• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.665-677
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• 2023

In the present study, the limit point buckling and postbuckling behaviors of sinusoidal, shallow arches with pinned supports subjected to localized sinusoidal loading, based on the Euler-Bernoulli beam theory, are numerically analyzed. There are some studies on the buckling of sinusoidal shallow arches under the effect of sinusoidal loading. However, in these studies, the sinusoidal loading acts along the horizontal projection of the entire shallow arch. No study has been found in the relevant literature pertaining to the stability of the shallow arches subjected to various lengths of sinusoidal loading. Therefore, the purpose of this paper is to contribute to the literature by examining the effect of the length of the localized sinusoidal loading and the initial rise of the shallow arch on the limit point buckling and postbuckling behaviors. Equilibrium paths corresponding to certain values of the length of the localized sinusoidal loading and various values of the initial rise parameter are presented. It has been observed that the length of the sinusoidal loading and the initial rise parameter affects the transition from no buckling to limit point instability remarkably. The deformed configurations of the sinusoidal shallow arch under localized loading regarding buckling and postbuckling states are illustrated, as well. The effects of the length of the localized sinusoidal loading on the internal forces of the shallow arch are investigated during various stages of the loading.

• Nuclear Engineering and Technology
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• v.48 no.2
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• pp.434-447
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• 2016

The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.

• Journal of the Korean Society of Combustion
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• v.17 no.3
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• pp.9-16
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• 2012

Nonlinear dynamics of pulsating instability in radiating counterflow diffusion flames is numerically investigated by imposing Damk$\ddot{o}$hler number perturbation. Stable limit-cycle solutions occur in small ranges of Damk$\ddot{o}$hler numbers past bifurcation point of instability. Period doubling cascade and chaotic behaviors appear just before dynamic extinction occurs. Nonlinear dynamics is also studied when large disturbances are imposed to flames. For weak steady flames, the dynamic extinction range shrinks as the magnitudes of disturbances are increased. However, strong steady flames can overcome relatively large disturbances, thereby the dynamic extinction range extending. Stable limit-cycle behaviors reappears prior to dynamic extinction when the steady flames are strong enough.

• Proceedings of the KIEE Conference
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• 2000.07a
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• pp.319-321
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• 2000

Today's power systems operate near their stability limit and numerous incidents closely related to voltage instability phenomena have been reported. In addition. a world-wide fashion towards restructuring in electricity industry can worsen the trend of voltage instability. In this environment, finding exact voltage instability points of practical power systems is a main concern of power system engineers. This paper reports change of static voltage instability point with respect to various load model in the KEPCO system.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.3
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• pp.277-289
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• 2005

The study examines the limit strength for steel cable-stayed bridges. A case studies have been performed in order to evaluate the limit strength lot steel cable-stayed bridges using nonlinear inelastic analysis approach and bifurcation point instability analysis approach, effective tangent modulus $(E_f)$ method. To realize it, a practical nonlinear inelastic analysis condoling the initial shape is developed. In the initial shape analysis, updated structural configuration is introduced instead of initial member forces for beam-column members at every iterative step. Geometric and material nonlinearities of beam-column members are accounted by using stability function, and by using CRC tangent modulus and parabolic function, respectively Besides, geometric nonlinearity of cable members is accounted by using secant value of equivalent modulus of elasticity. The load-displacement relationships obtained by the proposed method are compared well with those given by other approaches. The limit strengths evaluated by the proposed nonlinear inelastic analysis for the proposed cable-stayed bridges with tee dimensional configuration compared with those by the inelastic bifurcation point instability analyses.

• Wind and Structures
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• v.7 no.1
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• pp.55-70
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• 2004

Aerostatic instability of a suspension bridge may suddenly appears when the deformed shape of the structure produces an increase in the value of the three components of displacement-dependent wind loads distributed in the structure. This paper investigates the aerostatic stability of suspension bridges using an advanced nonlinear method based on the concept of limit point instability. Particular attention is devoted to aerostatic stability analysis of symmetrical suspension bridges. A long-span symmetrical suspension bridge (Hu Men Bridge) with a main span of 888 m is chosen for analysis. It is found that the initial configuration (symmetry or asymmetry) may affect the instability configuration of structure. A finite element software for the nonlinear aerostatic stability analysis of cable-supported bridges (NASAB) is presented and discussed. The aerostatic failure mechanism of suspension bridges is also explained by tracing aerostatic instability path.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.577-586
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• 1997

In nonlinear finite element stability analysis of structures, the foremost necessary procedure is the computation to precisely locate a singular equilibrium point, at which the instability occurs. The present study describes global and local procedures for the computation of stability points including bifurcation points and limit points. The starting point, at which the procedure will be initiated, may be close to or arbitrarily far away from the target point. It may also be an equilibrium point or non-equilibrium point. Apart from the usual equilibrium path, bypass and homotopy path are proposed as the global path to the stability point. A local iterative method is necessary, when it is inspected that the computed path point is sufficiently close to the stability point.

• Transactions of Materials Processing
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• v.18 no.8
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• pp.596-600
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• 2009

Finite element simulation is an alternative method to practically find the forming limit diagram(FLD). In this paper, the novel fracture criterion is utilized to predict the FLD in conjunction with finite element analysis for sheet forming. The principal scheme of the fracture criterion in this paper is that growth of the micro voids leads up to fracture in the viewpoint of micro-mechanics. The numerical FLD is verified by results of the out-of plane stretching test using hemispherical punch. The verification is also conducted about two types of material. These results are in good accord with the experimental results. Especially, the proposed scheme is appropriate to predict FLDs for a restricted material with low ductility after the instability point or ultimate tensile strength.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.9
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• pp.2223-2233
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• 1993

An engineering method is suggested to calculate the applied load versus crack extension in the elastic-plastic fracture. The condition for an increment of crack extension is set by a critical increment of crack-up opening displacement(CTOD). The ratio of the CTOD increment to the incremental crack extention is a critical crack-tip opening angle(CTOA), assumed to be constant for a material of a given thickness. The Dugdale model of crack-tip deformation in an infinite plate is applied to the method, and a complete solution for crack extension and crack instability is obtained. For finite-size specimens of arbitrary geometry in general yielding, an approximate generalization of the Dugdale model is suggested so that the approximation approaches the small-scale yielding solution in a low applied load and the finite-element solution in a large applied load. Maximum load is calculated so that an applied load attains either a limit load on an unbroken ligament or a peak load during crack extension. The proposed method was applied to three-point bend specimens of a carbon steel SM45C in various sizes. Reasonable agreements are found between calculated maximum loads and experimental failure loads. Therefore, the method can be a viable alternative to the J-R curve approach in the elastic-plastic fracture analysis.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.2
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• pp.130-137
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• 1988

The technique of dual-input describing function's synthesis is introduced and the construction of a nonlinear compensator, based on this technique, is proposed. A nonlinear compensator, describing a complex DIDF depending upon amplitude of the second sinusoidal input signal only, is also proposed, where the second sinusoidal input signal is supplied to the nonlinear compensator by external generator. This compensator, connected in a closed loop of the PI speed control of DC motor, can improve the speed response in view instability limit cycle, low speed response and disturbance of the dynamic shift of the Nyquist's critical point -1 + j O. It is verified theoretically that the improvement of speed response of DC motor using the proposed compensator is achieved by means of the dynamic shift of the Nyquist's critical point on the complex plane, and the speed characterstics of DC motor is to be tested through experiment for its performance.