Stress concentration near an inhomogeneity and experimental clarification of the couple-stress effect

Following the fundamental papers [1–3], many authors have recently exerted considerable efforts to develop a new mechanics of the microcontinuum in which displacements of microelements are taken into account. To apply these theories it is required to determine a sufficiently large quantity of new elastic constants. The effects which appear because of taking account of the microelement displacements have been examined theoretically by a number of authors. However, there is quite little experimental work in which the effect of this accounting would be explained and new elastic constants would be determined in materials [4–6]. The purpose of the present paper is to clarify the effect of the influence of couple stresses on stress concentration near an inhomogeneity in the case of plane strain by the experimental method of photoelasticity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 142–144, July–August, 1976.     

Interaction between the boundary layer and a supersonic flow when part of the wall is rapidly heated

There have been many theoretical studies of aspects of the unsteady interaction of an exterior inviscid flow with a boundary layer [1–9]. The mathematical flow models obtained in these studies by the method of matched asymptotic expansions describe a wide range of phenomena observed experimentally. These include boundary layer separation near the hinge of a flap, the flow in the neighborhood of the trailing edge of an oscillating airfoil [1–2], and the development and propagation of perturbations in a boundary layer excited by an oscillating wall or some other way [3–5]. The present paper studies the interaction of an unsteady boundary layer with a supersonic flow when a small part of the surface of a body in the flow is rapidly heated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 66–70, January–February, 1984.     

Principles of the mechanics of brittle fracture of materials with initial stresses

Conclusions for Fracture Criteria 1. With an increase in compressive stresses along cracks in materials with initial stresses, there is a reduction in the breaking loads corresponding to brittle fracture for normal-rupture and transverse-shear cracks. 2. When the initial stresses reach values corresponding to surface instability of the half-space (within the framework of plane strain), the breaking loads vanish for normal-rupture and transverse-shear cracks.The mechanical phenomenon corresponding to the second conclusion has the following explanation. Due to the use of the linearized theory at the indicated values of the initial stresses, a body with a crack is in a state of neutral equilibrium. In connection with this, it is not necessary to apply an additional finite load in order to remove the body from this state.Several other results on the mechanics of brittle fracture of materials with initial stresses have been published in studies mentioned in the survey [1].Corresponds to the text of a paper presented at the 6th International Conference on Fracture (New Delhi, India, 1984).Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 23, No. 10, pp. 34–39, October, 1987.     

Fracture mechanics of materials under compression along cracks (survey). Structural materials

Conclusions The results elucidated in this paper and in [A. N. Guz' and V. M. Nazarenko, Fracture mechanics of materials under compression along cracks (Survey). Highly-elastic material, Prikl. Mekh.,25, No. 9, 3–32 (1989)] of investigations on compression of materials along defects of crack type are exact since they are obtained within the framework of rigorous three-dimensional linearized formulations. Let us note that the fact that the mentioned result are standards for approximate approaches is of independent value.The investigations performed whose survey is represented above should be considered the beginning of a study of problems of material fracture under compression along cracks in a rigorous formulation (within the framework of the linearized mechanics of deformable bodies).The present paper continues the survey [A. N. Guz' and V. M. Nazarenko, Fracture mechanics of materials under compression along cracks (survey). Highly-elastic materials, Prikl. Mekh.,25, No. 9, 3–32 (1989)] of investigations of questions for fracture under compression along cracks as applied to extensively utilized structural materials, composites with elastic components and elastic-plastic bodies. In the interest of convenience in the exposition, a single system of numbering the sections and formulas, figures, tables, as well as the bibliographic references is used (the references in this paper are given in conformity with the bibliographic listing in the above-mentioned citation).Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 10, pp. 3–19, October, 1989.     

Evolution of three-dimensional gravitationally warped waves during the movement of a pressure zone of variable intensity

Three-dimensional, unestablished, gravitationally warped waves arising due to the motion of a harmonically time-varying pressure zone over a solid, thin plate floating on the surface of a homogeneous liquid of finite depth have been studied in the linear formulation. In the absence of a plate, three-dimensional waves are generated by the movement of a region of periodic perturbations, where established waves have been studied in [1, 2], and unestablished waves have been investigated in [3–5]. The evolution of three-dimensional, gravitationally warped waves formed during the motion of a constant load over a plate has been considered in [6].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 54–60, September–October, 1986.     

Equations for the migration of natural gases in porous media

Equations are given for the equilibrium and nonequilibrium migration of natural gases in variable and invariable porous media. In numerous works [1–4], migration has been considered principally in geological-geochemical terms, the qualitative side of the phenomenon being mainly investigated; its physicomathematical aspects have been inadequately studied [5, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 152–158, September–October, 1971.     

Nonlinear evolution of waves in forced decaying capillary jets

The investigation of nonlinear waves in decaying capillary jets is of great interest both from the point of view of nonlinear wave processes in media and for practical applications associated with the generation and propagation of flows of monodisperse droplets [1–4]. The formation and dynamics of satellite droplets are particularly important in the study of the decay of thin capillary jets [5–8]. Investigation of the conditions of formation of satellites open up important prospects for the preparation of monodisperse microscopic granules with diameters appreciably less than the diameter of the original jet. This is of great importance in modern technologies based on the use of materials in disperse form [9–13]. The present paper is devoted to the investigation of nonlinear waves in decaying capillary jets.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 54–60, May–June, 1993.     

Self-similar problems of propagation of an extended hydrofracture in a permeable medium

The propagation of an extended hydrofracture in a permeable elastic medium under the influence of an injected viscous fluid is considered within the framework of the model proposed in [1, 2]. It is assumed that the motion of the fluid in the fracture is turbulent. The flow of the fluid in the porous medium is described by the filtration equation. In the quasisteady approximation and for locally one-dimensional leakage [3] new self-similarity solutions of the problem of the hydraulic fracture of a permeable reservoir with an exponential self-similar variable are obtained for plane and axial symmetry. The solution of this two-dimensional evolution problem is reduced to the integration of a one-dimensional integral equation. The asymptotic behavior of the solution near the well and the tip of the fracture is analyzed. The difficulties of using the quasisteady approximation for solving problems of the hydraulic fracture of permeable reservoirs are discussed. Other similarity solutions of the problem of the propagation of plane hydrofractures in the locally one-dimensional leakage approximation were considered in [3, 4] and for leakage constant along the surface of the fracture in [5–7].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 91–101, March–April, 1992.     

Slip-band propagation at the tip of an edge crack during plastic deformation

Experimental investigations indicate that in many cases under plane deformation, the initial plastic strains in the vicinity of a separation crack are localized along two narrow bands at an angle of approximately 45° to the line of the crack [9]. Methods of solving elastoplastic problems in which these plasticity bands (slip bands) are modeled by fracture lines of tangential displacements have been developed in fracture mechanics; in that case, tangential stresses equal to the yield point in shear _y are assigned to these lines [2]. The problem of the development of slip bands then reduces to solution of the plane problem of the theory of elasticity for a branched notch; in that case, the dimensions and orientation of lateral branching corresponding to plasticity bands are determined during the solution. A series of results [1, 5, 6, 8, 10–16] for an infinite plane with a separation crack, where the slip bands are located symmetrical bout the line of the crack, have been obtained in this segment. In our study, we solve the plane elastoplastic problem (plane deformation) for a half space with an arbitrary oriented edge crack under an arbitrary load. Numerical results are obtained for a constant pressure on the crack or tensile forces at infinity.Physicomechanical Institute, Ukraine, Academy of Sciences of L'vov. Translated from Prikladnaya Mekhanika, Vol. 30, No. 1, pp. 56–61, January, 1994.     

Shock waves in flow of an incompressible liquid in collapsing pipes: Application to large blood vessels

Flow of a liquid in collapsing pipes is of great interest for problems in the mechanics of blood circulation, since collapse can take place in many blood vessels. This effect forms the basis for a large number of diagnostic and therapeutic methods, and also for methods of investigating the system of blood circulation. Consequently the mechanics of collapsing pipes has been studied intensively of late [1], but the available studies are far from exhausting the theoretical or the applied aspects of the problem. This applies also to the study of discontinuous solutions such as shock waves which describe steep fronts of opening or narrowing of a blood vessel. The most studied phenomenon is unsteady flow caused by change in the external pressure [2]. There is an explanation in [3–6] of the effect on the process of formation of discontinuities in collapsing pipes due to such factors as friction on the wall, distributed lateral outflow, the presence of a stagnant zone in the flow, and viscoelasticity of the wall. The origin of some acoustic phenomena in the arteries is connected by some with the propagation of discontinuities; these phenomena include Korotkov sounds, used in the determination of the arterial pressure of blood [1, 7]. The present study considers quasione-dimensional flow of a viscous incompressible liquid in a collapsing pipe of finite length and made of a nonlinear viscoelastic material; there is a study of the conditions in which discontinuities arise in such systems, and an investigation of the structure of shock waves with allowance for the effect of the surrounding tissues.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 44–50, November–December, 1987.     

Supersonic flow over elongated blunt bodies with a cross section of elliptical shape

Up to now computational algorithms have been developed for, and systematic studies have been made of, supersonic flow over axisymmetric bodies both by a stream of ideal gas and by an air stream with equilibrium and nonequilibrium physicochemical transformations [1–6]. Conical flows around bodies having cross sections of different shapes and in a wide range of angles of attack have been studied in detail [7–11]. With the further development of numerical methods the next problem has become the analysis of supersonic flow over blunt bodies of large elongation having cross sections of sufficiently arbitrary shape. The effects of essentially three-dimensional flow (without planes of symmetry) over bodies whose cross sections represent ellipses with a constant or variable ratio of axes along the length of the body are discussed in the present paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 155–159, November–December, 1976.     

ON PROBLEMS OF FRACTURE OF MATERIALS IN COMPRESSION ALONG TWO INTERNAL PARALLEL CRACKS

I.Relati0ns0fN0n-LinearThe0ryandDerivati0nofLinearizedRelati0nsinCoordinates0fN0n.DeformedStateNotationsareintroduced:x,-x'-Lagrangiancoordinateswhichinthenatural(non-def0rmed)statecoincidewithCartesiancoordinateswith0rthse,.Coordinatesx,willbeassumedtobe…     

Determination of the edge-effect zone with the help of the holographic MoirÉ method

In parts made from materials with a distinct anisotropy, it is necessary to take into account edge effects which, as is well known [1], can slowly decay away from the edge. The size of the edge-effect zone in composite materials has been estimated many times and, in addition, the problem has been solved theoretically and experimentally [1–3]. In this work such estimates are made with the help of the method of holographic interferometry.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 132–135, September–October, 1986.     

Dynamic stability analysis and DQM for beams with variable cross-section

The present paper deals with the dynamic behaviour of a clamped beam subjected to a sub-tangential follower force at the free end. The aim of this work is to obtain the frequency–axial load relationship for a beam with a variable circular cross-section. In this way, one can identify both divergence critical loads – where the frequency goes to zero – and the flutter critical load – in correspondence with two frequencies coalescence. The numerical approach adopted for solving the partial differential equation of motion is the differential quadrature method (henceforth DQM). This method was proposed by Bellmann and Casti [Bellmann, R.E., Casti, J., 1971. Differential quadrature and long-term integration. J. Math. Anal. 34, 235–238] and has been employed recently in the solution of solid mechanics problems by Bert and Malik [Bert, C.W., Malik, M., 1996. Differential quadrature method in computational mechanics: a review. Appl. Mech. Rev., ASME, 49 (1), 1–28] and Chen et al. [Chen, W., Stritz, A.G., Bert, C.W., 1997. A new approach to the differential quadrature method for fourth-order equations. Int. J. Numer. Method Eng. 40, 1941–1956]. More precisely, a modified version of this method has been used, as proposed by De Rosa and Franciosi [De Rosa, M.A., Franciosi, C., 1998a. On natural boundary conditions and DQM. Mech. Res. Commun. 25 (3), 279–286; De Rosa, M.A., Franciosi, C., 1998b. Non classical boundary conditions and DQM. J. Sound Vibrat. 212(4), 743–748] to satisfy all the boundary conditions.Some frequencies–axial loads relationships are reported in order to show the influence of tapering on the critical loads.     

Comparative analysis of methods of areal flooding of stratified reservoirs of anomalous oil

When anomalous oils in productive reservoirs are displaced by water [1], residual undisplaced oil remains [2, 3]. For calculating the volume of the unrecovered oil, most studies have been of homogeneous reservoirs [4–8]. In the present paper, the residual volume is assessed using an inhomogeneous-stratified-model. The inhomogeneity of the strata is described by the random distributions of Weibull or Pearson (gamma-distribution), which are characteristic of oilfields possessing anomalous properties (see, for example, [9]). A parametric study is made of four known schemes of areal flooding: two-point (straight line), five-, seven-, and nine-point [10]. The obtained estimates of the volume of the residual oil can be used for rational selection of the parameters for exploiting anomalous oilfields.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 121–126, May–June, 1985.     

Model of a fracture as an emitter of elastic vibrations

During the past two decades a new method has begun to be intensively developed for the investigation of fracture processes which is based on recording the mechanical vibrations generated by the defects of a medium [1]. The new method's problems include: extraction of a useful signal from the extraneous noises, identification of the type of defect, determination of its characteristic dimensions, and an estimate of the danger of the situation which has developed. The solution of the problems indicated has great meaning in such practical applications as nondestructive quality control and the engineering diagnostics of materials and manufactured goods. Therefore, the investigation of the spectrum of the signals produced by the formation of macroscopic fractures, such as the terminal and, consequently, most dangerous phase of fracture, is of great interest. The kinematical characteristics of a fracture as an emitter of elastic vibrations are formulated in this paper. The spatial and time spectra of the dynamical motions caused by the appearance of a growing fracture in a thin plate are discussed. Relationships are derived between the spectral characteristics of propagating disturbances and the parameters of the fracture.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 160–166, March–April, 1976.The author thanks L. I. Slepyan for valuable discussion and attention to this research.     

Oscillation of flat layered shells with local elastic supports

The study of oscillation in thin-walled construction elements on elastic supports is of great practical interest. Various aspects of the problems of mechanics arising in this regard have been considered by many authors, especially in recent years. The authors of [4, 8, 13, 14, 17–19, 22] have presented voluminous graphical and tabular material for solid beams with elastic supports and for rectangular plates supported on rigid point supports along the edges and in the inner area; moreover, the authors of [22] present results relating to linear supports and circular plates, while in [5, 13, 18, and 22] the results reported have to do with the forms of the fundamental oscillation. In [5] the elastic bond is modelled by means of a Vinkperovskii foundation with a discontinuous bed coefficient. Cylindrical shells are examined in [1, 6], while in [21], for a spherical shell with elastic supports, an analytical solution is constructed. The authors of [23, 24] investigate the effect of an attached mass and a linear support for a circular and a rectangular plate, and a comparison with experimental data is made for a lower frequency. The close connection between the problems in question with those involving oscillation of shells with attached masses is reflected in [3, 7, 11, 16]. Analysis of the results obtained in the works mentioned above and in others shows that, unlike the case of beam systems, numerical results for plates and shells are significantly more difficult to obtain. Therefore, in the overwhelming majority of publications, thin plates and shells are examined, while to describe the process of their deformation classical models are used; here the supports, as a rule, are assumed to be absolutely rigid. The oscillation of anisotropic and, in particular, layered construction elements on elastic supports with further consideration of the bending rigidity of the latter clearly has not been studied sufficiently, which makes further research in this field timely. The present article examines layered, flat, orthotropic shells on a rectilinear layout, for which a solution of the static problem has been obtained previously [9, 10]. The basic assumptions of the computation method, developed for calculating the stress-deformed state (SDS) arising during driven oscillation of these objects far from the resonance points, as well as for determining the fundamental oscillation frequencies (FOF), are presented. Unlike traditional approaches, this method realizes the possibility of calculating, along with the normal reactions of elastic supports, reactive moments and tangential forces; in describing the movement of the system, the relations of the improved theory of shells are used [2].S. P. Timoshenko Institute of Mechanics of the Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 55–60, February, 1994.     

A class of composite loads for an inelastic material

In solid mechanics a considerable role is played by flow, which in a certain sense is the simplest form. In hydrodynamics this relates to Couette flow between parallel plates and coaxial cylinders [1], in solid mechanics it relates to deformation of thin-walled tubular specimens [2], and in the mechanics of loose materials it relates to uniform shear of the material [3]. Construction of sufficiently general phenomenological models assumes an experimental study of different loading paths, including composite loading paths when the stress tensor axes are turned relative to the volume of the material. Composite loading of metals, rocks, and other solids may be realized by a combination of internal pressure, torsion, and tension for tubular specimens. However, for a broad class of materials this classic procedure is either markedly complicated (e.g., for soils [4]), or it is generally inapplicable. It is of interest to find a class of composite loads which on one hand might relate to the simplest, and on the other might be used in order to test loose, viscoelastoplastic, and other similar materials.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 150–158, September–October, 1986.     

Conservation of the resultant force vector in the plane of the angle of attack for slender star-shaped bodies in supersonic flows

At high supersonic flight speeds bodies with a star-shaped transverse and power-law longitudinal contour are optimal from the standpoint of wave drag [1–3]. In most of the subsequent experimental [4–6] and theoretical [6–9] studies only conical star-shaped bodies have been considered. For these bodies in certain flow regimes ascent of the Ferri point has been noted [10]. In [11] the boundary-value problem for elongated star-shaped bodies with a power-law longitudinal contour was solved for the case of supersonic flow. The present paper deals with the flow past these bodies at an angle of attack. It is found that for arbitrary star-shaped bodies with any longitudinal (in particular, conical) profile the aerodynamic forces can be reduced to a wave drag and a lift force, the lateral force on these bodies being equal to zero for any position of the transverse contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–141, November–December, 1989.     

Influence of an elastic plate on the motion of an inhomogenfous fluid

The influence of a thin elastic isotropic plate on the wave motion of an inhomogeneous fluid originating under the effect of external periodic perturbations is investigated. The fluid density increases constantly with depth. Analogous problems have been examined for an inhomogeneous fluid without a plate in [1, 2] and with a plate on the surface of a homogeneous fluid in [3–5].Sevastopol'. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 60–67, January–February, 1972.