• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.353-361
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• 2018

We develop a mathematical model of heat emission on the epidermis of a human body. We present a global existence theorem of solutions for a nonlinear model system of coupled partial differential equations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.347-354
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• 2004

Using an efficient adjoint variable method, we develop a unified design sensitivity analysis (DSA) method considering both steady state nonlinear heat conduction and geometrical nonlinear elasticity problems. Design sensitivity expressions with respect to thermal conductivity and Young's modulus are derived. Beside the temperature and displacement adjoint equations, another coupled one is defined regarding the obtained adjoint displacement field as the adjoint load in temperature field. The developed DSA method is shown to be very efficient and further extended to a topology design optimization method for the nonlinear weakly coupled thermo-elasticity problems using a density approach.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.3
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• pp.252-261
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• 2016

A spar-type floating substructure that is being widely used for offshore wind power generation is vulnerable to resonance in the heave direction because of its small water plane area. For this reason, the stable dynamic response of this floating structure should be ensured by accurately identifying the resonance characteristics. The purpose of this study is to analyze the characteristics of the combination resonance between the excitation frequency of a regular wave and natural frequencies of the floating substructure. First, the nonlinear equations of motion with two degrees of freedom are derived by assuming that the floating substructure is a rigid body, where the heaving motion and pitching motions are coupled. Moreover, to identify the characteristics of the combination resonance, the nonlinear term in the nonlinear equations is approximated up to the second order using the Taylor series expansion. Furthermore, the validity of the approximate model is confirmed through a comparison with the results of a numerical analysis which is made by applying the commercial software ANSYS AQWA to the full model. The result indicates that the combination resonance occurs at the frequencies of ${\omega}{\pm}{\omega}_5$ and $2{\omega}_{n5}$ between the excitation frequency (${\omega}$) of a regular wave and the natural frequency of the pitching motion (${\omega}_{n5}$) of the floating substructure.

• Proceedings of the KSR Conference
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• 2010.06a
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• pp.1478-1485
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• 2010

In this paper, the nonlinear dynamic response of Vehicle-Bridge interaction with the coupled equations of motion including nonlinear Hertzian contact is presented. The moving train model is chosen to have 10 degrees of freedom (DOF). The bridge is modeled as 2D Euler-Bernoulli beam element with 4 DOF for each element, two for rotations and another two for translations. The nonlinear Hertzian contact is used to simulate the interaction between vehicle and bridge. Base on the relationship of wheel displacement of the vehicle and the vertical displacement of the bridge in Hertzian contact, the coupled equations of motion of the whole system is derived. The convenient formulation was encoded into a computer program. The contact forces, contact area and stress of the rail surface were also computed. The accuracy and efficiency of the proposed program are verified and compared with exact analytical solution and other previous studies. Various numerical examples and parametric studies have demonstrated the versatility and applicability of the proposed program.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.455-465
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• 2010

In this paper, by using the semi-order method, two new existence theorems of coupled quasi-solutions for a class of nonlinear operator equations in Banach spaces are proved under some suitable conditions.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.485-500
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• 2014

In this paper, we establish coupled fixed point theorems for mixed monotone mappings satisfying nonlinear contraction involving a pair of altering distance functions in ordered G-metric spaces. Via presented theorems we extend and generalize the results of Harjani et al. [J. Harjani, B. L$\acute{o}$pez and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 (2011) 1749-1760] and Choudhury and Maity [B.S. Choudhury and P. Maity, Coupled fixed point results in generalized metric spaces. Math. Comput. Model. 54 (2011), 73-79].

• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.159-180
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• 2013

We establish a common fixed point theorem for mappings under ${\phi}$-contractive conditions on intuitionistic fuzzy metric spaces. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.61-64
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• 1986

The Fourier Spectral Analysis has been widely utilized in the analysis of linear dynamic systems. However, it may not be generaly extended to analyze nonlinear systems. In this paper, a linear underlying dynamic structure coupled with nonlinear elements is analyzed by using newly derived equations of motion after the linear dynamic structure is characterized by the Fourier spectral analysis.

• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.37-46
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• 2017

This paper is concerned with the numerical study on the resonance response of a rigid spar-type floating platform in coupled heave and pitch motion. Spar-type floating platforms, widely used for supporting the offshore structures, offer an economic advantage but those exhibit the dynamically high sensitivity to external excitations due to their shape at the same time. Hence, the investigation of their dynamic responses, particularly at resonance, is prerequisite for the design of spar-type floating platforms which secure the dynamic stability. Spar-type floating platform in 2-D surface wave is assumed to be a rigid body having 2-DOFs, and its coupled dynamic equations are analytically derived using the geometric and kinematic relations. The motion-variance of the metacentric height and the moment of inertia of floating platform are taken into consideration, and the hydrodynamic interaction between the wave and platform motions is reflected into the hydrodynamic force and moment and the frequency-dependent added masses. The coupled nonlinear equations governing the heave and pitch motions are solved by the RK4 method, and the frequency responses are obtained by the digital Fourier transform. Through the numerical experiments to the wave frequency, the resonance responses and the coupling in resonance between heave and pitch motions are investigated in time and frequency domains.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.513-521
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• 2018

In this paper, the resonance response of spar-type floating platform in coupled heave and pitch motion is investigated using a CPU time-effective numerical method. A coupled nonlinear 2-DOF equation of motion is derived based on the potential wave theory and the rigid-body hydrodynamics. The transient responses are solved by the fourth-order Runge-Kutta (RK4) method and transformed to the frequency responses by the digital Fourier transform (DFT), and the first-order approximation of heave response is analytically derived. Through the numerical experiments, the theoretical derivation and the numerical formulation are verified from the comparison with the commercial software AQWA. And, the frequencies of resonance arising from the nonlinear coupling between heave and pitch motions are investigated and justified from the comparison with the analytically derived first-order approximation of heave response.