• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2002년도 추계 학술발표회 논문집
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• pp.258-265
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• 2002

Most structures are expected deform nonlinear and inelastic behavior when subjected to strong ground motion. Nonlinear time history analysis(NTHA) is the most rigorous procedure to compute seismic performance in the various inelastic analysis methods. But nonlinear analysis procedures necessitate more reliable and practical tools for predicting seismic behavior of structures. Some building codes propose the capacity spectrum method. This method is the concept of an equivalent linear system, wherein a linear system having reduced stiffness and increased damping is used to estimate the response of the nonlinear system. This procedure are conceptually simple, but the iterative procedure is time-consuming and may sometimes lead to no solution or multiple solutions. This paper presents a nonlinear direct spectrum method(NDSM) to evaluate seismic performance of structures, without iterative computations, given by the structural initial elastic period and yield strength from the pushover analysis, especially for mixed building structure.

• Korean Journal of Mathematics
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• 제13권2호
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• 대한토목학회논문집
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• 제12권4호
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• pp.33-47
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• 1992

본 논문에서는 케이블로 지지된 프리스트레스트 콘크리트(PC) 뼈대의 시공중의 각 단계를 고려하고 콘크리트와 PC 강재, 케이블 재료의 시간의존적 특성 및 재료의 비선형성과 케이블의 색 및 구조물의 처짐에 의한 기하학적 비선형성도 고려하는 해석방법을 제시했다. 구조물의 비선형거동을 해석하기 위한 운동방정식은 Updated Lagrangian 방식을 이용하여 유도하고 시간의존적인 거동올 해석하기 위해서 시간영역을 시간단계로 나누어 순차적으로 적분했다. 시공중의 각 단계를 표현하기 위해 계속적인 구조계의 변화를 고려했다. 본 논문에서 제시한 해석방법에 근거하여 컴퓨터 프로그램 CFRAME을 개발하고 예제들을 통하여 해석방법의 정당성을 보였다.

• 대한전기학회논문지:시스템및제어부문D
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• 제49권2호
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• pp.68-73
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• 2000

This paper addresses the analysis and design of fuzzy control systems for a class of complex nonlinear systems. Firstly, the nonlinear system is represented by Takagi-Sugeno(TS) fuzzy model and the global controller is constructed by compensating each linear model in the rule of TS fuzzy model. The design of conventional TS fuzzy-model-based controller is composed of two processes. One is to determine the static state feedback gain of each local model and the other is to validate the stability of the designed fuzzy controller. In this paper, we propose an alternative methods for the design of TS fuzzy-model-based controller. The design scheme is based on the extension of conventional optimal control theory to the design of TS fuzzy-model-based controller. By using the proposed method, the design and stability analysis of the TS fuzzy model-based controller is reduced to the problem of finding the solution of a set of algebraic Riccati equations. And we use the recently developed interior point method to find the solution of AREs, where AREs are recast as the LMI formulation. A numerical simulation example is given to show the effectiveness and feasibiltiy of the proposed fuzzy controller design method.

• International Journal of Aeronautical and Space Sciences
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• 제16권2호
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• pp.264-277
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• 2015

This article investigates various transcription techniques for the Legendre pseudospectral (PS) method to compare the pros and cons of each approach. Eight combinations from four different types of collocation points and two discretization methods for dynamic constraints, which differentiate Legendre PS transcription techniques, are implemented to solve a carefully selected test set of nonlinear optimal control problems (NOCPs). The convergence property and prediction accuracy are compared to provide a useful guideline for selecting the best combination. The tested NOCPs consist of the minimum time, minimum energy, and problems with state and control constraints. Therefore, the results drawn from this comparative study apply to the solution of similar types of NOCPs and can mitigate much debate about the best combinations. Additionally, important findings from this study can be used to improve the numerical efficiency of the Legendre PS methods. Three PS applications to the aerospace engineering problems are demonstrated to prove this point.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.233-243
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• 2009

This paper concerns an algorithm that combines line search and trust region step for nonlinear optimization problems. Unlike traditional trust region methods, we incorporate the Armijo line search technique into trust region method to solve the subproblem. In addition, the subproblem is solved accurately, but instead solved by inaccurate method. If a trial step is not accepted, our algorithm performs the Armijo line search from the failed point to find a suitable steplength. At each iteration, the subproblem is solved only one time. In contrast to interior methods, the optimal solution is derived by iterating from outside of the feasible region. In numerical experiment, we apply the algorithm to nonlinear portfolio optimization problems, primary numerical results are presented.

• 한국해안·해양공학회논문집
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• 제23권5호
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• pp.335-344
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• 2011

곡면의 경계를 가지는 수로에서 비선형 파랑의 상호작용을 모의하기 위한 비정수압 자유수면 모형이 개발되었다. 제안된 모형은 비선형의 3차원 Navier-Stokes 방정식을 곡선좌표 영역에서 계산단계 분리법의 일종인 압력수정법에 의하여 수치적으로 해석된다. 특히, 연직방향으로 변형된 형태의 엇갈린 격자를 이용하여 상대적으로 간단하게 압력방정식과 자유수면 경계조건을 구성하였다. 개발된 모형의 수치해석 정확도는 2차원의 수치 파수조에서 파랑의 비선형 정도에 대하여 5차의 스토스우크스 해석해와 비교하였다. 본 모형의 실제적 적용은 원형의 수로에서 회절과 반사에 의해 변형되는 비선형 파의 변형에 초점을 맞추어 수행하였다. 두개의 파를 중첩한 고비선형의 파에 대한 경우를 제외하고 수치해석 결과는 비선형적인 영향을 고려하지 않은 해석해의 선형적인 중첩과 일치하였다. 두개의 파를 중첩한 고비선형의 파에 대한 모의를 통하여 본 모형은 원형의 수로에서 비선형 군파의 변형에관한 수치적인 모의 가능성을 제시하였다.

• 경영과학
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• 제13권1호
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• pp.97-109
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• 1996

Genetic Algorithms have been successfully applied to various problems (for example, engineering design problems with a mix of continuous, integer and discrete design variables) that could not have been readily solved with traditional computational techniques. But, several problems for which conventional Genetic Algorithms are ill defined are premature convergence of solution and application of exterior penalty function. Therefore, we developed an Improved Genetic Algorithms (IGAs) to solve above two problems. As a case study, IGAs is applied to several nonlinear optimization problems and it is proved that this algorithm is very useful and efficient in comparison with traditional methods and conventional Genetic Algorithm.

• 대한수학회논문집
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• 제33권2호
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• Coupled systems mechanics
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• 제9권1호
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• pp.5-28
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• 2020

Despite a widely-held belief that the finite element method is the method for the solution of solid mechanics problems, which has for 30 years dissuaded solid mechanics scientists from paying any attention to the finite volume method, it is argued that finite volume methods can be a viable alternative. It is shown that it is simple to understand and implement, strongly conservative, memory efficient, and directly applicable to nonlinear problems. A number of examples are presented and, when available, comparison with finite element methods is made, showing that finite volume methods can be not only equal to, but outperform finite element methods for many applications.