• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.2
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• pp.129-140
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• 1999

추계론적 해석은 구조계 내의 해석인수에 존재하는 공간적 또는 시간적 임의성이 구조계 반응에 미치는 영향에 대한 고찰을 목적으로 한다. 확률장은 구족계 내에서 특정한 확률분포를 가지는 것으로 가정된다. 구조계 반응에 대한 이들 확률장의 영향 평가를 위하여 통계학적 추계론적 해석과 비통계학적 추계론적 해석이 사용되고 있다. 본 연구에서는 비통계학적 추계론적 해석방법 중의 하나인 가중적분법을 제안하였다. 특히 구조계의 공간적 임의성이 큰 특성을 가지고 있는 반무한영역에 대한 적용 예를 제시하고자 한다. 반무한영역의 모델링에는 무한요소를 사용하였다. 제안된 방법에 의한 해석 결과는 통계학적 방법인 몬테카를로 방법에 의한 결과와 비교되었다. 제안된 가중적분법은 자기상관함수를 사용하여 확률장을 고려하므로 무한영역의 고려에 따른 해석의 모호성을 제거할 수 있다. 제안방법과 몬테카를로 방법에 의한 결과는 상호 잘 일치하였으며 공분산 및 표준편차는 무한요소의 적용에 의하여 매우 개선된 결과를 나타내었다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.2A
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• pp.383-390
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• 2006

In this paper, a stochastic field that is compatible with Monte Carlo simulation is suggested for an expansion-based stochastic analysis scheme of weighted integral method. Through investigation on the way of affection of stochastic field function on the displacement vector in the series expansion scheme, it is noticed that the stochastic field adopted in the weighted integral method is not compatible with that appears in the Monte Carlo simulation. As generally recognized in the field of stochastic mechanics, the response variability is not a linear function of the coefficient of variation of stochastic field but a nonlinear function with increasing variability as the intensity of uncertainty is increased. Employing the stochastic field suggested in this study, the response variability evaluated by means of the weighted integral scheme is reproduced with high precision even for uncertain fields with moderately large coefficient of variation. Besides, despite the fact that only the first-order expansion is employed, an outstanding agreement between the results of expansion-based weighted integral method and Monte Carlo simulation is achieved.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.5
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• pp.29-37
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• 1993

The extension of the weighted integral method in the area of stochastic finite element analysis is presented. The use of weighted integral method in numerical analysis was extended to CST(constant strain triangle) element by Deodatis to calculate the response variability of 2D stochastic systems. In this paper, the extension of the weighted integral method for general plane-elements is represented. It has been shown that the same mesh used in the deterministic FE analysis can be used in the stochastic FE analysis. Furthermore, because the CST element is a special case which has constant strain-displacement matrix the mingling of CST elements with the other quadrilateral elements in the analysis may also be possible.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.335-345
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• 2008

In this study, we suggest a stochastic finite element scheme for the probabilistic analysis of the composite laminated plates, which have been applied to variety of mechanical structures due to their high strength to weight ratios. The applied concept in the formulation is the weighted integral method, which has been shown to give the most accurate results among others. We take into account the elastic modulus and in-plane shear modulus as random. For individual random parameters, independent stochastic field functions are assumed, and the effect of these random parameters on the response are estimated based on the exponentially varying auto- and cross-correlation functions. Based on example analyses, we suggest that composite plates show a less coefficient of variation than plates of isotropic and orthotropic materials. For the validation of the proposed scheme, Monte Carlo analysis is also performed, and the results are compared with each other.

• Magazine of the Korea Concrete Institute
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• v.1 no.2
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• pp.121-132
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• 1989

유한요소법을 바탕으로 한 프리스트레스트 콘크리트 평면 보-기둥 구조의 후좌굴 거동에 대한 수직해석법을 제시하였다. 콘크리트의 균열, 변형연화 및 PS강재의 항복과 같은 재료 비선형성을 고려하였다. 좌굴 거동 연구에 필수적 요소인 기하학적 비선형성을 Updated Lagraugian Formulation에 의하여고려하였다. 현재의 재료성질 및 변형상태에 부합하는 단분형 평형방정식을 수립하고 이것을 불평형 가중보정에 의한 Newton-Raphson 반복법으로 푼다. 좌굴후 발생하는 하중변형 곡선의 하련부는 비선형 평형 방정식의 해법중 일반적으로 많이 사용되는 가중 단분법이 아니라 변위단분법을 사용함으로써 올바르게 추적한다. 요소내의 재료성질변화는 층적분법에 의하여 고려한다. 본 논문에서는 콘크리트 균열에 의한 중립축이동의 영향을 정확히 고려하기 위하여 추가적으로 축방향변위에 대한 내부자유도를 설정하였다. 본 논문에서 제안하는 방법의 정당성과 응용성을 나타내 보일 수 있는 수직해석 예제를 제시하였다.

• Geophysics and Geophysical Exploration
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• v.21 no.1
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• pp.1-7
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• 2018

In the two-dimensional (2D) modeling of electrical method, the potential in the space domain is reconstructed with the calculated potentials in the wavenumber domain using inverse Fourier transform. The inverse Fourier integral is numerically evaluated using the transformed potential at different wavenumbers. In order to improve the precision of the integration, either the logarithmic or exponential approximation has been used depending on the size of wavenumber. Two numerical methods have been generally used to evaluate the integral; interval integration and Gaussian quadrature. However, both methods do not consider the distance from the current source. Thus the resulting potential in the space domain shows some error. Especially when the distance from the current source is very small or large, the error increases abruptly and the evaluated potential becomes extremely unstable. In this study, we developed a new method to calculate the integral accurately by introducing the distance from the current source to the rescaled Gauss abscissa and weight. The numerical tests for homogeneous half-space model show that the developed method can yield the error level lower than 0.4 percent over the various distances from the current source.

• Proceedings of the Korea Water Resources Association Conference
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• 1987.07a
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• pp.201-214
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• 1987

하천에서 종, 횡방향이 고려된 확산-이송 현상을 수치기법인 유한요소법을 이용하여 2차원으로 해석하였다. 유한요소법으로는 Galerkin의 가중잔차 방법을 수십에 대해 적분을 취한 연속, 운동량 및 확산-이송방정식에 적용하였고, 선형보간함수와 선형삼각형요소가 이용되었다. 모형의 타당성을 입증하기 위해 단순화된 1차원 수로에서 수차례 검정한 결과 정확해와 거의 일치하는 만족할만한 결과가 도출되었다. 개발된 모형의 실험이 2차원수로에서 행하여져 지류의 유입에 따른 확산-이송현상이 모의되었으며, 실험적용은 개발사업후의 한강본류 9km 구간에 적용되어 탄천과 중량천의 지천 영향을 받는 오염 농도가 2차원적으로 도시되었다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.1
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• pp.1-8
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• 1990

In this paper, the transient electromagneti wave scattering at dielectric cylinder is studied by new numerical analysis method. Basic formulation of boundary integral equation (BIE) for numerical method is started weighted residual technique. BIE is made to two simultaneous equation at surface inner and outside point of dielectric cylinder in extended boundary condition (EBC) and surface boundary condition (SBC). Numerical method is used Boundary element method (BEM) that is two form, one is direct method and the other is indirect method, so that this method that transformes operator inversion martics is used numerical analysis. A good agreement of this numerical solution and the other results is obtained.

• Geophysics and Geophysical Exploration
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• v.3 no.2
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• pp.61-69
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• 2000

The free-surface boundary conditions are persistent problem in elastic wave equation modeling by finite-difference method, which can be summarized with the degradation of the accuracy of the solution and limited stability range in Poisson's ratio. In this paper, we propose the mid-point averaging scheme as an alternative way of implementing the free-surface boundary conditions, and present the solution to Lamb's problem to verify our approach.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.395-403
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• 2002

In the third phase of the response surface methods, the first-order model is assumed and the curvature of the response surface is checked with a fractional factorial design augmented by centre runs. We further assume that a true model is a quadratic polynomial. To choose an optimal design, Box and Draper(1959) suggested the use of an average mean squared error (AMSE), an average of MSE of y(x) over the region of interest R. The AMSE can be partitioned into the average prediction variance (APV) and average squared bias (ASB). Since AMSE is a function of design moments, region moments and a standardized vector of parameters, it is not possible to select the design that minimizes AMSE. As a practical alternative, Box and Draper(1959) proposed minimum bias design which minimize ASB and showed that factorial design points are shrunk toward the origin for a minimum bias design. In this paper we propose a robust AMSE design which maximizes the minimum efficiency of the design with respect to a standardized vector of parameters.