Fluids with microstretch

Summary In this paper fluids with stretch are introduced as a subclass of simple microfluids. In these fluids the local fluid elements are allowed to undergo only a uniform stretch, or contraction without microrotation. These fluids might find applications especially inNewtonian fluids with bar-like polymeric additives. The field equations are obtained, initial and boundary conditions discussed and the thermodynamics of such fluids is studied. The solution of the problem ofPoiseuille flow between two parallel plates is given. Microstretch fluids with constrained microrotation are also discussed briefly as another subclass of simple microfluids.     

Singular integral inequalities with several nonlinearities and integral equations with singular kernels

We deal with an integral inequality with a power nonlinearity on its left-hand side, n nonlinearities on its right-hand side, and weakly singular kernels. The obtained result is an extension of the Bihari, Henry, Pachpatte, and Pinto inequalities and results obtained by the author. Using these results, we prove sufficient conditions for the existence of global solutions of some nonlinear Volterra integral equations with singular kernels and n nonlinearities. Published in Neliniini Kolyvannya, Vol. 11, No. 1, pp. 71–80, January–March, 2007.     

Migration of salts with the leaching of soils with piecewise-homogeneous salinization

The article discusses the one-dimensional problem of the leaching of a soil with piecewise-homogeneous initial salinization under conditions of a movable wetting front. Depending on the character of the salinization and the water-physical properties of the soil at the moving boundary, there are given either the values of the sought function or of its derivative with respect to the spatial variable. The solution of the problem is represented as the superposition of solutions of an auxiliary process modelling the process of the leaching of a soil with homogeneous salinization with the presence of an upper desalinated layer. A numerical example is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 76–81, May–June, 1977.     

Anisotropic yield functions with plastic-strain-induced anisotropy

In most anisotropic yield functions, the stress exponent, M, associated with the shape of the yield surface is usually independent of plastic-strain accumulation. This does not allow for different work-hardening characteristics under various strain states, as has been observed in aluminum alloys. Assuming coefficients characterizing anisotropy do not change with plastic deformation, the M value should vary with plastic strain, relaxing the isotropic hardening assumption. To verify this, plane-strain tests along with numerical analysis were carried out with 2008-T4 aluminium and 70/30 brass. The effective stress and effective plastic-strain curve assuming plane strain and plane stress was fit to the corresponding stress-strain data obtained in uniaxial tension. This was done by allowing M value to vary with effective plastic-strain. Hill's 1979 (case iv),Hosford's 1979 and Barlat's 1991 (6 component) yield functions were evaluated. Results showed that, with all the yield functions tested, the aluminum exhibited substantial variation of M value especially at larger strains while the brass showed minor change. Relevant numerical analysis indicated that, even though all the yield functions showed noticeable changes of M as strain increases in order for the plane-strain curve to match with the uniaxial curve, this variation of M will not affect much to the prediction with Hosford's and Barlat's yield functions, of which the typically valid M is much higher than that of Hill's. FEM simulation of plane-strain sheet forming with 2008-T4 aluminium alloy verified that implementation of varying M-value with Hill's yield function led to better agreement with experimental measurements, while the variation of M with Barlat's yield function exhibited little influence on the strain prediction.     

Gas ejector with nozzle perforated with longitudinal slots

We consider the possibility of altering the choking conditions of a supersonic gas ejector by installing a cylindrical wall perforated by longitudinal slots in the initial segment of the mixing chamber; this wall is an extension of the high-pressure nozzle. A diagram of the ejector and results of an experimental study of a series of ejectors of various permeabilities for the perforated wall are presented. A comparison is made with the classical ejector, which shows that in several regimes the ejector characteristics may be improved several fold.     

On Second-Order Differentiability with Respect to Parameters for Differential Equations with State-Dependent Delays

In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the $C$ -norm on the state-space, assuming that the state-dependent time lag function is piecewise strictly monotone.     

Approximate models of salt transfer with washings of soils with water-impermeable base

On the basis of an approximate model of filtration with drainage washings of a soil layer with a water-impermeable base [1], shown schematically in Fig. 1, an investigation is made of the desalinization process of soils for several forms of the equations of salt transfer between the moving solution and the fixed phase. Neglect of the external diffusion makes it possible to reduce the investigation to the solution of one-dimensional boundary-value problems, characterizing salt transfer along fixed streamlines. Analogous problems were discussed in [2] with application to the one-dimensional filtration of wash waters in a dry soil.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 44–51, January–February, 1978.The author thanks V. N. Émikh and V. I. Pen'kovskii for their repeated and useful evaluations of the work.     

Percolation with a limiting gradient in a medium with random inhomogeneities

The coverage of a medium by percolation and the effective permeability of a medium with stagnant zones are determined. It is shown that effective permeability is a function of external conditions, particularly the average pressure gradient. Three-, two-, and one-dimensional flows are discussed. The theory of overshoots of random functions and fields beyond a prescribed level [1, 2] is used for the investigation. Overshoots of elements of the percolation field in media with random inhomogeneities are studied. Overshoots of energy being dissipated in a volume are discussed in particular; this permits an approximate determination of the coverage of an inhomogeneous porous medium by migration during percolation with a limiting gradient, i.e., in the case of formation of stagnant zones chaotically disseminated in the flow region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 159–165, September–October, 1970.The authors thank V. M. Entov for discussing the article and useful comments.     

Dynamic behaviour of cylinder with spring and concentrated mass collided with rigid body

Summary The Dynamic behaviour of a cylinder is investigated for the case where it collides with a rigid body with constant velocity. Spring and concentrated mass are attached to both ends of the cylinder. The relationships between the dimensions of cylinder and spring and the maximum values of dynamic stresses are obtained. Dynamic behaviour of the spring is also taken into consideration. The fundamental equations of oscillation are solved by the Laplace transformation method. From the results of theoretical analysis, it becames evident that impulsive stresses are damped considerably by the spring.

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Übersicht Es wird das dynamische Verhalten eines Zylinders untersucht, der mit konstanter Geschwindigkeit mit einem starren Körper zusammenstößt. An beiden Enden des Zylinders sind Federn und konzentrierte Massen angebracht. Für diesen Fall werden die maximalen Beanspruchungen in Abhängigkeit von den Abmessungen des Zylinders und der Feder abgeleitet. Dabei wird auch das dynamische Verhalten der Feder berücksichtigt. Die Schwingungsgleichungen werden mit Hilfe der Laplace-Transformation gelöst. Die Ergebnisse zeigen, daß die Stoßbeanspruchungen durch die Federn erheblich reduziert werden.

     

Use of flows with straight sonic line in nozzles with corners

The optimal scheme of a Laval nozzle is discussed. In the case of a profiled nozzle with a corner it is possible to use in the region of mixed flow both flows of general form with curvilinear sonic line as well as the special case when the sonic line is straight. It is shown that the latter alternative is preferable: when the supersonic part of the profile is determined by the simple wave method, the velocity at the wall increases monotonically and the flow does not contain shock waves. In contrast, in nozzles with curvilinear sonic line, a section in which the velocity decreases is formed immediately behind the corner, which can lead to boundary layer separation. In addition, for values of the supersonic velocity at the nozzle exit near the velocity of sound it is proved that the characteristics of the simple wave intersect in the flow region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 168–170, January–February, 1981.     

Vibrations of plates with initial geometrical periodical imperfections interacting with a periodic elastic foundation

Summary  The aim of this contribution is to formulate an engineering theory describing the effect of periodic structure of the elastic foundation on the dynamic behaviour of a plate with geometrical periodical imperfections, Fig. 1. It is shown that the obtained solutions depend on the structure length parameter l of the elastic foundation and the wave length of imperfections. The general results are illustrated by an example and compared with the known theories of orthotropic plates. Received 7 February 1999; accepted for publication 6 October 1999     

Some properties of gases with vibrational relaxation when viewed as materials with memory

Summary In recent years there has been developed a general thermodynamics of materials for which the stress, temperature, and energy depend on the histories of the strain and another variable, such as the entropy. Here we discuss the compatibility of that thermodynamical theory with a special theory of mechanical dissipation which has been successfully used in physical gas dynamics: the theory of gases with vibrational relaxation. Granting, without detailed study, certain technical points involving the uniqueness and stability of solutions of a class of non-linear integral equations, we observe that the theory of relaxing gases can be imbedded in the framework of the thermodynamics of materials with memory, provided only that we identify the temperature of the thermodynamical theory with the translational or (activemode) temperature of the internal-relaxation theory.We conclude our discussion with a report of a calculation we have made of the isentropic, pressure-volume, relaxation function exhibited by a gas with vibrational relaxation when regarded as a linearly viscoelastic material.

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Sommario Si è ultimamente sviluppata una termodinamica generale dei materiali per i quali la tensione, la temperatura e l'energia dipendono dalla storia passata dello strain e da un'altra variabile, come l'entropia.Studiamo qui la compatibilità di questa teoria termodinamica con una teoria speciale di dissipazione meccanica, che è stata applicata con successo nella dinamica dei gas reali: la teoria dei gas con rilassamento vibrazionale.Accettati, senza un esame dettagliato, certi punti tecnici che comportano l'unicità e la stabilità delle soluzioni di una classe di equazioni integrali non lineari, osserviamo che la teoria dei gas con rilassamento vibrazionale può essere inquadrata nella struttura della termodinamica dei materiali con memoria, a patto che la temperatura della teoria termodinamica venga identificata con la temperatura di traslazione o di modo attivo della teoria del rilassamento interno.Concludiamo la nostra discussione riportando i risultati ottenuti nella derivazione della funzione che descrive il rilassamento isoentropico di pressione che segue una variazione di volume rivelata da un gas con rilassamento vibrazionale quando è considerato come materiale visco-elastico lineare.

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This research was supported in part by the U. S. Air Force Office of Scientific Research and the U. S. Office of Naval Research.     

Interaction of continuous-spectrum waves with each other and with discrete-spectrum waves

The nonlinear problem of the evolution of an initial perturbation in Couette flow is solved in the quadratic approximation and it is shown that the energy of the initial perturbation is transmitted to the main flow so that its profile is somewhat modified. The evolution of the initial perturbation in a fluid with a very simple model flow profile which, in addition to continuous-spectrum waves, also admits the existence of a single neutral mode of the discrete spectrum is then investigated. It is shown that as a result of the linear resonant interaction of the discrete-spectrum and continuous-spectrum waves disturbances that grow linearly with time may be formed. A flow that does not contain exponentially growing modes will be unstable with respect to certain initial disturbances; this instability is called algebraic [6, 7]. A physical interpretation of this effect is given. From this interpretation it is clear that algebraic instability is possible in a fluid with flow profiles of a more general type, in which there are neutral or weakly damped discrete-spectrum modes having a critical layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 116–123, July–August, 1989.The author is grateful to G. I. Barenblatt, S. Ya. Gertsenshtein, M. A. Mironov, S. A. Rybak, O. S. Ryzhov, and E. D. Terent'ev for their interest and useful comments.     

Experimental study of massive wall systems with fins attached on the heated wall and with glazing

 Natural convection, radiation and conduction heat transfer in passive solar massive wall systems with fins attached to the heated surface and with glazing is experimentally studied. The system was 0.78 m high, 0.40 m wide and 0.10 m thick concrete wall with a glazing placed at 0.0265 m from the surface. It had 0.025 m long, 0.004 m thick horizontal fins made as an integral part of the massive wall and placed at 0.01 m intervals. A heat source was used to impose a constant heat flux which could be varied from about 200–800 W/m². Temperatures at various points and heat flux by convection at the back were measured. Using various assumptions, the systems was also analyzed theoretically. The results show that about 40% of the heat flux imposed on the finned surface goes through the system and is dissipated at the back. Received on 7 September 2000     

Heat and mass transfer with phase change in a rectangular enclosure packed with unsaturated porous material

The paper has presented a seven-field mathematical model with ten variables to describe the simultaneous heat and mass transfer with phase change in the unsaturated porous medium that is enclosed in a rectangular enclosure. Both liquid and vapor migration in the porous matrix are evaluated at the same time, and gaseous bulk motion is simulated numerically. The numerical results are discussed with emphasis on the effect of evaporation and condensation of R113 in the vertical enclosure, which may have an application in the room passive heating for the buildings in winter. As solar energy or low-grade waste heat could be used if the enclosure is adequately designed to transfer heat from the outside to the room of the building, the present method may be propitious to the energy conservation. Aimed to this purpose, the heat transfer character of the enclosure is analyzed for the change of Nu number with different Ra number and Da number.     

Composite shells with interlaminar imperfections

Summary In this contribution the effect of interlaminar initial imperfections on a composite shell behavior is investigated. The constitutive equations for shells with initial interlaminar bonding imperfections are obtained.

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Verbundstoffschalen mit Zwischenschichtdefekten

Übersicht In diesem Beitrag wird der Einfluß von anfänglichen Zwischenschichtdefekten auf das Verhalten einer Verbundstoffschale untersucht und die Materialgesetze für solche Schalen werden aufgestellt.

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The main theses of this paper have been presented on EUROMECH 292, Sept. 1992     

Integro-Differential Inclusions with Hukuhara Derivative

For an integro-differential inclusion with Hukuhara derivative, we introduce the notion of quasisolution and present conditions under which the set of quasisolutions coincides with the set of ordinary solutions. We also prove theorems on the relaxation of ordinary solutions and the compactness of the set of these solutions.__________Translated from Neliniini Kolyvannya, Vol. 8, No. 1, pp. 80–88, January–March, 2005.     

Soil collapse computations with finite elements

Summary The elastic-plastic finite element method is reviewed with a view to predict collapse loads of geotechnical constructions. The basic technique of using an incremental-iterative approach with a constant stiffness matrix is well-known, but we fill a gap by proving that the procedure converges not only for small steps but also for large load increments. Here restriction is made to associated plasticity, as uniqueness of solution is not ensured for non-associated plasticity problems. Differences between associated and nonassociated problems are illustrated by showing results of numerical analyses. Finally, a number of practical aspects associated with the method are discussed.

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Finite-Element-Berechnungen des Versagens von Böden

Übersicht Im Hinblick auf die Vorhersage der Versagenlasten von Erdbauten wird ein Überblick über die elastisch-plastische Finite-Element-Methode gegeben. Das grundlegende Verfahren mit inkrementelliterativem Vorgehen mit einer konstanten Steifigkeitsmatrix ist wohlbekannt. Durch den Beweis, daß das Verfahren nicht nur bei kleinen Schrittweiten, sondern auch bei großen Laststufen konvergiert, werden jedoch neuartige Erkenntnisse vorgestellt. Hierbei muß einschränkend assoziierte Plastizität gelten, da bei nicht-assoziierter Plastizität die Eindeutigkeit von Lösungen nicht gewährleistet ist. Anhand von numerischen Ergebnissen werden Unterschiede zwischen Aufgabenstellungen mit assoziierter und nichtassoziierter Plastizität aufgezeigt. Schließlich werden auch noch praktische Gesichtspunkte des Verfahrens erörtert.

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Presented at the workshop on Limit Analysis and Bifurcation Theory, held at the University of Karlsruhe (FRG), February 22–25, 1988     

Dynamics of a rigid body with an ellipsoidal cavity filled with viscous fluid

We revisit the approach proposed by F.L.  Chernousko to modeling the dynamics of a rigid body with a cavity entirely filled with a highly viscous fluid. Within the approach, a finite-dimensional model of the body+fluid system is offered and the influence of the fluid is represented as a special torque acting upon the body with solidified fluid. Our aim is to develop further and expand a few technical aspects of the Chernousko model. In particular, we offer a coordinate-free form for some essential formulas and consider the case of constrained dynamics. To illustrate the results obtained we explore the motion of a physical pendulum with a fluid-filled cavity on a rotating platform.