The stressed state of an elastic space with a rectangular crack

By using the method of mechanical quadratures we reduce the resolvent integral equation for the problem of an infinite elastic space with a rectangular crack to a system of linear algebraic equations. We give the results of numerical experiments in varying the stress intensity factor on one side of the crack in the case of tension in the direction perpendicular to the plane of the crack. One figure. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 24–28.     

The stressed state of a transversally isotropic body with inner elliptic crack. A linearly varying pressure on the surface of the crack

An exact solution to the problem of the distribution of stresses in a transversally isotropic elastic body with inner elliptic crack is given. An assumption that the linearly varying pressure acts on the surface of the crack is made. The intensity coefficients of stresses at the vertex of the crack are found. Bibliography: 5 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 79, 1995, pp. 117–124. Original     

The stressed state in a neighborhood of a plane crack whose border has points of negative curvature

Using the example of a plane crack bounded by the limaçon of Pascal we study the influence of the points of negative curvature on the stressed state of a body in a neighborhood of border of the crack. It is shown that under tensile loads the damage of the body begins in a neighborhood of such points. In the case of shear loads prescribed on the edges of the crack damage of the body begins in a neighborhood of points of the border farthest from the points of negative curvature.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 83–90.     

Cylindrical cavity with a circumferential edge crack subjected to a uniform shearing stress

This paper contains an analysis of the stress distribution in an elastic medium having cylindrical cavity with a circumferential edge crack when it is deformed by the application of uniform shearing stress. By making a suitable representation of the stress function for the problem, the problem is reduced to the solution of a pair of singular integral equations. This pair of singular integral equations is solved numerically, and the stress intensity factor due to the effect of the crack size is calculated. Also the crack opening displacements are displayed in graphical forms.Received: January 24, 2002; revised: October 17, 2002     

Cylindrical cavity with a circumferential edge crack subjected to a uniform shearing stress

This paper contains an analysis of the stress distribution in an elastic medium having cylindrical cavity with a circumferential edge crack when it is deformed by the application of uniform shearing stress. By making a suitable representation of the stress function for the problem, the problem is reduced to the solution of a pair of singular integral equations. This pair of singular integral equations is solved numerically, and the stress intensity factor due to the effect of the crack size is calculated. Also the crack opening displacements are displayed in graphical forms.     

Strong evaporation into a half space

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis of the one-dimensional BGK model linearized about a drifting Maxwellian distribution. A unique solution is shown to exist if the downstream speed remains subsonic. Exact analysis is used, and numerical results are given.

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Zusammenfassung Auf der Basis eines eindimensionalen BGK-Modells, das über eine driftende Maxwell-Verteilung linearisiert ist, wird die Verdampfung einer Flüssigkeit in ein einen Halbraum ausfüllendes Vakuum untersucht. Es wird gezeigt, daß nur eine einzige Lösung existiert, wenn die Geschwindigkeit im Unterschallbereich bleibt. Exakte Analysis wird verwendet und numerische Resultate angegeben.

     

The stressed state of a three-dimensional plate with rigid inclusions

We study the stressed state of an isotropic plate with two rigid round inclusions stretched by uniform forces at infinity in the three-dimensional formulation. We give the results of numerical investigation. We exhibit the error of the corresponding applied theory. Four tables. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 34–42.     

Diffraction by a curved half space

A method is proposed for finding the asymptotic expansion of the solution and current in a neighborhood of the edge of a curved half plane. For the two-dimensional Dirichlet problem (the incident radiation is assumed to be a plane wave) the first two terms of the expansion are found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 244–249, 1974.     

Motion of a vortex filament with axial flow in the half space

We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensional half space. We prove the unique solvability of initial–boundary value problems as an attempt to analyze the motion of a tornado.     

The thermally stressed state of a half-space with a cylindrical foreign inclusion

We propose a method of determining the thermally stressed state of semibounded bodies containing a defect in the form of a cylindrical foreign inclusion. We give the results of numerical study of the thermal stresses as functions of the geometric parameters of the inclusion. Four figures. Bibliography: 4 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 41–45.