• Structural Engineering and Mechanics
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• 제58권4호
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• pp.641-659
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• 2016

This paper deals with the pure bending of incompressible elastic perfectly plastic two-layer sheets under plane strain conditions at large strains. Each layer is classified by its yield stress, shear modulus of elasticity and its initial percentage thickness in relation to the whole sheet. The solution found is semi-analytic. In particular, a numerical technique is only necessary to solve transcendental equations. The general solution is cumbersome because different analytic expressions for the radial and circumferential stresses should be adopted in different regions of the whole sheet. In particular, there are several alternative ways a plastic region (or plastic regions) can propagate. However, for any given set of material and process parameters the solution to the problem consists of a sequence of rather simple analytic expressions connected by transcendental equations. The general solution is illustrated by a simple example.

• 한국해안해양공학회지
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• 제19권3호
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• pp.183-193
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• 2007

부분반사 전면 및 완전반사 후면을 갖는 반무한 방파제 및 방파제 개구부에 의한 파의 산란 현상에 대한 해석 해를 유도하였다. 이는 수심이 일정하고 파가 방파제에 직각으로 입사하는 경우에 적용 가능하며, 선형파 이론에 근거하여 변수 변환 및 좌표 변환을 통해 지배 방정식을 상미분 방정식으로 전환하여 구하였다. 본 연구에서 유도된 해석 해는 유한 요소 수치 모델의 결과와 비교하여 그 정확도를 비교하였는데, 꽤 정확한 결과를 보인다는 것을 알 수 있었다. 유도된 해석 해를 이용하여 방파제에서의 반사율에 따른 항 입구에서의 정온도에 미치는 효과를 조사하였다.

• 한국지구물리탐사학회:학술대회논문집
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• 한국지구물리탐사학회 2003년도 Proceedings of the international symposium on the fusion technology
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• pp.238-243
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• 2003

As there are many advantages on underground caverns, such as safety and operation, they can also be used for gas storage purpose. When liquefied gas is stored underground, the cryogenic temperature of the gas will affect the stability of the storage cavern. In order to store the liquefied gas successfully, it is essential to estimate the exact temperature distribution of the rock mass around the cavern. In this study, an analytic solution and a conceptual model that can estimate three-dimensional temperature distribution around the storage cavern are suggested. When calculating the heat transfer within a solid, it is likely to consider the solid as the intersection of two or more infinite or semi-infinite geometries. Therefore heat transfer solution for the solid is expressed by the product of the dimensionless temperatures of the geometries, which are used to form the combined solid. Based on the multi-dimensional transient heat transfer theory, the analytic solution is successfully derived by assuming the cavern shape to be of simplified geometry. Also, a conceptual model is developed by using the analytic solution of this study. By performing numerical experiments of this multi-dimensional model, the temperature distribution of the analytic solution is compared with that of numerical analysis and theoretical solutions.

• 한국지하수토양환경학회지:지하수토양환경
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• 제13권2호
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• pp.54-61
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• 2008

수평 혹은 경사 형태 특수 정호 양수량에 대한 시공간적 수위 강하를 지하수 수치 모델링을 활용하여, 평가하였다. 지하수 수치 모델링은 상용 프로그램인 FEFLOW(version 5.1)의 1차원 선형 불연속 특징 요소를 활용하여 수행되었으며, 수치해의 검증을 위해 Zhan과 Zlotnik(2002)이 제안한 연속된 점 형태 배출원 배열 방식 준 해석해와 비교하였다. 비교 검증 결과, 수치해와 준해석해는 최대 수위 강하가 나타나는 양수 최인접부를 제외하고는 거의 일치한 형태를 보여주었다. 검증된 수치적 방법을 이용하여, 강변여과 방식 취수가 검토되는 현장에 대한 수위강하를 정량적으로 평가할 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권4호
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• pp.289-294
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• 2018

In this work, a recently developed semi-analytic technique, so called the residual power series method, is generalized to process higher-dimensional linear and nonlinear partial differential equations. The solutions obtained takes a form of an infinite power series which can, in turn, be expressed in a closed exact form. The results reveal that the proposed generalization is very effective, convenient and simple. This is achieved by handling the (m+1)-dimensional Burgers equation.

• 설비공학논문집
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• 제22권7호
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• pp.468-473
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• 2010

This paper deals with approximate integral solutions to the one-dimensional model describing the charging process of stratified thermal storage tanks. Temperature is assumed to be the form of Fermi-Dirac distribution function, which can be separated to two sets of cubic polynomials for each hot and cold side of thermal boundary layers. Proposed approximate integral solutions are compared to the previous works of the approximate analytic solutions and show reasonable agreement. The approach, however, has benefits in mathematical difficulties, complicated solution form and unstable convergence of series solution founded in the previous analytic solutions. Solutions for a semi-infinite region, which have simple closed form solutions, give close agreement to those for a finite region. Thermocline thickness is obtained in closed form and shows proportional behavior to the square root of time and inverse proportional behavior to the square root of flow rate.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권4호
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• pp.283-300
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• 2019

In this paper, we propose a new semi-analytic approach based on the generalized Taylor series for solving nonlinear differential equations of fractional order. Assuming the solution is expanded as the generalized Taylor series, the coefficients of the series can be computed by solving the corresponding recursive relation of the coefficients which is generated by the given problem. This method is called the generalized differential transform method(GDTM). In several literatures the standard GDTM was applied in each sub-domain to obtain an accurate approximation. As noticed in [19], however, a direct application of the GDTM in each sub-domain loses a term of memory which causes an inaccurate approximation. In this work, we derive a new recursive relation of the coefficients that reflects an effect of memory. Several illustrative examples are demonstrated to show the effectiveness of the proposed method. It is shown that the proposed method is robust and accurate for solving nonlinear differential equations of fractional order.

• Structural Engineering and Mechanics
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• 제44권3호
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• pp.289-303
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• 2012

Existing plane stress solutions for thin plates and disks have shown several qualitative features which are difficult to handle with the use of commercial numerical codes (non-existence of solutions, singular solutions, rapid growth of the plastic zone with a loading parameter). In order to understand the effect of temperature and pressure-dependency of the yield criterion on some of such features as well as on the distribution of residual stresses and strains, a semi-analytic solution for a thin hollow disk fixed to a rigid container and subject to thermal loading and subsequent unloading is derived. The material model is elastic-perfectly/plastic. The Drucker-Prager pressure-dependent yield criterion and the equation of incompressibity for plastic strains are adopted. The distribution of residual stresses and strains is illustrated for a wide range of the parameter which controls pressure-dependency of the yield criterion.

• Journal of Electrical Engineering and information Science
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• 제1권1호
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• pp.29-38
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• 1996

To improve the reliability of control systems, certain robustness to plant uncertainties and disturbance inputs is required in terms of well founded mathematical basis. Robust control theory was set up and developed until now from this motivation. In this field, H$_2$or H\ulcorner norm performance measures are frequently used nowadays. Moreover a mixed H$_2$/H\ulcorner control problem is introduced to combine the merits of each measure since H$_2$control usually makes more sense for performance while H\ulcorner control is better for robustness to plant perturbations. However only some partial analytic solutions are developed to this problem under certain special cases at this time. In this paper, the mixed H$_2$/H\ulcorner control problem is considered. The analytic(or semi-analytic) solutions of (sub)optimal mixed H$_2$/H\ulcorner state-feedback controller are derived for the scalar plant case and the multivariable plant case, respectively. An illustrative example is given to compare the proposed analytic solution with the existing numerical one.

• 한국방재학회:학술대회논문집
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• 한국방재학회 2008년도 정기총회 및 학술발표대회
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• pp.439-442
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• 2008

Diffraction of multi-directional random waves passing semi-infinite breakwater is investigated by using analytic solution derived by Penny and Prices(1952). An irregylarity of period and incident angle of waves and regular periods for regular waves are considered in addition by expanding from the past study which used only monochromatic wave in general. The Bretschneider-Mitsuyasu frequency spectrum and Mitsuyasu directional spectrum are used for incident waves. And diffraction of multi-directional random waves is reappeared by decomposing numerical results of several monochromatic waves which have variable period and incident angle. Analytic solution on the diffraction of regular waves and multi-directional random waves calculated in this study.