Interaction of an Ellipsoidal Inclusion with an Elliptic Crack in an Elastic Medium

An approach is considered to how to allow for the interaction between an ellipsoidal heterogeneity (inclusion) and an elliptic crack in an elastic medium. Using the superposition of perturbed stress states, the boundary conditions are satisfied on the ellipsoidal surface by the method of equivalent inclusion and on the crack surface by the least-squares method. A numerical analysis is carried out. Typical mechanical effects are revealed. In the calculations, the stress state near the ellipsoidal heterogeneity is approximated by a polynomial of the second degree in Cartesian coordinates, whereas the load on the crack surface is simulated by a polynomial of the fourth degree in Cartesian coordinates. In particular cases, the results are in good agreement with the data obtained by other authors     

Flow past an airfoil at an angle of attack to an oncoming sonic stream

Guderley [1] proposed a theoretical example of sonic flow of gas past a symmetric airfoil at zero angle of attack to an oncoming stream. The linear distribution of the velocity over the airfoil surface was found from the solution describing this flow. It is of interest to generalize this example to the case of nonsymmetric sonic flow past an airfoil. In the present paper a study is made of sonic flow past a Guderley airfoil at an angle of attack and a study is made of the dependence of the velocity over the surface of the airfoil on the angle of attack. This dependence is obtained by means of the parabolic method of Spreiter and Alksne [2], which makes it possible to solve this problem directly in the plane of the flow. For comparison, flow past a parabolic airfoil at an angle of attack is considered, and an expression is obtained for the dependence of the distribution of the velocity over the surface on the angle of attack, this being a generalization of the formula of Zierep [3], who considered sonic flow past a parabolic airfoil at zero angle of attack.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 81–86, September–October, 1982.     

Separation of an Inclusion in an Orthotropic Composition

The problem on separation of a rigid linear inclusion in an orthotropic matrix is analytically solved by using Cherepanov's -concept in the theory of cracks. It is assumed that plastic or prefracture zones, which are modeled by discontinuities of tangential displacements along the matrix–inclusion interface, develop near the inclusion apices under loading. The problem is reduced to the Cauchy problem for a differential equation of the first order. The effective length of the inclusion is found for specific values of its initial length and external loads     

Motion of an electrolyte-gas interface in an electrical field

The article discusses the phenomenon of the motion of an electrolyte-gas interface, first observed on electrical levels. It gives a comparative characterization of the phenomena, for purposes of practical use, with a solution of problems of control by the position of a liquid-liquid interface.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 25–28, November–December, 1975.     

Buckling of an elastic hemispherical shell with an obstacle

We study the buckling of an axially symmetric elastic hemispherical shell, uniformly compressed, subject to a constraint to the radial shifting of the equatorial circumference. The static equilibrium equations, using tensorial notations, are obtained applying the virtual displacements principle to the energy functional. The presence of a constraint does not modify the field equations with respect to the case of a constraint-free buckling, but only influences the boundary conditions, so that, instead of a boundary value problem, we deal with a problem with complementarity conditions on the boundary. We revisit and improve some previously obtained mathematical results, adapting them for the subsequent numerical treatment. Finally, by suitably using a delicate quasi-static shooting technique, numerical results are obtained, which complete the theoretical analysis and give an interesting insight into the behavior of the bifurcation branches.     

Diffraction of an elastic wave by an embedded quarter-space

A method of matching asymptotic fields has recently been applied to the problem of the diffraction of a plane time-harmonic acoustic wave by an embedded quarter-space with different acoustic properties from the rest of space. The method is here applied to the equivalent problem of elastic waves. The normal to the incident wavefront is perpendicular to the apex of the quarter-space and so the problem is two-dimensional in plane strain.Exact expressions are found for the far-field on the boundary of the quarter-space, neglecting those terms which decay faster than the inverse half power of the distance. The main case of interest is where the incident wave propagates parallel to one of the interfaces.The method, unfortunately, does not lead to any information about the amplitude of any interface (Stoneley or Rayleigh) wave which may exist.     

Fluctuating flow of an elastico-viscous fluid along an infinite porous plate with an applied magnetic field

The problem of oscillating free stream flow of an elastico-viscous, incompressible, and electrically conducting fluid along an infinite plate with suction varying periodically with time, is considered in the presence of a transverse magnetic field. The effect of the elasticity of the fluid, the magnetic fluid, and the fluctuation of suction velocity on the velocity and the skin friction is examined.     

Magneto-elastic stress induced by an electric current in an infinite thin plate with an elliptical hole

Two-dimensional magnetic field and stress analyses have been presented for soft ferromagnetic, paramagnetic, and diamagnetic materials of an infinite thin plate with an elliptical hole under steady electric current. The magnetic stress has been analyzed in the Maxwell Stress Model. Except for the approximation of the plane stress state since the plate is the thin plate, any assumption is not made for the stress analysis, though the Maxwell stress components are expressed by nonlinear terms. The boundary condition expressed by Maxwell’s stress is completely satisfied without any linear assumptions on the boundary. Two ways for the boundary condition are stated. The analysis of σ _z in the direction of the plate thickness is also carried out. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived, and the magnitude of the stress intensity factor for the magnetic stress and thermal stress due to the Joule heat caused by the electric current is discussed.     

Charging of an inductive accumulator from an explosive-type magnetic generator through an electrical explosive-type current breaker

Analytical investigations were made of electromagnetic processes with the work of an explosive-type magnetic generator, in a series-connected inductive-type accumulator and a current breaker based on an exploding wire. A solution is obtained in dimensionless form for a model of a current breaker based on an ohmic resistance, whose value rises linearly with the temperature. The conditions are determined under which an inductive load can be connected in parallel to the current breaker; under these circumstances, the current of the load branch remains small during the whole charging stage.     

Interaction of an Ellipsoidal Inclusion with an Elliptic Crack in an Elastic Material under Triaxial Tension

The interaction of an elastic ellipsoidal inclusion with an elliptic crack in an infinite elastic medium under triaxial loading is analyzed. The stress state in the elastic space is represented as a superposition of the principal state and perturbed states, which are due to the presence and interaction of the inclusion and the crack. The analytical solution of the problem is found using the method of equivalent inclusion, the potential of an inhomogeneous ellipsoid, and a system of harmonic functions for an elliptic crack. The effect of triaxial loading on the stress intensity factors is analyzed     

Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack

A uniform electric current at infinity was applied to a thin infinite conductor containing an elliptical hole with an edge crack. The electric current gives rise to two states, i.e., uniform and uneven Joule heat. These two states must be considered to analyze the heat conduction problem. The uneven Joule heat gives rise to uneven temperature and thus to heat flux, and to thermal stress.Using a rational mapping function, problems of the electric current, the Joule heat, the temperature, the heat flux, the thermal stress are analyzed, and each of their solutions is obtained as a closed form. The distributions of the electric current, the Joule heat, the temperature, the heat flux and the stress are shown in figures.The heat conduction problem is solved as a temperature boundary value problem. Solving the thermal stress problem, dislocation and rotation terms appear, which complicates this problem. The solutions of the Joule heat, the temperature, the heat flux and the thermal stress are nonlinear in the direction of the electric current. The crack problems are also analyzed, and the singular intensities at the crack tip of each problem are obtained. Mode II (sliding mode) stress intensity factor (SIF) is produced as well as Mode I (opening mode) SIF, for any direction of the electric current. The relations between the electric current density and the melting temperature and between the electric current density and SIF are investigated for some crack lengths in an aluminum plate.     

The equations of an inverted pendulum with an arbitrary number of links and an asymmetric follower force

This paper formulates a problem for and gives the differential equations of plane-parallel motion of an inverted n-link pendulum subject to an asymmetric follower force applied at the upper end via a spring. The physical nonlinearities of springs are taken into account. The possible mechanisms of energy dissipation are described __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 106–114, May 2007.     

Torsional oscillations of an infinite plate in an elastico-viscous fluid

Summary The equations of motion of an infinite plate performing torsional oscillations in Walters elastico-viscous liquid B have been solved by expanding the velocity profile in powers of the amplitude of oscillation of the plate. The first order solution consists of a transverse velocity and the second-order solution gives a radial-axial flow composed of a steady part and a fluctuating part. The steady part of the radial flow does not vanish outside the boundary layer and hence the equations are solved by another approximate method for the steady part of the flow. The effects of the non-Newtonian term is to increase the non-dimensional boundary layer to start with and subsequently to decrease it and to increase the shearing stress at the plate. The steady radial and the steady axial velocities fall short of the inelastic flow in the beginning but later on their values lie above.