Dynamic buckling of a simple elastic-plastic model under pulse loading

The dynamic buckling of an elastic-plastic imperfection-sensitive model subjected to rectangular- and triangular-shaped loading pulses is examined to provide some insight into the dynamic buckling behaviour of structures. The loading pulse is expressed as a function of the horizontal displacement, which allows an analytical method to be used for determining the stability domains for both pulses. The estimates obtained are compared with some previously published results on the dynamic elastic-plastic buckling of the same model under a step loading. It transpires that for the pulse loading of models with large imperfections dynamic instability occurs either elastically or plastically depending on the pulse duration, while for a step loading only an elastic instability is possible for the parameters examined.     

Bifurcation and chaos of a simple walking model driven by a rhythmic signal

The walk of animals is achieved by the interaction between the dynamics of their mechanical system and the central pattern generator (CPG). In this paper, we analyze dynamic properties of a simple walking model of a biped robot driven by a rhythmic signal from an oscillator. In particular, we examine the long-term global behavior and the bifurcation of the motion that leads to chaotic motion, depending on the model parameter values. The simple model consists of a hip and two legs connected at the hip through a rotational joint. The joint is driven by a rhythmic signal from an oscillator, which is an open loop. In order to analyze the bifurcation, we first obtained approximate solutions of the walking motion and then constructed discrete dynamics using the Poincaré map. As a result, we found that consecutive period-doubling bifurcations occur as the model parameter values change, and that the walking motion leads to chaotic motion over the critical value of the model parameters. Moreover, we approximately obtained the period-doubling solutions and the critical value by employing a Newton-Raphson method. Our analytical results were verified by the numerical simulations.     

A simple equilibrium model for shallow-cumulus-topped mixed layers

A new equilibrium model for shallow-cumulus-topped mixed layers is presented. A variant on the w _* closure for the shallow-cumulus mass flux is applied that retains the convective area-fraction in its formulation. As opposed to being constant, the fraction is explicitly modeled using a statistical closure as a function of the saturation deficit and humidity variance at cloud base. As a consequence, important new interactions are introduced between the convective transport, humidity, and depth of the mixed layer. This mechanism, which we call the mass-flux humidity feedback, helps determine the character of the equilibrium state such that the mixed-layer top is maintained close to the cloud-base height. Due to the strong sensitivity of the mass flux to the area fraction, the latter thus acts as a regulator or valve mechanism on moist convective transport. As a consequence, the mixed-layer model is able to explain the robustness of many aspects of the shallow-cumulus boundary layer that is typically found in observations and large-eddy simulations (LESs). The model is evaluated for a single-LES case as well as for global climatology obtained from a 40-year reanalysis of meteorological data by the European Centre for Medium-range Weather Forecasts (ECMWF). LES characteristics of convective mass flux, cloud fraction, humidity variance, cloud-base height, and surface fluxes of heat and humidity are reproduced. The solution on reanalysis fields reproduces the spatial structure of mixed-layer temperature and humidity and their associated surface fluxes in the subtropical Atlantic and Pacific trade wind regions. Furthermore, the spatial structure of the convective area-fraction matches that of synoptic surface observations of frequency of occurrence of shallow cumulus. Particularly striking is the smooth onset of the convective area-fraction and mass flux along the trade-wind trajectory that is reproduced, from zero to typical trade-wind values. The cumulus onset represents the necessity for shallow-cumulus mass flux to occur in order to close the mixed-layer budgets of heat, moisture, and mass, as a response to the changing magnitude of large-scale subsidence and free tropospheric humidity along the trajectory. Finally, the mass flux model is implemented in an intermediate-complexity tropical climate model to study its behavior when fully interactive with the larger-scale flow. A climate run then shows that the model is stable, due to the mass-flux humidity feedback acting to keep the shallow-cumulus boundary layer close to its equilibrium state for long, climatological timescales.     

简单刚架中的纵横弯曲效应问题

以一个简单刚架为例, 详细讨论了拉、压两种纵横弯曲效应对位移计算结果的影响; 并得出了拉力加强而压力削弱了梁的抗弯曲能力, 两种效应并不对称等结论.     

Bifurcation problem of critical points for quadratic differential systems

1.IntroductionWeconsiderthequadraticdifferentialsystemoftype(II)and(ill):.z~~y sx IXZ mxg g','~x(l ox)(1.1)f~~g 6x lx' mxy ny','~x(l ax by)(1.2)Asacontributionofsolvingbifurcationproblemofquadraticsystems,westudyinthispaperbifurcationofcriticalpoints(CPs)…     

The simple shear oscillation and the restrictions to elastic-plastic constitutive relations

Based on the definitions of hardening, softening and ideal plastic behavior of elastic-plastic materials in the true stress tensor space, the phenomena of simple shear oscillation are shown to be relative to the oscillatory occurrence of hardening and softening behavior of elastic-plastic materials, namely the oscillation of hardening behavior, by analyzing a simple model of rigid-plastic materials with kinematical hardening under simple shear deformation. To make the models of elastic-plastic materials realistic, must be satisfied the following conditions: for any constitutive model, its response stresses to any continuous plastic deformation must be non-oscillatory, and there is no oscillation of hardening behavior during the plastic deformation.     

A dynamic model for a Timoshenko beam in an elastic-plastic state

Summary In this paper, equations which describe the propagation of elastic-plastic waves of combined stress resultants in a Timoshenko beam under symmetrical bending and tension or compression are derived. It is assumed that the beam material exhibits a weak work-hardening and strain-rate independent behaviour. The normality rule is postulate for the plastic strain rates of an infinitesimal volume element. The wave propagation is described by a hyperbolic system of differential equations, the state variables of which are the stress resultants and the strain rates of an infinitesimal beam element. It is shown that the actual distribution of shear stress in the plastic range need not be taken into account by means of a plastic shear correction factor.

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Ein dynamisches Modell für einen Timoshenko-Balken im elastisch-plastischen Zustand

Übersicht Diese Arbeit stellt ein Modell vor, das die Ausbreitung von elastischen und plastischen Wellen kombinierter Schnittgrößen in dynamisch hochbeanspruchten Balken unter gerader Biegung und Normalkraft beschreibt. Das Werkstoff-verhalten wird als schwach verfestigend und zeitunabhängig angenommen. Die Normalitätsregel wird für die plastischen Verzerrungsgeschwindigkeiten eines Volumenelements postuliert. Die Ausbreitung der Wellen wird durch ein hyperbolisches System von Differentialgleichungen beschrieben, dessen Zustandsvariablen die Schnittgrößen und die Formänderungs-geschwindigkeiten eines Balkenelements sind. Schließlich wird gezeigt, daß die Einführung eines plastischen Schubkorrekturfaktors nicht erforderlich ist.

     

Bifurcation analysis of a tri-neuron neural network model in the frequency domain

In this paper, a class of neural network models with three neurons is considered. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of the bifurcation parameter point is determined. If the coefficient μ is chosen as a bifurcation parameter, it is found that Hopf bifurcation occurs when the parameter μ passes through a critical value. The direction and the stability of Hopf bifurcation periodic solutions are determined by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also provided.     

Stability domains of the vertical equilibrium state of a triple simple pendulum

The stability boundaries for the vertical equilibrium position of a triple simple pendulum subject to asymmetric follower force are analyzed. The effect of the upper spring and the magnitude of the follower force on the roots of the characteristic equation is studied Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 122–134, October 2008.