On a new electromechanical switch using the reversible wavy elastic response of metallic glass ribbons

For the first time, practical applications as an alarm device and automatic filling of an aquarium using an electromechanical switch manufactured from metallic glass (MG) ribbon is proposed. The elastic response of an initial arc-shaped MG ribbon-based Fe_90.65B_3.9Cr_2.75Si_2.7 is studied and exploited. Under the applied load F, the amorphous material exhibits a reversible elastic wavy response. During the elastic deformation and multiplication of harmonic undulations, a perfect linear contact between the waves and support is established. This contact position is the same for the pair waves, and can be employed to ensure the passage of an electric current, since the ribbon is Fe-based. The reversible elastic wavy response of MG ribbon can be used as an electromechanical switch. The lifespan of the ribbon used as a switch is also considered.     

On pattern selection in mixed convection in rectangular ducts

Mixed convection in a horizontal rectangular duct has the same critical Rayleigh number as natural convection in a rectangular cavity for the onset of convection. The linear stability analysis predicts either an odd or an even number of convective rolls to appear depending on the aspect ratio of the cross section. However, it has been shown both experimentally and numerically that an even number of convective rolls appears under supercritical conditions for fully developed mixed convection. The paper first presents an analytical solution for the buoyancy-induced mainstream velocity, w ^b , at the onset of buoyancy-induced motion in a forced convective flow. Then, a comparison in the initial growth rate of w ^b is made between the case of an odd and an even number of rolls; which shows the selection of an even number of rolls over an odd number in mixed convection except for low aspect ratio ducts.     

Solutions exactes de fissure d'interface sous contact frottant avec un milieu indéformableExact solutions of the interface crack between elastic and rigid bodies under contact with friction

One considers an interface crack between an elastic half-plane and a rigid half-plane, in the presence of Coulomb's friction. There exists two singular solutions at the semi-infinite crack tip, which correspond physically to the push-in and the pull-out of a rigid fiber in an elastic matrix. The exact solutions show that only the mode II is present and there is no oscillatory behavior of the stress and the displacement near the crack tip, but an oscillatory behavior is observed at the transition point with the stress free zone. There exists four types of singular solutions for finite crack in bounded medium, but only one in an infinite medium. To cite this article: H.D. Bui, A. Oueslati, C. R. Mecanique 332 (2004).     

Mode III effects on interface delamination

For crack growth along an interface between dissimilar materials the effect of combined modes I, II and III at the crack-tip is investigated. First, in order to highlight situations where crack growth is affected by a mode III contribution, examples of material configurations are discussed where mode III has an effect. Subsequently, the focus is on crack growth along an interface between an elastic-plastic solid and an elastic substrate. The analyses are carried out for conditions of small-scale yielding, with the fracture process at the interface represented by a cohesive zone model. Due to the mismatch of elastic properties across the interface the corresponding elastic solution has an oscillating stress singularity, and this solution is applied as boundary conditions on the outer edge of the region analyzed. For several combinations of modes I, II and III crack growth resistance curves are calculated numerically in order to determine the steady-state fracture toughness. For given values of K_I and K_II the minimum fracture toughness corresponds to K_III=0 in most of the range analyzed, but there is a range where the minimum occurs for a nonzero value of K_III.     

西安地铁二号线沿线地裂缝未来位错量估算及工程分级

地裂缝在地铁设计使用期内的最大垂直位错量是西安地铁二号线穿越地裂缝结构设计的一个十分重要的参数。本文以历史水准监测资料为基础,分析了西安地铁二号线沿线各地裂缝在不同历史阶段的活动特征与活动原因,对各地裂缝的未来活动趋势进行了预测。然后通过基于不同时间段地裂缝活动速率的最大垂直位错量估算结果的对比分析,得出了地铁设计使用期内各条地裂缝与地铁交汇点处地裂缝的最大垂直位错量,并以此为依据,将西安地铁二号线沿线地裂缝分为Ⅰ、Ⅱ、Ⅲ和Ⅳ级等4个工程级别。     

Stress state in the vicinity of an inclined elliptical defect and stress intensity factors for biaxial loading of a plate

The problem of determining the stress state of a plate with an inclined elliptical notch under biaxial loading is considered. The Kolosov-Muskhelishvili method is used to obtain an expression for the stress near the vertex of an inclined ellipse, whose particular case are expressions for the stress in the case of an inclined crack. The stress intensity factors K _I and K _II were determined experimentally by holographic interferometry in the case of extension of a plate with an inclined crack-like defect. The calculation results are compared with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 118–127, January–February, 2009.     

Über den geraden Knickstab mit begrenzter Durchbiegung

Zusammenfassung Die Untersuchung des durch ebene, starre Flächen in seiner Durchbiegung begrenzten geraden Knickstabes mit Hilfe der elementaren Biegetheorie führt auf eine interessante Durchschlagerscheinung. Unabhängig von der Art der Lagerung der Stabenden stützt sich nach Überschreitung der zugehörigen Eulerschen Knicklast der Stab an der Stelle seiner größten Durchbiegung gegen eine der Stützflächen ab. Die sich dabei ausbildende Stützkraft wächst mit zunehmender Stablast an, während sich gleichzeitig die Stabkrümmung an der Anlagestelle verringert.Erreicht die Stabkrümmung an der Anlagestelle die Krümmung der Stützfläche, dann bildet sich bei weiterer Steigerung der Stablast ein an der Stützfläche anliegendes, ungekrümmtes und daher momentenfreies Stabstück aus, an dessen Enden Einzelkräfte von der Stützfläche auf den Stab übertragen werden. Die Länge dieses Stabteiles wächst mit der Stablast solange an, bis diese die Größe der Eulerschen Knicklast des als an beiden Enden eingespannt anzusehenden geraden Stabteiles erreicht. Der nun einsetzende Knickvorgang des bis dahin an der Stützfläche anliegenden Stabteiles kann wegen der zunehmenden Knicklänge mit sich verringernder Stablast aufrecht erhalten werden. Bei unveränderter Stablast schlägt daher der mittlere Stabteil durch und kommt an der gegenüberliegenden Stützfläche zur Anlage.Bei weiterer Steigerung der Stablast kann der Stab immer als aus Teilstäben zusammengesetzt aufgefaßt werden, deren Lagerung den hier untersuchten drei Grundfällen entspricht. Es ist daher nicht zu erwarten, daß eine Weiterführung der Untersuchung noch zu grundsätzlich neuen Erkenntnissen führt.     

Two Theories of Complex Bodies, one Lagrangean, the other Kinetic, Have a Common Ground

I have found in previous works that most special models proposed to represent bodies with some type of microstructure can be classified easily under the general umbrella of a theory where each element of the continuum is thought of as a Lagrangian system. To study phenomena in ‘kinetic’ continua I proposed an apparently different approach; the outcome is again a set of evolution equations. They mimic equations familiar in continua with affine microstructure: a Cauchy’s equation and an equation of balance of tensor moment of momentum, with the addition, however, of an equation of balance for a ‘Reynolds’ tensor’, an equation which, in a sense, shifts the boundary between kinetic and thermal properties of matter. I will show that there is no contrast between the two approaches. The latter one is based on an adequate and appropriately justified expression of the kinetic energy of the continuum, comprising the trace of the quoted Reynolds’ tensor and thus importing into the mechanical energy a term usually accounted by additional heat.     

An Optimal control least-squares method for the solution of advection dispersion problems

This paper discusses the numerical solution of advection dispersion equations using an Optimal control,H ¹, least-squares formulation, associated with a quasi-Newton conjugate gradient algorithm. The suggested algorithm represents an extension of the method proposed by Bristeauxet al., for the solution of nonlinear fluid flow problems.At each time step, the discretized differential equation is transformed into an optimal control problem. This problem is then stated as an equivalent minimization one, whose objective function allows the capture of the advective behavior of the equation for high values of the P_e number.A general presentation is made of the optimization algorithm. Validation runs, for a one-dimensional example, show fairly accurate results for a wide range of Péclet and Courant numbers. Comparisons with several numerical schemes are also presented.     

Exact solution of problem of deflection of an anisotropic plate with an aperture

The exact solution of the problem of the deflection of an anisotropic plate weakened by an aperture is known only for the case in which the aperture has the shape of a circle or an ellipse [1, 2]. An exact solution has not been derived for any other aperture shapes. Approximate methods [3–6] which are widespread for the case of multiply connected anisotropic plates [7] are applied to the determination of the bending moments in an anisotropic plate near an aperture differing little from an elliptical or circular one.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 168–177, September–October, 1977.     

On a Resolvent Estimate of the Stokes Equation on an Infinite Layer Part 2, λ=: 0 Case

This paper is concerned with the standard L_p L_p estimate of solutions to the Stokes resolvent problem on an infinite layer in the case where 5 is close to zero (see eq.(1.1)). Combining this result with that in [1], we find that the Stokes operator on an infinite layer generates an analytic semigroup. As an application, we prove the local stability of some steady flows.     

Flow and heat transfer in a moving fluid over a moving flat surface

In this paper, a numerical analysis of the momentum and heat transfer of an incompressible fluid past a parallel moving sheet based on composite reference velocity U is carried out. A single set of equations has been formulated for both momentum and thermal boundary layer problems containing the following parameters: r the ratio of the free stream velocity to the composite reference velocity, σ (Prandtl number) the ratio of the momentum diffusivity of the fluid to its thermal diffusivity, and E _c (E _ck ) (Eckert number). The present study has been carried out in the domain 0 ≤ r ≤ 1. It is found that the direction of the wall shear changes in such an interval and an increase of the parameter r yields an increase in temperature.      

西安地铁二号线沿线地裂缝特征、危害及对策

地裂缝是西安地区典型的地质灾害,对该地区的各类工程建筑、交通设施、城市生命线工程及土地资源造成威胁,尤其是对拟建的西安地铁二号线的施工与安全运营影响更大。本文首先介绍了西安地裂缝的基本特征,然后阐述了西安地铁二号线穿越地裂缝的基本情况。根据实际观测数据及地表累计活动量确定了地铁二号线穿越的各条地裂缝在不同时间段的活动速率及地裂缝活动的影响范围,在此基础上提出了针对地裂缝灾害的防治措施。     

On the possible formation of a vortex flow in a supersonic inlet with three-dimensional compression

The structure of the flow in an inlet with three-dimensional compression and an adjoining channel of rectangular cross-section is experimentally investigated for the external flow parameters M_∞ = 4 and Re ≈ 52 · 10⁶ 1/m. The phenomenon of vortex generation in the air-intake and its breakdown at the channel entry, where it encounters an elevated pressure gradient, is studied     

Der Einfluß von Carbonylgruppen auf die viskosimetrische Bestimmung des Molekulargewichtes von Zellstoffen in Lösungen

Zusammenfassung Durch Anwendung von Natriumborhydridreduktion wird gezeigt, daß Carbonylgruppen, die durch Oxydation in der Bleiche oder beim längeren Lagern von Zellstoff an der Luft eingeführt werden, eine wesentliche Rolle für die Nichtübereinstimmung der DP_Nitrat- und DP_{Cuoxam, Cuoxan}-Werte spielen.Die anomalen Gruppen verursachen einerseits einen Abbau der Zellstoffe in alkalischen Lösungsmitteln und andererseits Querbindungen zwischen den Ketten in der Nitrat-Aceton-Lösung.Die Gruppen können sowohl an den niedermolekularen Hemicellulosen wie auch an der höhermolekularen reinen Cellulose nachgewiesen werden.Durch einen Vergleich zwischen der Zahl der alkalilabilen Gruppen und dem gemessenen DP_Cuoxen-Wert, wird weiter gezeigt, daß die Verteilung der Gruppen an den Ketten nicht regelmäßig ist. Wahrscheinlich liegen sie an den Hemicellulosen und an den zugänglichen Bereichen des reinen Cellulosematerials angereichert vor.Vorgetragen auf der Jahrestagung der Deutschen Rheologen vom 11.–13. Mai 1964 in Berlin-Dahlem.     

From imaging to material identification: A generalized concept of topological sensitivity

To establish a compact analytical framework for the preliminary stress-wave identification of material defects, the focus of this study is an extension of the concept of topological derivative, rooted in elastostatics and the idea of cavity nucleation, to 3D elastodynamics involving germination of solid obstacles. The main result of the proposed generalization is an expression for topological sensitivity, explicit in terms of the elastodynamic Green's function, obtained by an asymptotic expansion of a misfit-type cost functional with respect to the nucleation of a dissimilar elastic inclusion in a defect-free “reference” solid. The featured formula, consisting of an inertial-contrast monopole term and an elasticity-contrast dipole term, is shown to be applicable to a variety of reference solids (semi-infinite and infinite domains with constant or functionally graded elastic properties) for which the Green's functions are available. To deal with situations when the latter is not the case (e.g. finite reference bodies or those with pre-existing defects), an adjoint field approach is employed to derive an alternative expression for topological sensitivity that involves the contraction of two (numerically computed) elastodynamic states. A set of numerical results is included to demonstrate the potential of generalized topological derivative as an efficient tool for exposing not only the geometry, but also material characteristics of subsurface material defects through a local, point-wise identification of “optimal” inclusion properties that minimize the topological sensitivity at sampling location. Beyond the realm of non-invasive characterization of engineered materials, the proposed developments may be relevant to medical diagnosis and in particular to breast cancer detection where focused ultrasound waves show a promise of superseding manual palpation.     

Analytical approach to bonded repair of elliptical dent, corrosion grind-out, and cut-out

The problem of an isotropic sheet with an internal elliptical dent, corrosion grind-out, or cut-out repaired with an elliptical bonded patch is analyzed, following the similar two-stage analysis originally proposed by Rose [International Journal of Solid and Structures 17 (1981) 827; in: Bakers, Jones (Eds.), Bonded Repair of Aircraft Structures, Martinus Nijhoff, Dordrecht, 1988, p. 77] for a crack patching problem. For simplicity, the bending effect is ignored in the analysis. In the first stage, an infinite sheet reinforced by an elliptical patch under a prescribed far-field stress is analyzed using the inclusion analogy, without considering the dent, grind-out or cut-out. The constant stresses inside the patched area (σ_0ij) are then calculated and later used as the far-field boundary conditions for the second (stage II) problem. In the second stage, the patch is assumed to be infinite and an integral part of the sheet. Stage II analysis then involves solving a problem of an infinite patched sheet containing a circular dent, grind-out, or cut-out under far-field stresses σ_0ij. The latter problem is also solved using the inclusion analogy. Because the patch in a typical design is much larger than the damage area, the solutions of the first and second problems are approximately the same as the solutions of the original problem inside and outside the patched area, respectively.     

Solving axisymmetric dynamic problems for reinforced shells of revolution on an elastic foundation

The dynamic behavior of reinforced shells of revolution in an elastic medium is modeled. Pasternak’s model is used. A problem of vibration of discretely reinforced shells of revolution is formulated and a numerical algorithm is developed to solve it. Results from an analysis of the dynamic behavior of a reinforced spherical shell on an elastic foundation are presented as an example Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 99–106, February 2009.     

Green’s functions for multi-phase isotropic laminated plates

This work develops a series of Green’s functions for multi-phase Kirchhoff isotropic laminated plates. First, we derive the Green’s functions for a composite laminated plate composed of two bonded dissimilar isotropic laminated semi-infinite plates. Second, the obtained results for bimaterials are judiciously applied to obtain the Green’s function solution for a circular elastic inclusion embedded in an infinite isotropic laminated plate. Third, Green’s functions for a composite space composed of an arbitrary number of wedges of different isotropic laminated plates are derived. Finally, we derive Green’s functions for a laminated plate with an elliptical and a parabolic boundary, respectively.     

Uniform difference scheme for a singularly perturbed linear 2nd order hyperbolic problem with zeroth order reduced equation

In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.