Elastic-plastic states of two-layer curved bar under pure bending

Analytical solution of an elastic-partially plastic two-layer curved bar subjected to couples at both ends is obtained. The solution is based on Tresca's yield criterion and its associated flow rule. Numerical results for real engineering materials in partially plastic stress state are presented in graphical form. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Delamination of a two-layer corroded ring under radial vibrations

A two-layer ring, with account of its initial state caused by internal pressure and corrosion, leading to wear, is considered. The ring is subjected to an additional pressure causing its radial vibrations. It is shown that, under certain conditions, there is a vibration frequency at which the delamination of the ring is possible. Expressions are found which determine this frequency as a function of problem parameters, in particular, of the time of corrosive wear.     

Magneto-elastic torsional waves in a bar under initial stress

The magneto-elastic torsional wave in a bar under initial stress is studied. Most of the equations have been formulated on Biot’s incremental deformation theory and the initial stress has been taken in the form of uniform tension. Two cases have been considered: first when the material of the rod is homogeneous and second when it is non-homogeneous. In both the cases frequency equations for the wave have been calculated     

Estimation of an Exponential Quantile under a General Loss and an Alternative Estimator under Quadratic Loss

Estimation of the quantile + of an exponential distribution with parameters (, ) is considered under an arbitrary strictly convex loss function. For obeying a certain condition, the inadmissibility of the best affine equivariant procedure is established by exhibiting a better estimator. The LINEX loss is studied in detail. For quadratic loss, sufficient conditions are given for a scale equivariant estimator to dominate the best affine equivariant one and, when exceeds a lower bound specified below, a new minimax estimator is identified.     

On the equilibrium of a two-layer elastic body with a crack

We analyze a free boundary value problem that describes an equilibrium state of a two-layer elastic body with a crack. The existence of a solution is proved. Invariant integrals over curves surrounding the crack tip are found. Passages to the limit are studied as the rigidity parameter of the layer vanishes.     

向量损失函数下参数估计的容许性

在向量损失函数下，本文研究了在一般线性模型，多元线性模型和增长曲线模型中参数估计在给定估计类及一切类中的可容许性，给出了可容许的充要条件。     

一种对称损失函数下一类指数分布族刻度参数的估计

在p,q对称熵损失函数L(θ,δ)=θp/δp+δq/θq-2(p,q0)下,研究了一类指数分布族c(x,n)θ-ve-T(x)/θ的刻度参数θ的Bayes估计与可容许估计,并应用积分变换定理证明了这两个估计具有不变性.     

Dynamics of a two-layer fluid sloshing problem

A second-order ordinary differential equation, which is a reducedform of the periodically forced extended Korteweg–de Vries(eKdV) equation, is derived in the physical context of sloshinga two-layer fluid tank. In the limit of small dispersion, numericalevidence is given of multiple periodic solutions displayingfast oscillations superimposed on slow periodic waves and ahigher-order Melnikov method is then used to verify the existenceof such solutions. The dynamical behaviour of a similar equationwith more general coefficients is also examined, demonstratingthe existence of periodic and chaotic behaviour. We highlightnew aspects which arise due to the presence of mixed nonlinearity.     

Recovering the surface temperature history of a two-layer composite body

We consider the problem of recovering the surface temperature history of a two-layer composite body from interior measurements. The problem is ill-posed. We shall use the Fourier transform and the method of truncated integration to regularize the problem. Error estimate is given.     

Dynamic problem of thermoelasticity for a two-layer space

The method of influence functions is applied to construct a closed-form solution of the dynamic problem of thermoelasticity for a two-layer space (in one-dimensional framework) with nonideal thermal contact and ideal mechanical contact at the layer interface. The influence functions are constructed by the operational method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 57, pp. 95–102, 1985.     

Dynamics of a two-layer beam with layer slip

A possible type of structural damping in mechanical systems when there is a distinct dependence of the oscillation decrement on the amplitude is investigated, using the example of the solution of a model problem on the oscillations of a two-layer beam. It is assumed that layer slip only occurs along the beam axis and that the layers together in the transverse direction. The interaction between the layers is of an elastic-friction form. The equations of motion of the beam in Timoshenko's form are numerically integrated using Godunov's difference scheme.     

Bending of a two-layer beam with non-rigid contact between the layers

The bending, under plane stress state conditions, of a two-layer beam-strip with identical isotropic linearly elastic layers with non-rigid contact between them is considered. The effect of the contact interaction between the layers, simulated by an elastic or elastoplastic gasket of negligibly small thickness with a finite shear stiffness, on the deflection of the beam is studied. Absolute slippage and rigid contact between the layers are the two limiting values of the shear stiffness. The values of the flexural stiffness of the beam differ by a factor of four in these limiting situations. The problem is reduced to a one- dimensional problem in the case of harmonic external load and an asymptotic solution is constructed for it. In the case of a load of general form, the Kirchhoff - Love hypotheses are used to construct an approximate solution and the problem is reduced to a one-dimensional problem. The difficulties which arise in simulating of the interaction forces between the layers using Coulombic dry friction forces are discussed.     

对称熵损失下的一类指数族刻度参数估计

In this paper we investigate the estimator for the rth power of the scale parameter in a class of exponential family under symmetric entropy loss L（θ, δ） = v（θ/δ ＋ δ/θ - 2）. An exact form of the minimum risk equivariant estimator under symmetric entropy loss is given, and the minimaxity of the minimum risk equivariant estimator is proved. The results with regard to admissibility and inadmissibility of a class of linear estimators of the form cT（X） ＋ d are given, where T（X） Gamma（v, θ）.     

Generalized dynamic problem of thermoelasticity for a two-layer space

A closed-form solution of the generalized unsteady heat-conduction problem and dynamic thermoelasticity problem is constructed for an elastic isotropic two-layer space free from external disturbances. Some common practical cases are examined.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 62, pp. 56–64, 1987.