• 오토저널
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• 제13권3호
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• pp.58-67
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• 1991

A theory of continuum damage mechanics based on the theory of materials of type N was developed and its nonlinear finite element approximation and numerical simulation was carried out. To solve the finite elastoplasticity problems, reasonable kinematics of large deformed solids was introduced and constitutive relations based on the theory of materials of type-N were derived. These highly nonlinear equations were reduced to the incremental weak formulation and approximated by the theory of nonlinear finite element method. Two types of problems, compression moulding problem and pure bending problem, were solved for aluminum 2024.

• Journal of the Optical Society of Korea
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• 제9권4호
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• pp.131-134
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• 2005

We have proposed a method to calculate the absorption coefficients for the bound-to-continuum transitions in a strong biased quantum-well infrared photodetector. We have applied this method to a manufactured sample of typical device parameters, and obtained good agreements with experiments. The absorption coefficients evaluated are up to 5,700/cm at some particular operating conditions. We have also been able to make a qualitative explanation for the bias dependence of response.

• 한국과학교육학회지
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• 제31권3호
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• pp.475-489
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• 2011

The purposes of this study were to inform the exemplary models of integrated science and mathematics and to analyze and discuss their similarities and differences of the models. There were two steps to select the exemplary models of integrated science and mathematics. First, the second volume (Berlin & Lee, 2003) of the bibliography of integrated science and mathematics was analyzed to identify the models. As a second step, we selected the models that are dealt with in the School Science Mathematics journal and were cited more than three times. The findings showed that the following four exemplary theoretical models were identified and published in the SSM journal: the Berlin-White Integrated Science and Mathematics (BWISM) Model, the Mathematics/Science Continuum Model, the Continuum Model of Integration, and the Five Types of Science and Mathematics Integration. The Berlin-White Integrated Science and Mathematics (BWISM) Model focused an interpretive or framework theory for integrated science and mathematics teaching and learning. BWISM focused on a conceptual base and a common language for integrated science and mathematics teaching and learning. The Mathematics/Science Continuum Model provided five categories and ways to clarify the extent of overlap or coordination between science and mathematics during instructional practice. The Continuum Model of Integration included five categories and clarified the nature of the relationship between the mathematics and science being taught and the curricular goals for the disciplines. These five types of science and mathematics integrations described the method, type, and instructional implications of five different approaches to integration. The five categories focused on clarifying various forms of integrated science and mathematics education. Several differences and similarities among the models were identified on the basis of the analysis of the content and characteristics of the models. Theoretically, there is strong support for the integration of science and mathematics education as a way to enhance science and mathematics learning experiences. It is expected that these instructional models for integration of science and mathematics could be used to develop and evaluate integration programs and to disseminate integration approaches to curriculum and instruction.

• 한국수학사학회지
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• 제31권2호
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• pp.73-91
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• 2018

This study begins with the awareness of problem that the education of mathematics teachers has failed to link the limit and the infinite set conceptually. Thus, this study analyzes the historical and reciprocal development of the limit and the infinite set, and discusses how to improve the education of these concepts and their relation based on the outcome of this analysis. The results of the study confirm that the infinite set is the historical tool of linking the limit and the real numbers. Also, the result shows that the premise of 'the component of the straight line is a point.' had the fundamental role in the construction of the real numbers as an arithmetical continuum and that the moral certainty of this premise would be obtained through a thought experiment using an infinite set. Based on these findings, several proposals have been made regarding the teacher education of awakening someone to the fact that 'the theoretical foundation of the limit is the real numbers, and it is required to introduce an infinite set for dealing with the real numbers.' in this study. In particular, by presenting one method of constructing the real numbers as an arithmetical continuum based on a thought experiment about the component of the straight line, this study opens up the possibility of an education that could get the limit values psychologically connected to the infinite set in overcoming the epistemological obstacle related to the continuum concept.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2006년도 춘계 학술발표회 논문집
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• pp.219-228
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• 2006

In urban areas, tunnelling induced ground deformations, particularly ground settlements should be considered in order to minimize the damage of adjacent structures. Therefore, an appropriate monitoring system for the tunnel construction should be setup at the planning or design stage. A number of studies on ground settlements due to tunnelling in soft ground have been carried out so far. However, most studies have focused on clay soil rather than sand soil. In particular, a few studies on behaviour of subsurface deformations in granular material have been reported. In this study, two-dimensional laboratory model test with aluminium rods regarded as continuum granular material and close range photogrammetric technique, and numerical analysis were carried out in order to identify the behaviour of subsurface deformations due to shallow tunnelling. Direction and magnitude of displacement vectors from the model test was identical to the numerical analysis. In particular, the vector direction was appeared to be toward a point below the tunnel invert level. A narrow 'chimney or tulip like' pattern of vertical displacement was confirmed by both the model test and numerical analysis. This is consistent with the field data. In addition to the qualitative comparison, the quantitative comparison of subsurface settlements according to 2D volume loss showed good agreement between the model test and numerical analysis. Therefore, close range photogrammetric technique applied in the model test may be used to validate the result from the continuum numerical analysis.

• 지질공학
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• 제26권3호
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• pp.325-330
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• 2016

현재 경주 중저준위방사성폐기물 처분장(이하 '경주방폐장')에서는 2단계 표층처분시설이 계획중에 있으며, 포화대에 위치한 1단계 처분시설과는 달리 불포화대 상부에 위치하게 된다. 단열을 포함하는 불포화대의 특성상 지하수 및 용질의 대부분이 단열을 통해 이동할 것으로 예상된다. 따라서 불포화 암반 매질에 대한 정밀한 해석을 위하여 단열망 연속체와 암반 매질 연속체를 구분하여 해석하는 TOUGH2 전산코드의 meshmaker 모듈의 MINC 기법을 활용하였다. TOUGH2 MINC 기법의 기존 국내 연구 사례가 미미하여 본 연구에서는 MINC를 이용한 mesh 구성 방법에 대한 절차를 개발하였으며, 단열 연속체와 암반매질 연속체의 k-field를 생성하였다. 이와 같이 생성된 도메인은 향후 이중 연속체를 기반으로 경주방폐장의 지하수 유동 및 오염물질 이동 등에 활용될 뿐만 아니라 단열이 발달한 암반에서 단열-암반매질 연결성을 고려한 단열망 유동 특성을 분석하는데 참고가 될 것으로 기대한다.

• 한국농공학회지
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• 제22권2호
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• pp.83-100
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• 1980

This study was intended to computerize the structural analysis of two-dimensional continuum by finite element method, and to provide a preparatory basis for more sophisticated and more generalized computer programs of this kind. A computer program, applicable to any shape of two-dimensional continuum, was formulated on the basis of 16-degree-of- freedom rectangular element. Various computational aspects pertaining to the implementation of finite element method were reviewed and settled in the course of programming. The validity of the program was checked through several case studies. To assess the accuracy and the convergence characteristics of the method, the results computed by the program were compared with solutions by other methods, namely the analytical Navier's method and the framework method. Through actual programming and analysis of the computed results, the following facts were recognized; 1) The stiffness matrix should necessarily be assembled in a condensed form in order to make it possible to discretize the continuum into practically adequate number of elements without using back-up storage. 2) For minimization of solution time, in-core solution of the equilibrium equation is essential. LDLT decomposition is recommended for stiffness matrices condensed by the compacted column storage scheme. 3) As for rectangular plates, the finite element method shows better performances both in the accuracy and in the rate of convergence than the framework method. As the number of elements increases, the error of the finite element method approaches around 1%. 4) Regardless of the structural shape, there is a uniform tendency in convergence characteristics dependent on the shape of element. Square elements show the best performance. 5) The accuracy of computation is independent of the interpolation function selected.

• Structural Engineering and Mechanics
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• 제35권6호
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• 한국지반공학회논문집
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• 제19권3호
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• pp.65-74
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• 2003

본 연구에서는 말뚝이 근입된 연약지반의 탄소성 해석을 수행하여 말뚝에 작용하는 하향력을 산정하였다. 이때 단독말뚝과 군말뚝(3$\times$3, 5$\times$5)을 대상으로 각각 2차원과 3차원 유한요소해석을, 말뚝주면에서 slip의 유무에 따라 수행하여 그 영향정도를 파악하였다. 하향력의 발생정도는 말뚝주면에서의 마찰계수, 지표면과 말뚝두부에 작용하는 상재하중에 큰 영향을 받는다. 이와 같은 영향인자를 토대로 수치해석 결과, 하향력은 no-slip의 경우가 slip의 경우에 비해서 상당히 과대하게 산정되었으며, 또한 말뚝두부에 하중이 증가함에 따라 하향력은 감소하는 것을 알 수 있었다. 한편 그룹효과가 있는 군말뚝의 하향력은 단독말뚝의 하향력에 비해서 크게 감소 하는 것으로 나타났으며, 수치 및 사례분석을 통해 slip 해석의 적절함을 확인하였다.

• 터널과지하공간
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• 제29권5호
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• pp.318-331
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• 2019

본 연구에서는 3차원 불연속균열망을 이용하여 불연속 암반을 모사하여 스미어드 균열 모델을 적용한 불연속 암반의 등가연속체 해석기법에 대해 연구를 실시했다. 연속체 해석 코드인 FLAC3D를 이용하여 모델링을 수행하였고, 해당 적용 모델의 신뢰성을 검증하기 위해 불연속체 해석에 널리 사용되는 3DEC 코드를 통해 모델의 메쉬 사이즈, 불연속면의 밀도 및 불연속면의 간극에 대한 민감도 분석을 함께 실시하여 제안 모델의 신뢰성을 검증할 수 있었다. 본 논문에서 제안된 등가연속체 해석기법을 이용한 불연속 암반의 수리해석에 대한 연구결과는 교통 터널, 석유비축기지, 방사성폐기물 처분장 등의 지하 구조물 설계 및 건설 분야에 기초자료로 활용될 것이라고 판단된다.