• Structural Engineering and Mechanics
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• 제35권4호
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• pp.431-457
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• 2010

This article provides a discussion of the mathematic modeling of connections for designing and qualifying structures, systems, and components subject to monotonic or cyclic loading. To characterize the force-deformation behavior of connections under monotonic loading, a review of the Ramberg-Osgood, Richard-Abbott, and Menegotto-Pinto models is conducted, and it is shown that these nonlinear functions can be mathematically derived by scaling up or down a linear force-deformation function. A generalized four-parameter model for simulating connection behavior is investigated to facilitate nonlinear regression analysis. In order to perform seismic analysis of frameworks, a hysteretic model accounting for loading, unloading, and reloading is described using the established monotonic model. For preliminary analysis, a method is provided to quickly determine the model parameters that fit approximately with the observed data. To reach more accurate values of the parameters, the methods of nonlinear regression analysis are investigated and the modified Levenberg-Marquardt and separable nonlinear least-square algorithms are applied in determining the model parameters. Example case studies illustrate the procedure for the computation through the use of experimental/analytical data taken form the literature. Transformation of connection curves from the three-parameter model to the four-parameter model for structural analysis is conducted based on the modeling of connections subject to fire.

• 한국경영과학회지
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• 제12권1호
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• pp.10-18
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• 1987

This paper discusses algorithmic properties of a class of complementarity programs involving strictly diagonally isotone and off-diagonally isotone functions, i. e., functions whose Jacobian matrices have positive diagonal elements and nonnegative off-diagonal elements, A typical traffic equilibrium under elastic demands is cast into this class. Algorithmic properties of these complementarity problems, when a Jacobi-type iteration is applied, are investigated. It is shown that with a properly chosen starting point the generated sequence are decomposed into two converging monotonic subsequences. This and related will be useful in developing solution procedures for this class of complementarity problems.

• 한국산업정보학회논문지
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• 제15권5호
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• pp.179-185
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• 2010

시스템의 민감도 분석을 위한 불확실성 중요도 측도란 어떠한 입력변수의 불확실성이 반응변수의 불확실성에 미치는 영향의 정도를 평가하여, 반응변수의 불확실성을 감소시키기 위해서는 어떤 입력변수들의 불확실성을 감소시키는 것이 효과적인지를 밝히는데 사용된다. 본 논문에서는 입력변수와 반응변수 간의 관계식이 단조함수일 때, 어떤 입력변수의 불확실성이 제거될 때 반응변수 분산의 기대되는 감소량을 백분율로 측정하는 측도를 평가하기 위한 방법을 제안한다. 제안된 평가 방법은 입력변수와 반응변수 간의 관계식이 선형 및 비선형 단조함수 모두에 적용될 수 있으며 입력변수의 분포에 제한이 없으며, 입력변수의 분포를 이산형 분포로 근사화하는 기법을 사용함으로써 불확실성 중요도 측도의 안정적인 추정치를 얻을 수 있다 반면에 제안된 평가 방법은 몬테칼로 시뮬레이션을 기반으로 하기 때문에 계산량이 많은 단점이 있다.

• 대한수학회논문집
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• 제31권2호
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• pp.355-363
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• 2016

By employing a refined version of the $P{\acute{o}}lya$ type integral inequality and other techniques, the authors establish some inequalities and absolute monotonicity for modified Bessel functions of the first kind with nonnegative integer order.

• International Journal of CAD/CAM
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• 제6권1호
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• pp.59-64
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• 2006

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

• 대한수학회보
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• 제50권1호
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• pp.263-273
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• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• 한국지진공학회논문집
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• 제23권2호
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• pp.131-140
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• 2019

Diagonally reinforced concrete coupling beams (DRCBs) have been widely adopted in reinforced concrete (RC) bearing wall systems. DRCBs are known to act as a fuse element dissipating most of seismic energies imparted to the bearing wall systems during earthquakes. Despite such importance of DRCBs, the damage estimation of such components and the corresponding consequences within the knowledge of performance based seismic design framework is not well understood. In this paper, drift-based fragility functions are developed for in-plane loaded DRCBs. Fragility functions are developed to predict the damage and to decide the repair method required for DRCBs subjected to earthquake loading. Thirty-seven experimental results are collected from seventeen published literatures for this effort. Drift-based fragility functions are developed for four damage states of DRCBs subjected to cyclic and monotonic loading associated with minor cracking, severe cracking, onset of strength loss, and significant strength loss. Damage states are defined in a consistent manner. Cumulative distribution functions are fit to the empirical data and evaluated using standard statistical methods.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권2호
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• pp.175-183
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• 2010

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

• Journal of the Korean Data and Information Science Society
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• 제23권6호
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• pp.1223-1229
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• 2012

In this paper, we propose a generalized Kullback-Leibler (KL) information for measuring the distance between two distribution functions where the extension to the censored case is immediate. The generalized KL information has the nonnegativity and characterization properties, and its censored version has the additional property of monotonic increase. We also extend the discussion to the discrete case and propose a generalized censored measure which is comparable to Pearson's chi-square statistic.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권2호
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• pp.141-145
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• 2014

In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function ${\psi}^{\prime}(t)$ on (0, ${\infty}$).