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.     

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     

Stress distribution in a transversely isotropic body with a thermally insulating parabolic crack subjected to a uniform heat flux

An explicit static thermoelastic solution is constructed for an infinite transversely isotropic body containing a thermally insulating parabolic crack in the plane of isotropy. The surface of the crack is free of stress. A uniform thermal flux is incident on the crack perpendicular to its surface. Formulas are obtained for the stress intensity factors near the tip of the crack. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev; Catholic University, Portugal. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 54–66, 1999.     

Torsional wave propagation in a finite inhomogeneous cylindrical shell under time-dependent shearing stress

Torsional wave motion in a finite hollow cylinder of piezoelectric material of (622) crystal class, under a time-dependent mechanical boundary condition is investigated. The inhomogeneity is restricted to the variations of density and other physical constants of the medium as a certain power of the radial distance. The expressions for the displacement and the electric potential of the present solution are compared with those under time-dependent electric boundary condition. Numerical values of the roots of the frequency equation for β-quartz are presented.     

On equations of the state of stress in a plate of variable thickness

Method of asymptotic integration of three-dimensional equations of the theory of elasticity is used to construct the internal state of stress in a plate of variable thickness /1/. It is shown that it can generally be described by a system of differential equations of eighth order in the components of the displacement vector of the points of a plane projected inside the plate, with the equations of flexure and of plane state of stress not separated. In a particular case when the face surfaces are symmetrical with respect to this plane, the flexure and the plane state of stress are described by separate equations. The accuracy of the equations obtained is of the order of square of relative thickness of the plate away from the edge and other distortion lines of the stress state.

The boundary layer is not considered and conditions at the plate edge are not formulated.     

A numerical study of the flow in the wake of a plate of finite thickness

We give a numerical study of the flow near the backside of a plate of finite thickness past which a supersonic flow of viscous compressible heat-conducting gas is occurring, as a function of the Reynolds number, symmetry conditions, and temperature conditions on the surface. Thirteen figures. Bibliography: 7 titles. Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 184–192.     

Stress intensity factors for a finite plate with an inclined crack by boundary collocation

In this paper, we combine the Muskhelishvili＇s complex variable method and boundary collocation method, and choose a set of new stress function based on the stress boundary condition of crack surface, the higher precision and less computation are reached. This method is applied to calculating the stress intensity factor for a finite plate with an inclined crack. The influence of θ （the obliquity of crack） on the stress intensity factors, as well as the number of summation terms on the stress intensity factor are studied and graphically represented.     

Mathematical model for crack arrest of an infinite plate weakened by a finite and two semi-infinite cracks

The problem of an unbounded plate weakened by three quasi-static coplanar and collinear straight cracks: two semi-infinite cracks and a finite crack situated symmetrically between two semi-infinite cracks, is investigated. The plate is subjected to uniform unidirectional in-plane tension at infinite boundary. Developed plastic zones are arrested by distributing cohesive yield point stress over their rims. The solution is obtained using complex variable technique. Closed form analytic expressions are derived for load bearing capacity and crack-tip-opening displacement (CTOD). A case study is presented for CTOD and load bearing capacity versus crack length, plastic zone length and inter-crack distance etc. Results are presented graphically and analyzed.     

Stresses in a long hollow cylinder subjected to a band of uniform pressure on the outer surface

Zusammenfassung Die Arbeit gibt eine Fourier-Integral-Lösung für den Spannungsverlauf in einem Hohlzylinder, der einer axialsymmetrischen Radiallast längs eines Bandes an der Aussenfläche unterworfen wird. Es wird für dünne Wände eine Methode für die Approximation der Integranden entwickelt. Damit wird die Auswertung der Interale mit der Residuenmethode möglich. Numerische Ergebnisse werden für den Fall eines unendlich schmalen Lastbandes für ein Radienverhältnis von 910 und für eine Poissonsche Zahl von 0,3 ausgegeben. Die Ergebnisse werden mit denjenigen zweier Näherungstheorien verglichen sowie mit Ergebnissen früherer numerischer Integrationen.     

Ovoids in finite uniform linear spaces

The concept of an ovoid is extended to linear spaces, and it is shown that a finite uniform linear space with an ovoid is either a trivial structure on a finite set, or else either two or three dimensional. In the three dimensional case, the ovoid is directly related to an inversive plane, in much the same way that an ovoid in a finite projective space is.Dedicated to Professor Tallini on the occasion of his 60th birthday     

The uniform heating and bending of a two-layer plate

The problem of the uniform heating of a two-layer plate is solved. The transversely isotropic layer considered (a soft plate) is in ideal contact with a rigid isotropic thin elastically deformed layer. The ends of the plate are load-free. A boundary layer of the soft plate (a thin contact layer) is introduced, which enables the boundary conditions on the ends of the plate to be formulated in such a way that the problem has a bounded smooth solution [1]. The two-layer plate, generally speaking, is bounded along the axis perpendicular to the axes directed along the length and thickness of the plate. The resultant force and the resultant moment, applied to the end transverse sections, are equal to zero. The exact solution of the temperature problem is sought using the equations of the theory of elasticity. The plane problem of the bending of a two-layer plate acted upon by a uniformly distributed pressure applied to the side surface of an anisotropic layer is solved by a similar method. The ends of the rigid isotropic layer are clamped.     

Electroelastic thickness vibrations of a quartz SC-cut plate

Analytic solutions are obtained of the boundary value problem of steady motions of a thick piezocrystalline SC-cut quartz plate describing thickness modes of harmonic elastic vibrations. The plate endfaces have no electrodes and adjoin a vacuum or a rarefied gas. The measure of the difference between the found values of the five lowest eigenfrequencies of the thickness vibrations of a plate without electrodes and the values of the corresponding frequencies of a plate whose endfaces are covered by massive short-circuited electrodes is determined.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 83–85, 1988.     

Dynamic response of an infinite plate subjected to a steadily moving transverse force

Zusammenfassung Es wird das dynamische Verhalten einer dünnen unendlichen Platte studiert unter dem Einfluss einer fortschreitenden transversalen Kraft. Die Untersuchung geschieht mit Hilfe der Theorie der Platten, welche Schubdeformation und Trägheitsmomente berücksichtigt. Es wird angenommen, dass die Kraft sich mit einer konstanten Geschwindigkeit bewegt, die grösser als die beiden wellengeschwindigkeiten in der Platte ist. Indem man die Kraft als Delta-Funktion ansetzt, wird die Green'sche Funktion für das dynamische Verhalten der Platte unter dem Einfluss einer Klasse von fortschreitenden Kräften in der Form von bestimmten Integralen konstruiert. Die Green'sche Funktion ist regulär mit Ausnahme der Ränder der beiden «Mach» Sektoren, wo sie singulär wird. Die Green'sche Funktion ist ausserhalb des äusseren Sektors identisch Null. Die Singularitäten der Green'schen Funktion werden ebenfalls untersucht.

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A preliminary account of the results contained herein was presented at the 5h U.S. National Congress of Applied Mechanics held in Minneapolis, Minnesota, U.S.A., June 1966.     

Steady vortical flow around a finite plate

An explicit solution for a layer of fluid with constant vorticitysurrounding a thin plate of finite length is obtained usingelementary conformal mapping methods. In the limit of largeplate length the behaviour of the solution near the ends ofthe plate tends to that of the previously known solution fora semi-infinite plate. Contour dynamics is used to investigatethe stability of the steady solutions.     

Viscous incompressible flow past a finite plate

We consider the problem of viscous incompressible flow past a finite plate. The apparatus of hydrodynamic potential reduces the problem to Volterra— Fredholm boundary-value equations. Numerical results are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 103–107, 1988.     

Effect of shearing forces on the stressed state of a half space with crack

Using the method of boundary integral equations, we study the stressed state in the neighborhood of a plane crack perpendicular to the boundary of a half space. The crack surfaces are subjected to the action of shearing forces. The problem is reduced to two-dimensional hypersingular integral equations, and their regular kernels, taking into account interaction between the crack and boundary of the half space, are written in explicit form. The dependences of stress intensity factors on the angular coordinate are presented for different loads of the crack. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 112–120, January–March, 2008.