• Proceedings of the Korea Concrete Institute Conference
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• 1998.04a
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• pp.353-358
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• 1998

The strain localization is a discontinuous phenomenon that addresses the formation of jumps of the field variables across a singularity surface. It has become widely accepted that the localization may occur as the result of discontinuous bifurcation which corresponds to the loss of ellipticity of the governing differential equations for elasto-plastic continua. In this paper, condition for strain localization in concrete based on bifurcation theory is studied and localization tensor analysis algorithm is employed to determine the directions of localization of deformations in concrete. By applying a plasticity model of concrete into the algorithm, localization analysis is performed concrete under uniaxial tension, pure shear and uniaxial compression.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.659-676
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• 2006

In this paper, we consider three-component reaction-diffusion system. With an integral condition and a global coupling, this system gives us an interesting free boundary problem. We shall examine the occurrence of a Hopf bifurcation and the stability of solutions as the global coupling constant varies. The main result is that a Hopf bifurcation occurs for global coupling and this motion is transferred to the stable motion for strong global coupling.

• Journal of Ocean Engineering and Technology
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• v.19 no.2 s.63
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• pp.60-66
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• 2005

This paper investigates the relationship between the fleet-angle of the hoisting rope and the swaying and pitching angles of a cargo in container cranes. It is found that for a given disturbance, when the fleet-angle is large, the sway Angle becomes smaller, but the pitching angle becomes larger. Therefore, for a quick suppression of a sway motion, it is desirable to have a large fleet-angle. The compatibility and bifurcation conditions, regarding instability, are characterized.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.471-489
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• 2014

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.553-567
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• 1997

This paper is concerned with the control problem $$ \dot{x}(t) = F(x) + u(t)G(x), t \in [0,T], x(0) = 0, $$ where F and G are smooth vector fields on $R^n$, and the admissible controls u satisfy the constraint $$\mid$u(t)$\mid$ \leq 1$. We provide the sufficient condition that the bang-bang trajectories having different switching orders intersect.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.265-285
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• 2017

In this article, a mathematical model is proposed and analyzed to study the delayed dynamics of a system having a predator and two preys with distinct growth rates and functional responses. The equilibrium points of proposed system are determined and the local stability at each of the possible equilibrium points is investigated by its corresponding characteristic equation. The boundedness of the system is established in the absence of delay and the condition for existence of persistence in the system is determined. The discrete type gestational delay of predator is also incorporated on the system. Further it is proved that the system undergoes Hopf bifurcation using delay as bifurcation parameter. This study refers that time delay may have an impact on the stability of the system. Finally Computer simulations illustrate the dynamics of the system.

• Transactions of Materials Processing
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• v.9 no.2
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• pp.128-139
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• 2000

Wrinkling is one of the major defects in sheet metal products and may be also attributable to the wear of the tool. The initiation and growth of wrinkles are influenced by many factors such as stress state, mechanical properties of the sheet material, geometry of the body, and contact condition. It is difficult to analyze the wrinkling initiation and growth considering the factors because the effects of the factors are very complex and the wrinkling behavior may show a wide variation for small deviations of the factors. In this study, the bifurcation theory is introduced for the finite element analysis of wrinkling initiation and growth. All the above mentioned factors are conveniently considered by the finite element method. The finite element formulation is based on the incremental deformation theory and elastic-plastic elements considering the planar anisotropy of the sheet metal. The proposed method is verified by employing a column buckling problem. And then, the initiation and growth of wrinkling in deep drawing of cylindrical cup are analyzed.

• Proceedings of the Korea Concrete Institute Conference
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• 1996.10a
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• pp.459-465
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• 1996

This paper is about unstable behavior in concrete during the localized deformation and the crack growths in concrete. By modeling the strain localization phenomenon of concrete, the stability condition of the localization is obtained and analyzed. And the stability and bifurcation condition of crack growths in two parallel cracks under different loading conditions are derived and discussed.

• Advances in nano research
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• v.14 no.4
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• pp.303-312
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• 2023

In this study, the bifurcation analysis of functionally graded material is done using exponential volume fraction law. Shell theory of Love is used for vibration of shell. The Galerkin's method is applied for the formation of three equations in eigen value form. This eigen form gives the frequencies using the computer software MATLAB. The variations of natural frequencies (Hz) for Type-I and Type-II functionally graded cylindrical shells are plotted for exponential volume fraction law. The behavior of exponent of volume fraction law is seen for three different values. Moreover, the frequency variations of Type-I and -II clamped simply supported FG cylindrical shell with different positions of ring supports against the circumferential wave number are investigated. The procedure adopted here enables to study vibration for any boundary condition but for brevity, numerical results for a cylindrical shell with clamped simply supported edge condition are obtained and their analysis with regard various physical parameters is done.

• Bulletin of the Korean Chemical Society
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• v.28 no.9
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• pp.1489-1492
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• 2007

Belousov-Zhabotinsky (BZ) reaction containing oxalic acid and acetone as a mixed organic substrate catalyzed by Ce(IV) in a flow system has been investigated. The reaction system is analyzed by varying flow rate, inflow concentrations, and temperature. Interchangeable oscillating patterns are observed in a certain range of concentrations, and above or below the condition a steady state is obtained. The increase in temperature increases the frequency and decreases the amplitude of oscillations. The apparent activation energy for the system is calculated by using the Arrhenius equation, which means that temperature has a greater effect on the reaction. Bifurcation phase diagrams for the system show the region of oscillations or steady states along with a small region of multistability. Further the behavioral trend observed in this system is discussed by mechanistic character of the system.