• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.633-656
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• 2022

Many regions of the world are now facing the second wave of boomed cases of COVID-19. This time, the second wave of this highly infectious disease (COVID-19) is becoming more devastating. To control the existing situation, more mass testing, and tracing of COVID-19 positive individuals are required. Furthermore, practicing to wear a face mask and maintenance of physical distancing are strongly recommended for everyone. Taking all these into consideration, an optimal control problem has been reformulated in terms of nonlinear ordinary differential equations in this paper. The aim of this study is to explore the control strategy of coronavirus-2 disease (COVID-19) and thus, minimize the number of symptomatic, asymptomatic and infected individuals as well as cost of the controls measures. The optimal control model has been analyzed analytically with the help of the necessary conditions of very well-known Pontryagin's maximum principle. Numerical simulations of the optimal control problem are also performed to illustrate the results.

• 대한토목학회논문집
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• 제26권4B호
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• pp.405-412
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• 2006

본 연구에서는 직립벽을 따른 규칙파의 연파특성을 평면수조를 이용한 수리실험과 포물형근사식을 이용한 수치해석을 통해 검토하였다. 본 연구는 파랑의 비선형성이 연파의 전파특성에 미치는 영향을 검토하는 것으로서 수리실험결과와 수치해석 결과가 잘 일치함을 알 수 있었다. 본 연구로부터 입사각이 작아지고 입사파의 비선형성이 증가할수록 연파의 파고는 감소하고, 연파의 폭은 증가함을 알 수 있었다.

• Structural Engineering and Mechanics
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• 제84권3호
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• pp.361-373
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• 2022

This paper examines the flexural performance of concrete beams reinforced with glass fibre-reinforced polymer (GFRP) bars under fatigue loading. Experiments were carried out on concrete beams of size 1500×200×100 mm reinforced with 10 mm and 13 mm diameter GFRP bars under fatigue loading. Experimental investigations revealed that fatigue loading affects both strength and serviceability properties of GFRP reinforced concrete. Experimental results indicated that (i) the concrete beams experienced increase in deflection with increase in number of cycles and failed suddenly due to snapping of rebars and (ii) the fatigue life of concrete beams drastically decreased with increase in stress level. Analytical model presented a procedure for predicting the deflection of concrete beams reinforced with GFRP bars under cyclic loading. Deflection of concrete beams was computed by considering the aspects such as stiffness degradation, force equilibrium equations and effective moment of inertia. Nonlinear finite element (FE) analysis was performed on concrete beams reinforced with GFRP bars. Appropriate constitutive relationships for concrete and GFRP bars were considered in the numerical modelling. Concrete non linearity has been accounted through concrete damage plasticity model available in ABAQUS. Deflection versus number of cycles obtained experimentally for various beams was compared with the analytical and numerical predictions. It was observed that the predicted values are comparable (less than 20% difference) with the corresponding experimental observations.

• Ocean Systems Engineering
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• 제12권3호
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• pp.359-384
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• 2022

We develop in this work a new well-balanced preserving-positivity path-conservative central-upwind scheme for Saint-Venant-Exner (SVE) model. The SVE system (SVEs) under some considerations, is a nonconservative hyperbolic system of nonlinear partial differential equations. This model is widely used in coastal engineering to simulate the interaction of fluid flow with sediment beds. It is well known that SVEs requires a robust treatment of nonconservative terms. Some efficient numerical schemes have been proposed to overcome the difficulties related to these terms. However, the main drawbacks of these schemes are what follows: (i) Lack of robustness, (ii) Generation of non-physical diffusions, (iii) Presence of instabilities within numerical solutions. This collection of drawbacks weakens the efficiency of most numerical methods proposed in the literature. To overcome these drawbacks a reformulation of the central-upwind scheme for SVEs (CU-SVEs for short) in a path-conservative version is presented in this work. We first develop a finite-volume method of the first order and then extend it to the second order via the averaging essentially non oscillatory (AENO) framework. Our numerical approach is shown to be well-balanced positivity-preserving and shock-capturing. The resulting scheme could be seen as a predictor-corrector method. The accuracy and robustness of the proposed scheme are assessed through a carefully selected suite of tests.

• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.607-623
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• 2024

This article studies the effects of heat generation/absorption and thermal radiation on the unsteady magnetohydrodynamic (MHD) Casson fluid flow past a vertical plate through rotating porous medium with constant temperature and mass diffusion. It is assumed that the plate temperature and concentration level are raised uniformly. For finding the exact solution, a set of non-dimensional partial differential equations is solved analytically using the Laplace transform technique. The influence of various non-dimensional parameters on the velocity are discussed, including the effects of the magnetic parameter M, heat generation/absorption Q, thermal radiation parameter R, Prandtl number Pr, Schmidt number Sc, permeability of porous medium parameter, Casson fluid parameter γ, on velocity, temperature, and concentration profiles, which are discussed through several figures. It is found that velocity, temperature, and concentration profiles in the case of heat generation parameter Q, Casson fluid parameter γ, thermal Grashof number Gr, mass Grashof number Gc, Permeability Porous medium parameter K, and time t have retarding effects. It is also seen that the magnetic field M, Thermal Radiation parameter R, Prandtl field Pr, Schmidt number Sc have reverse effects on it.

• Structural Engineering and Mechanics
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• 제91권4호
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• pp.417-426
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• 2024

Nanotechnology has emerged as a promising avenue for enhancing musical structures. In this study, we analyze the static behavior of laser harp (i.e., electronic musical instrument) reinforced with Zinc Oxide (ZnO) nanoparticles. Leveraging the piezoelectric properties of ZnO nanoparticles, the structure is subjected to an electric field for intelligent control. The electronic musical structure is situated in a foundation with vertical springs and shear modulus constants. We employ the exponential Shear Deformation Beam Theory (ESDBT) to mathematically model the structure. A micro-electro-mechanical model is employed to determine the equivalent properties of the system. By utilizing nonlinear stress-strain relations, energy methods, and Hamilton's principle, we derive the motion equations. The buckling load of the electronic musical beam is calculated using the Difference Quadrature Method (DQM). The primary objective of this study is to present a mathematical model for electronic musical beams and determining the buckling load of the structure and to investigate the influence of nanotechnology and electric fields on its buckling behavior. The buckling is the case when the structure becomes deforms and unstable. Our findings reveal that the application of negative external voltage to the electronic musical structure increases both the stiffness and the buckling load of the musical system. Furthermore, reinforcing the electronic musical structure with ZnO nanoparticles results in an increased buckling load. Notably, the maximum enhancement in the 28-day compressive and tensile strengths of samples containing zinc oxide nanoparticles compared to the control sample resulting in increases of 18.70% and 3.77%, respectively.

• Computers and Concrete
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• 제34권3호
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• pp.297-305
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• 2024

This study investigates the buckling behavior of CNTRC beams on a Winkler-Pasternak elastic foundation, considering their stiffness. To achieve the highest accuracy, the shear stiffness is taken into account based on the Higher-order Shear Deformation Theory (HSDT). A novel exponential power-law distribution of the CNT volume fraction across the beam thickness is employed to model CNTRC beams. Various reinforcement patterns are incorporated into the polymer matrix, featuring single-walled carbon nanotubes (SWCNT) that are both aligned and distributed. The effective mechanical properties of the CNTRC beam are predicted using the rule of mixtures. Hamilton's principle is applied to derive the differential equations of motion. This theoretical framework enables the validation of the approach by comparing numerical simulation results with previous studies. The impact of the exponent order (n), CNT volume fraction, geometrical ratio, and Winkler-Pasternak parameters on buckling analysis is thoroughly presented and discussed. The results indicate that, among the different types of analyzed CNTRC beams, the X-Beam pattern demonstrates the highest buckling load capacity.

• 한국지진공학회논문집
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• 제2권4호
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• pp.73-86
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• 1998

본 논문의 목적은 현재 국내에서 개발중인 KALIMER(Korea Advanced Liquid Metal Reactor) 액체금속로의 면진설계지침서에 포함될 고감쇠 적층고무베어링에 대한 전단 강성 평가법 히스테레틱 거동해석법 그리고 대변형에서의 종국거동 해석법을확립하고자하는데 있다 이를 위하여 1/8축소규모의 고감쇠 적층고무베어링을 설계제작하고 특성실험을 수행하여 제안된 전단강성식의 타당성을 검토하였다 그리고 비선형 수정 Rate 모델을 사용한 적층고무베어링의 히스테레틱 거동해석을 수행하기 위하여 히스테레틱실험결과로부터 성능특성식을 구하고 이를 1자유도계를 이용한 지진해석에 적용하여 실험결과와 비교함으로서 제안된 모델의 정확성을 입증하였다 본 논문에서 사용한 고감쇠 적층고무베어링에 대한 대변형에서의 안정성을 평가하기 위하여 수정 Macro 모델을 이용한 종국거동해석을 수행하였다 종국거동 해석결과로부터 안정성평가를 위하여 안정전단변형한계(Critcal shear strain)를 정의하였으며 해석결과 수직하중이 증가함에 따라서 안정전단변형한계가 급격히 감소함을 알수 있었다 본논문에 사용된 고감쇠 적층고무베어링은 설계수직하중에 대해서는 종국거동에서이 존재하지 않았으나 설계수직하중의 약 5배가 작용할 경우가 350% 전단변형률부터 불안정 천이현상이 발생하였으며 약 7배가 작용할 경우에 안정전단변형한계는 340%로 나타났다.

• 한국강구조학회 논문집
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• 제23권6호
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• pp.669-677
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• 2011

다경간 현수교란 3개 이상의 주탑을 가지는 현수교로 중앙부에 주 경간을 2개 이상 가지는 현수교이다. 다경간 현수교 설계시 중앙주탑과 측주탑의 적절한 강성비를 가지도록 설계하는 것이 경제성이나 구조적인 효율성 측면에서 중요하다. 본 연구는 다경간 현수교의 중앙주탑과 측주탑의 적절한 강성비를 찾기 위해 다경간 현수교의 거동을 용이하게 파악할 수 있는 간편한 방법을 제안하는 것을 목적으로 하고 있다. 그 방법으로 다경간 현수교의 주케이블을 등가의 케이블 스프링으로 이상화하고, 주케이블에 작용하는 장력을 주탑상단에 수평력과 수직력의 외력으로 치환시키는 방법으로 다경간 현수교를 등가 다경간 현수교 모델로 치환하였다. 등가 다경간 현수교 모델에 대한 평형방정식을 유도하고 비선형해석을 통해 방정식의 해를 구하였다. 중앙지간장 3,000m의 4경간 현수교의 FEM 해석을 통해 각 주탑에서 발생하는 변위와 모멘트 반력을 계산하고, 이 결과를 등가 4경간 현수교 모델의 해석결과와 비교하여 본 연구의 연구결과를 검증하였다. 검증 결과, 본 연구의 제안방법은 FEM 해석결과와 비슷한 경향을 나타내었다.

• Korean Chemical Engineering Research
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• 제53권3호
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• pp.295-301
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• 2015

폴리설폰 분리막을 이용한 바이오 메탄 가스 농축 특성을 이론적 방법으로 분석하였다. 병류 흐름 분리막 공정의 지배 방정식을 유도하고 Compaq Visual Fortran 6.6 소프트웨어를 이용하여 유도된 비선형 상미분 방정식을 수치 해석하였다. 공급 메탄 몰분율이 0.7로 주어진 전형적 운전조건에서 분리막 입구로부터 출구로 이동하면서 잔류 측 메탄몰분율은 0.7에서 0.76로 증가하였고 공급유량 대비 잔류유량 비는 1에서 0.79로 감소하였다. 공급 메탄 몰분율 또는 공급 압력이 증가할수록 잔류 측 메탄 몰분율은 증가하였다. 분리막 길이를 고정한 상태에서 분리막 면적이 감소하거나 투과 측 압력 대 공급 측 압력 비가 증가함에 따라 잔류 측 메탄 몰분율이 감소함을 확인하였다. 총 투과 분율이 증가할수록 잔류 측 메탄 몰분율은 증가하였고 메탄 회수율은 감소함을 관찰할 수 있었다.