Torsional oscillations of a circular stamp on an elastic layer with a cylindrical cavity

The problem of torsional oscillations of a stamp that is linked with an elastic stratum which contains a cylindrical cavity is considered. The problem is formulated in the form of conjugate integral equations that are related to the integral Weber transforms. The conjugate equations are reduced to an equivalent Fredholm equation of the second kind.Translated from Dinamicheskie Sistemy, No. 9, pp. 54–59, 1990.     

Vertical vibration of a circular stamp on an elastic-porous half-space with saturation fluid

A specific problem concerning the vertical vibrating response of a composite layer (elastic-porous and saturation fluid) under rigid circular stamp is studied. The motion of the medium is governed byBiot’s dynamic potential equations and the problem is solved by the method of Fourier-Bessel transformation. Formulae are obtained for the vertical displacement of the rigid phase. Graphs are presented for the amplitude of vibration.     

Boundary layer growth on a magnetised circular cylinder

Résumé Dans le problème considéré, un cylindre parfaitement conducteur et magnetisé est mis en mouvement par impulsion dans un fluide visqueux incompressible et non-conducteur. On suppose de même qu'il y a un champ uniforme et magnétique imposé sur tout le champ d'écoulement. On demontre que la force du champ uniforme et magnétique et l'amplitude du champ normal initial à la surface solide jouent un rôle important dans la croissance de la couche limite sur le cylindre.     

Axisymmetric indentation of a circular stamp with adhesion into an elastic half-space with a spherical cavity

On the basis of the expansion formulas of the vector solutions of the Lame equations in cylindrical and spherical coordinates, the problem of a circular stamp is formulated in the form of an integro-algebraic system of equations. By the method of orthogonal polynomials, it is reduced to a collection of infinite systems of linear algebraic equations, for which the method of reduction is justified. Formulas for the normal and tangential stresses under the stamp are given.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 14–20, 1987.     

Boundary layer growth on a circular cylinder in a semi-infinite fluid

In this paper we study the problem of the boundary layer growth on a circular cylinder in a planar stagnation flow by the method of inner and outer expansions at small times and for finite but large Reynolds numbers. The emphasis is on the influence of the plane wall on the boundary layer detachment from the cylinder and the interaction between the cylinder and the flow. Certain correlations between some of the basic parameters are shown graphically.

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Zusammenfassung In dieser Arbeit wird das Anwachsen der Grenzschicht um einen kreisrunden Zylinder in einer ebenen Staupunktströmung behandelt. Verwendet wird die Methode der inneren und äußeren Entwicklung für große Reynoldssche Zahlen und kurze Zeiten. Betont wird der Einfluß einer ebenen Grenzplatte auf die Ablösung der Grenzschicht, und der gegenseitige Einfluß von Zylinder und Strömung. Gewisse Abhängigkeiten zwischen den Hauptparametern des Problems wurden auch graphisch dargestellt.

     

Pressure pulse from a laser pulse acting on a composite

Conclusions These tests on quasistationary irradiated for polyethylene-matrix powder-filled composites show that the filler composition and content have marked effects on the damage.There are ranges where the specific loss, the pressure, and the integral recoil pulse decrease as the power density increases because of changes in the damage mechanism, which are most prominent for zirconium oxide as filler. Bulk absorption contributes considerably, and causes various types of defect. Estimates have been made of the pressures arising in explosive matrix decomposition in the bulk together with the specific damage energies.These measurements are useful in modeling laser effects on composites.Translated from Mekhanika Kompositnykh Materialov, No. 5, pp. 868–872, September–October, 1988.     

Boundary layer flow on a circular cylinder moving in a fluid at rest

Summary This paper deals with the flow generated by a cylinder issuing from an orifice into a still fluid. The cylinder generates a boundary layer whose thickness increases with increasing distance from the orifice.The properties of the boundary layer are considered (i) very close to the orifice and (ii) at large distances from the orifice. In the former case the boundary layer is very much thinner than the cylinder; in the latter case the reverse holds. Asymptotic series solution are developed in both cases. The results of (ii) are compared with the experimental evidence due to Koldenhof.

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Zusammenfassung Die Arbeit behandelt die Strömung, die von einem Zylinder erzeugt wird, welcher von einer Mündung in eine ruhende Flüssigkeit eintritt. Am Zylinder entsteht eine Grenzschicht, deren Dicke mit zunehmendem Abstand von der Mündung zunimmt.Die Eigenschaften der Grenzschicht werden sehr nahe und im großen Abstand von der Mündung betrachtet. Im ersten Fall ist die Grenzschicht viel dünner als der Zylinder; im zweiten Fall sind die Verhältnisse umgekehrt. Für beide Fälle werden asymptotische Lösungen entwickelt. Ergebnisse im zweiten Fall werden mit experimentellen Ergebnissen von Koldenhof verglichen.

     

Mechanics of transition in an axisymmetric laminar boundary layer on a circular cylinder

Measurements of the growth of artificially generated turbulent spots and intermittency distribution in the transition region on a circular cylinder in axial flow show that the instability Reynolds number of 11,000 has a marked effect on the properties. In particular, it is found that the spot production in the initial region when a single turbulent spot has not yet wrapped around the cylinder and the propagation is essentially two-dimensional, is significantly altered. But the transition in the downstream or latter region, where most of the turbulent spots propagate onedimensionally (like the turbulent plugs in a pipe), is not affected. When the radius Reynolds number is more than 11,000, the intermittency law in the initial region is essentially the same as in twodimensional flow on a flat plate and in the latter region it is the one-dimensional flow in a pipe, the demarcation between the two regions being quite sharp.     

Pressure of a plane stamp of nearly circular cross section on an elastic half-space : PMM vol. 40, n 6, 1976, pp. 1143–1145

An approximate method of solving the contact problem of impressing a plane stamp of nearly circular cross section into an elastic half-space is suggested. The friction of the contact surface is neglected. A numerical algorithm for the method is produced. An elliptical and rectangular stamps are considered as examples.There is no general method of solving the problems for stamps of nearly circular cross section. Apart from the classical problem of a plane elliptical stamp, the literature gives solutions for the problems of polygonal stamps, with each problem however requiring a different approach. An approximate solution for the problem of impressing a stamp of nearly circular cross section into an elastic half-space is given in [1]. The method makes it possible to use the same approach to solve the contact problem for an arbitrary region of contact, and to construct an universal numerical algorithm. The program can be adapted to each particular case by making the corresponding changes in the procedure of computing the Fourier coefficients of the equation of the boundary of the area of contact. Below a numerical algorithm for the approximate method in question is given. A more effective formulation of the solution is given for the case of the elliptical stamp.     

Impact response of a cracked layer embedded in a composite

The impact response of a laminate composite with a crack or flaw normal to the interface is studied in terms of the intensification of the dynamic stresses around the crack border. Analytically, the laminate is modeled by a single layer with the crack sandwiched between two other layers of dissimilar material. Fourier and Laplace transforms are employed such that the problem reduces to the solution of a system of dual integral equations. Numerical results for the dynamic stress intensity factor are obtained by solving a Fredholm integral equation. The dynamic stress intensity factors are shown to fluctuate as a function of time, reaching a maximum that depends on the elastic properties of the composite and the flaw size.Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, Pennysylvania 18015. Published in Mekhanika Polimerov, No. 5, pp. 835–840, September–October, 1978.     

Indentation of an incompressible inhomogeneous layer by a rigid circular indenter

This work deals with an incompressible inhomogeneous layer bondedto a rigid substrate and indented without friction by a rigidcircular indenter. The corresponding mixed boundary-value problemof elasticity is reduced to equivalent dual integral equations.It is shown that the pliability function in these equationsmay be found from a system of nonlinear differential equationsand that its behaviour is peculiar when the elastic medium isincompressible. A novel technique taking into account this peculiarityis developed in order to reduce the dual integral equationsto Fredholm integral equations of the second kind with symmetricstrictly coercive operators. For a homogeneous layer and a flatindenter, the structure of the Fredholm integral equations permitsan approximate analytical solution which is very accurate forany layer thickness. For an indenter of three-dimensional profile,leading asymptotic terms of the solution are derived in thecase of a thin inhomogeneous layer.     

Action of a flat stamp on a half-plane of viscoelastic material

A plane problem concerning the action of a flat stamp on a reinforced, linearly viscoelastic medium is considered. One of the main axes of elasticity is parallel to the boundary of the half-plane. The reinforcing material is supposed to be perfectly elastic, and the matrix material linearly viscoelastic. The solution of the problem is based on the assumption that up to the moment of application of the forces, the medium is stress-free and at rest. The formulation of the problem is given, and a method of solution presented. A numerical example is offered.Mekhanika Polimerov, Vol. 2, No. 5, pp. 688–692, 1966     

Yield condition for circular cylindrical shells made of a fiber-reinforced composite

A yield condition is obtained for circular cylindrical shells made of a definite class of fiber-reinforced composite material whose components possess plastic properties. It is shown that, in the plane of generalized stresses — the axial bending moment and the circumferential force (when the axial force is absent) — the yield curve consists of two linear and four curvilinear sections. By approximating the curvilinear sections, we get a piecewise linear yield condition described by a hexagon in the plane indicated. The nonlinear equations and the corresponding piecewise linear equations of the yield condition for particular cases are given in the form of tables. In solving specific boundary-value problems, we consider a circular cylindrical shell simply supported at its ends and loaded with a uniform internal pressure, for which the load-carrying capacity is determined in relation to the mechanical properties of composite components and some characteristic geometrical parameters. The results of numerical calculations are represented in the form of graphs. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 655–666, September–October, 2006.     

Temperature field of a layer of a fibrous composite material under conditions of external thermal radiation

On the basis of an expression for the scattering phase function of an individual fiber, relations modeling radiative properties of fibrous composites are obtained. We calculate the temperature state of a layer of such a material under condition of external thermal radiation. Dependences of temperature distributions on the volume fraction of fibers in the composite, their reflectance, and size are investigated. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 185–193, January–March, 2008.     

Three-dimensional contact problem of the motion of a stamp with friction

There is considered the three-dimensional contact problem of elasticity theory with friction forces collinear to the motion direction. Such a case holds during stamp motion along the boundary of an elastic half-space with anisotropic friction /1/. In the case of an arbitrary friction surface, the mentioned force distribution is satisfied approximately during stamp motion.