• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.527-541
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• 2006

In this paper, an existence theorem for a nonlinear two point boundary value problem of second order differential equations in Banach algebras is proved using a nonlinear alternative based on Leray-Schauder alternative.

• Journal of the Earthquake Engineering Society of Korea
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• v.27 no.1
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• pp.13-24
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• 2023

In this study, alternative seismic force-resisting systems for plant structure supporting equipment were designed, and the seismic performance thereof was compared using nonlinear dynamic analysis. One alternative seismic force-resisting system was designed per the requirement for ordinary moment-resisting and concentrically braced frames but with a reduced base shear. The other seismic force-resisting system was designed by accommodating seismic details of intermediate and unique moment-resisting frames and special concentrically braced frames. Different plastic hinge models were applied to ordinary and ductile systems based on the validation using existing test results. The control model obtained by code-based flexible design and/or reduction of base shear did not satisfy the seismic performance objectives, but the alternative structural system did by strengthened panel zones and a reduced effective buckling length. The seismic force to equipment calculated from the nonlinear dynamic analysis was significantly lower than the equivalent static force of KDS 41 17 00. The comparison of design alternatives showed that the seismic performance required for a plant structure could be secured economically by using performance-based design and alternative seismic-force resisting systems adopting minimally modified seismic details.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.81-87
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• 2010

In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem(BVP) $-D_0^{\alpha}+u(t)=\lambda[f(t, u(t))+q(t)]$, 0 < t < 1 u(0) = u(1) = 0, where $\lambda$ > 0 is a parameter, 1 < $\alpha$ $\leq$ 2, $D_{0+}^{\alpha}$ is the standard Riemann-Liouville differentiation, f : [0, 1] ${\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is continuous, and q(t) : (0, 1) $\rightarrow$ [0, $+\infty$] is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when $\lambda$ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.119-130
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• 2000

We give alternative proof of the existence theorem for certain elliptic systems describing competing interactions with nonlinear di usion. The existence of positive solution depends on the sign of the principal eigenvalue of suitable operators of Schr$\ddot{o}$dinger type. If the sign of such operators are both positive, then system has a positive solution. The main tool employed is the fixed point index of compact operator on positive cones.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.431-450
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• 2016

In this paper, the existence, uniqueness, stability via continuous dependence and Ulam stabilities of nonlinear integro-differential equations with random impulses are studied under sufficient condition. The results are obtained by using Leray-Schauder alternative fixed point theorem and Banach contraction principle.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.141-152
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• 1994

We consider a numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulation the nonlinear boundary value problem (BVP). We give a simple alternative to the standard collocation method for the nonlinear BIE. This method consists of one conventional linear system and another coupled linear system resulting from an auxiliary BIE which is obtained by differentiating both side of the nonlinear interior integral equations. We obtain an analogue BIE through the perturbation of the fundamental solution of Laplace's equation. We procure the super-convergence of approximate solutions.

• Structural Engineering and Mechanics
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• v.31 no.3
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• pp.265-276
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• 2009

Various Pushover analysis methodologies have evolved as an easy as well as designers-friendly alternative of nonlinear dynamic analysis for estimation of the inelastic demands of structures under seismic loading for performance based design. In fact, the established nonlinear dynamic analysis to assess the same, demands considerable analytical and computational background and rigor as well as intuitive insight into inelastic behavior for judging suitability of the results and its interpretation and hence may not be used in design office for frequent practice. In this context, the simple and viable alternative of Pushover analysis methodologies can be accepted if its efficacy is thoroughly judged over all possible varieties of the problems. Though this burning issue has invited some research efforts in this direction, still a complete picture evolving very clear guidelines for use of these alternate methodologies require much more detailed studies, providing idea about how the accuracy is influenced due to various combinations of basic parameters regulating inelastic dynamic response of the structures. The limited study presented in the paper aims to achieve this end to the extent possible. The study intends to identify the range of applicability of the technique and compares the efficacy of various alternative Pushover analysis schemes to general class of problems. Thus, the paper may prove useful in judicial use of Pushover analysis methodologies for performance based design with reasonable accuracy and relative ease.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.91-110
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• 2013

This paper proposes a novel iterative procedure for the design of planar reinforced concrete structures in which the reinforcement is designed for stresses calculated in a nonlinear finite element analysis. The procedure is intended as an alternative to strut and tie modeling for the design of complex structures like deep beams with openings. Practical reinforcement arrangements are achieved by grouping the reinforcement into user defined horizontal and vertical bands. Two alternative strategies are proposed for designing the reinforcement which are designated A and B. Design constraints are specified in terms of permissible stresses and strains in the reinforcement and strains in the concrete. A case study of a deep beam with an opening is presented to illustrate the method. Comparisons are made between design strategies A and B of which B is shown to be most efficient. The resulting reinforcement weights are also shown to compare favorably with those previously reported in the literature.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.201-208
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• 1993

Given the specific mean shift outlier model, the score test for multiple outliers in nonlinear regression is discussed as an alternative to the likelihood ratio test. The geometric interpretation of the score statistic is also presented.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.04a
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• pp.180-189
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• 2001

In this study, recently developed unscented Kalman filter (UKF) technique is studied for identification of nonlinear structural dynamic systems as an alternative to the extended Kalman filter (EKF). The EKF, which was originally developed as a state estimator for nonlinear systems, has been frequently employed for parameter identification by introducing the state vector augmented with the unknown parameters to be identified. However, the EKF has several drawbacks such as biased estimations and erroneous estimations especially for highly nonlinear dynamic systems due to its crude linearization scheme. To overcome the weak points of the EKF, the UKF was recently developed as a state estimator. Numerical simulation studies have been carried out on nonlinear SDOF system and nonlinear MDOF system. The results from a series of numerical simulations indicate that the UKF is superior to the EKF in the system identification of nonlinear dynamic systems especially highly nonlinear systems.