-787
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• 2007

This paper presents a highly efficient moving least squares finite difference method (MLS FDM) for a heat transfer problem of bi-material with interfacial boundary. The MLS FDM directly discretizes governing differential equations based on a node set without a grid structure. In the method, difference equations are constructed by the Taylor polynomial expanded by moving least squares method. The wedge function is designed on the concept of hyperplane function and is embedded in the derivative approximation formula on the moving least squares sense. Thus interfacial singular behavior like normal derivative jump is naturally modeled and the merit of MLS FDM in fast derivative computation is assured. Numerical experiments for heat transfer problem of bi-material with different heat conductivities show that the developed method achieves high efficiency as well as good accuracy in interface problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.315-322
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• 2009

This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.

• Geophysics and Geophysical Exploration
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• v.21 no.3
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• pp.198-206
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• 2018

In this preliminary study, dehydration of the subducting slab and behavior of the expelled water are numerically modeled using 2-dimensional model scheme. The hydrated minerals in the oceanic crust of the subducting slab experience dehydration by increases in temperature and pressure and expel their water into the overlying mantle wedge. Behavior of the expelled water is governed by both the corner flow in the mantle wedge and porous flow of the expelled water through the pores of the mantle minerals. The effects of convergence rate and age of the subducting slab as well as grain size of the minerals on the dehydration of the subducting slab and behavior of the expelled water are evaluated. The water solubility of the oceanic crust measured from the laboratory experiments is considered for modeling dehydration of the oceanic crust. The model calculations show most of the hydrated minerals in the oceanic crust is dehydrated by a depth of 100 km and the effects of the convergence rate and age of the subducting slab on the dehydration of the subducting slab and behavior of the expelled water are not significant. The larger grain size allows faster porous flow of the expelled water through the oceanic crust, mantle wedge and overlying continental crust and reduces the volume fraction of the expelled water there. The developed technique will be used for future studies on arc volcanism and has a potential implication for the other fields such as seismic tomographic study.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.5
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• pp.577-588
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• 2011

This paper provides a novel extended Moving Least Squares(MLS) difference method for the potential problem with weak and strong discontinuities. The conventional MLS difference method is enhanced with jump functions such as step function, wedge function and scissors function to model discontinuities in the solution and the derivative fields. When discretizing the governing equations, additional unknowns are not yielded because the jump functions are decided from the known interface condition. The Poisson type PDE's are discretized by the difference equations constructed on nodes. The system of equations built up by assembling the difference equations are directly solved, which is very efficient. Numerical examples show the excellence of the proposed numerical method. The method is expected to be applied to various discontinuity related problems such as crack problem, moving boundary problem and interaction problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.5
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• pp.411-420
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• 2009

This study presents an extended finite difference method based on moving least squares(MLS) method for solving potential problems with interfacial boundary. The approximation constructed from the MLS Taylor polynomial is modified by inserting of wedge functions for the interface modeling. Governing equations are node-wisely discretized without involving element or grid; immersion of interfacial condition into the approximation circumvents numerical difficulties owing to geometrical modeling of interface. Interface modeling introduces no additional unknowns in the system of equations but makes the system overdetermined. So, the numbers of unknowns and equations are equalized by the symmetrization of the stiffness matrix. Increase in computational effort is the trade-off for ease of interface modeling. Numerical results clearly show that the developed numerical scheme sharply describes the wedge behavior as well as jumps and efficiently and accurately solves potential problems with interface.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.9
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• pp.859-869
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• 2015

In this study, we analyze the problem of wedge cracks, which are geometrically unsymmetrical in transversely piezoelectric materials. A single concentrated antiplane mechanical load and inplane electrical load are applied at the point of the wedge surface, while one concentrated antiplane load is applied at the crack surface. The crack surfaces are considered as permeable thin slits, where both the normal component of electric displacement and the electric potential are assumed to be continuous across these slits. Using Mellin transform method, the problem is formulated and the Wiener-Hopf equation is derived. By solving the equation, the solution is obtained in a closed form. The intensity factors of the stress and the electric displacement are obtained for any crack length as well as inclined and wedge angles. Based on the results, the intensity factors are independent of the applied electric loads. The electric displacement intensity factor is always dependent on that of stress intensity factor, while the electric field intensity factor is zero. In addition, the energy release rate is computed. These solutions can be used as fundamental solutions which can be superposed to arbitrary electromechanical loadings.

• The Journal of Engineering Geology
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• v.19 no.2
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• pp.131-138
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• 2009

A simulation-optimization model is developed for development of groundwater and control of a saltwater wedge for protecting over-exploiting freshwater pumping wells. To achieve the goal an objective function is developed for three types of wells: freshwater pumping, freshwater injection and saltwater pumping. Integrity of groundwater environment is accounted for by including three indices. Illustrative cross-sectional examples show that both types of barriers can protect freshwater pumping wells from saltwater intrusion. A barrier well operating at the same rate located anywhere within a certain reach can protect a pumping well. However, the location of the reach appears to contradict the common practice of barrier placements. Consideration of the groundwater environment yields a unique optimal location for barrier wells.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.2
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• pp.143-147
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• 2006

The rail clamp is the device to prevent that a crane slips along rails due to the wind blast as well as locate the crane in the set position for loading and unloading containers. The wedge type rail clamp should be designed to consider the structural stability and the durability because it compresses both rail side with large clamping force by the wedge working as the wind speed increases. In this research, the kriging interpolation method using sequential sampling is utilized to find the optimum shape of the jaw in the rail clamp. The suggested method predicts more accurate response value than the response surface method. The optimum results obtained by the proposal method are compared with those by the commercial software.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.11
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• pp.1067-1074
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• 2010

In this study, RBDO(Reliability Based Design Optimization) was performed for a supersonic double-wedge inlet. By considering uncertainty of design with given design space, the pressure recovery was transformed into the probabilistic constraint while the inlet drag was considered as a deterministic objective function. To save computational analysis cost and to search good design space, Latin-Hypercube design of experiment and the Kriging model were incorporated and then RBDO was performed. Monte-Carlo simulation was performed to verify the accuracy of AFORM(Advanced First Order Reliability Method). It was found that AFORM result agreed very well with the Monte-Carlo simulation result. The system reliability was guaranteed by considering uncertainty of the design variables. In case of considering diverse uncertainty of system design, RBDO was found to be useful.