• Bulletin of the Korean Chemical Society
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• 제24권8호
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• pp.1107-1110
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• 2003

Valuable insight into the nonlinear dynamics of a system can be gleaned from its response to a single intense short pulse. We derive expressions for the corresponding nonlinear response functions and show that the fluctuation-dissipation theorem may be extended beyond the linear response limit to an arbitrary pulse intensity. As an illustrative example, we calculate response functions up to 11th order for the regular Lorentz gas in two dimensions.

• Interaction and multiscale mechanics
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• 제1권2호
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• pp.231-250
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• 2008

The statistical two-order and two-scale method is developed for predicting the mechanics parameters, such as stiffness and strength of core-shell particle-filled polymer composites. The representation and simulation on meso-configuration of random particle-filled polymers are stated. And the major statistical two-order and two-scale analysis formulation is briefly given. The two-order and two-scale expressions for the strains and stresses of conventionally strength experimental components, including the tensional or compressive column, the twist bar and the bending beam, are developed by means of their classical solutions with orthogonal-anisotropic coefficients. Then a new effective mesh generation algorithm is presented. The mechanics parameters of core-shell particle-filled polymer composites, including the expected stiffness parameters, minimum stiffness parameters, and the expected elasticity limit strength and the minimum elasticity limit strength, are defined by means of the stiffness coefficients and elasticity strength criterions for core, shell and matrix. Finally, the numerical results for predicting both stiffness and elasticity limit strength parameters are compared with the experimental data.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.565-571
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• 2008

In this paper we present some trace inequalities for positive definite matrices in statistical mechanics. In order to prove the method of the uniform bound on the generating functional for the semi-classical model, we use some trace inequalities and matrix norms and properties of trace for positive definite matrices.

• 한국암반공학회:학술대회논문집
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• 한국암반공학회 2011년도 추계 총회 및 창립 30주년 기념 심포지엄
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• pp.89-97
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• 2011

Brittle failure of rock is a classical rock mechanics problem. Rock failure not only involves initiation and propagation of single crack, but also is a complex problem associated with initiation, propagation and coalescence of many cracks. As the most important feature of rock material properties is the heterogeneity, the Weibull statistical distribution is employed in the rock failure process analysis (RFPA) method to describe the heterogeneity in rock properties. In this paper, the applications of the RFPA method in geotechnical engineering and rockburst modeling are introduced with emphasis, which can provide some references for relevant researches.

• Structural Engineering and Mechanics
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• 제23권6호
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• pp.599-613
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• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Structural Engineering and Mechanics
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• 제60권1호
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• pp.71-90
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• 2016

In this paper, the normalized variable V=(log N-B)(log ${\Delta}{\sigma}-C$-C), as derived from the probabilistic S-N field of Castillo and Canteli, is taken as a reference for calculation of damage accumulation and probability of failure using the Miner number in scenarios of variable amplitude loading. Alternative damage measures, such as the classical Miner and logarithmic Miner, are also considered for comparison between theoretical lifetime prediction and experimental data. The suitability of this approach is confirmed for it provides safe lifetime prediction when applied to fatigue data obtained for riveted joints made of a puddle iron original from the Fao bridge, as well as for data from experimental programs published elsewhere carried out for different materials (aluminium and concrete specimens) under distinct variable loading histories.

• 한국응용과학기술학회지
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• 제27권4호
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• pp.452-460
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• 2010

Any theory of liquid should account for interactions between molecules, since molecules in a liquid are close to each other. For this matter statistical-mechanical methodology has been used and various models have been proposed on the basis of this methodology. Among them Kirkwood-Buff solution theory has attracted a lot of interest, because it is regarded as being the most powerful. In this article Kirkwood-Buff solution theory is revisited and its key equations are derived. On the way to these equations, the concepts of pair correlation function, radial distribution function, Kirkwood-Buff integration are explained and implemented. Since complexity of statical mechanics involved in this theory, the equations are applied to one-component systems and the results are compared to those obtained by classical thermodynamics. This may be a simple way for Kirkwood-Buff solution theory to be examined for its validity.

• Structural Engineering and Mechanics
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• 제72권2호
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• pp.203-216
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• 2019

Reliability analysis of composite structures considering random variation of involved parameters is quite important as composite materials revealed large statistical variations in their mechanical properties. The reliability analysis of such structures by the first order reliability method (FORM) and Monte Carlo Simulation (MCS) based approach involves repetitive evaluations of performance function. The response surface method (RSM) based metamodeling technique has emerged as an effective solution to such problems. In the application of metamodeling for uncertainty quantification and reliability analysis of composite structures; the finite element model is usually formulated by either classical laminate theory or first order shear deformation theory. But such theories show significant error in calculating the structural responses of composite structures. The present study attempted to apply the RSM based MCS for reliability analysis of composite shell structures where the surrogate model is constructed using higher order shear deformation theory (HSDT) of composite structures considering the uncertainties in the material properties, load, ply thickness and radius of curvature of the shell structure. The sensitivity of responses of the shell is also obtained by RSM and finite element method based direct approach to elucidate the advantages of RSM for response sensitivity analysis. The reliability results obtained by the proposed RSM based MCS and FORM are compared with the accurate reliability analysis results obtained by the direct MCS by considering two numerical examples.

• 한국전산구조공학회논문집
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• 제18권3호
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• pp.291-302
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• 2005

구조응답에 기여하는 중요성으로 인하여 추계론적 해석에서는 재료탄성계수의 불확실성에 의한 응답변화도에 대한 연구가 주로 진행되어 왔다. 그러나 추계론적 해석이 의미있는 값을 제공하기 위해서는 가능한 많은 인수에 대한 불확실성을 동시에 고려하여야 한다. 본 연구에서는 구조재료의 중요한 두 인수인 탄성계수와 포아송비에 나타나는 불확실성을 고려한 추계론적 해석을 위한 정식화를 평면문제에 대하여 제안하였다. 이를 위하여 이들 두 인수의 함수로 주어지는 구성행렬의 각 요소에 대한 다항식 전개를 채용하였으며, 두 인수의 불확실성에 따라 나타나는 자기 및 상호상관함수는 n-차 모멘트에 대한 일반식을 적용하여 구성하였다. 다항식 전개에 따라 부행렬의 무한합으로 변형된 구성행렬은 계산상의 편의를 위하여 요구되는 정확도 내에서 절삭하여 사용하였다. 제안된 방법의 검증을 위하여 단순 평면구조를 예제로 택하여 해석하었으며, 해석결과는 국부평균법을 채용한 고전적인 몬테카를 해석 결과와 비교하였다.

• 한국과학교육학회지
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• 제40권3호
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• pp.253-269
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• 2020

본 연구는 2015 개정 과학과 교육과정에 제시된 성취기준에 기초하여 현대물리 개념지식에 대한 예비 물리교사의 이해를 진단할 수 있는 개념 진단지를 개발하고 타당도와 신뢰도를 확인하였다. Messick(1995)의 분류에 따른 5가지 타당도 중 검사내용에 기초한 타당도는 일련의 전문가 내용타당도 검사로 진행하여 확인한 후 24문항의 설문용 현대물리 개념 진단지를 구성하였다. 국내 15개 사범대학의 467명의 예비 물리교사에게 개발된 현대물리 개념 진단지를 적용하여 문항의 신뢰도와 Messick(1995)의 나머지 4가지 타당도를 확인하였다. 실제에 기초한 타당도는 Rasch 모형이 적용된 통계분석방법으로 문항적합도(MNSQ)를 확인한 결과, 23문항이 적합한 수준으로 나타났다. 이중 오타가 발생한 문항을 제외한 22문항에 대하여 내적구조에 기초한 타당도 분석을 하여 개발된 현대물리 개념 진단지의 일차원성을 확인하였다. 일반화에 기초한 타당도 확인 결과에 따르면 개발된 개념 진단지가 집단특성에 대해 독립적이라고 판단된다. 양자역학 수강 여부에 따른 검사점수의 t-검증 결과, 유의미한 차이가 나타났으며, 이를 외적준거에 기초한 타당도 확인으로 활용하였다. Cronbach alpha 및 Rasch 모형 분석에서의 피험자 신뢰도와 문항신뢰도 값은 검사자료가 적합한 수준의 신뢰도를 갖는다는 보여주었다. 또한 고전검사이론에 의한 문항분석 결과, 양호한 문항난이도를 보여주었으며 문항변별도는 두 문항이 준거값을 벗어났으나 다른 나머지 문항들은 양호한 값을 보여주었다. 양류상관계수는 한 문항을 제외한 나머지에 대해서 양호한 값을 나타내었다. KR-20과 Ferguson's delta 값 역시 검사지가 양호하다는 것을 보여주었다. 마지막으로 문항반응 이론에 의한 문항난이도(추정치)를 Rasch 모형 분석으로 추정하였으며, 이 값들은 피험자 집단 특성에 영향을 받지 않을 것으로 판단된다.