Torsion problem for elastic multilayered finite cylinder with circular crack

An axisymmetric tangent stress is applied to a lateral surface of a multilayered elastic finite cylinder with a fixed bottom face. The problem is solved for an arbitrary number of layers. The layers are coaxial, and the conditions of an ideal mechanical contact are fulfilled between them. A circular crack is situated parallel to the cylinder's faces in the internal layer with branches free from stress. The upper face of the cylinder is also free from stress. Concretization of the problem is done on examples of two-and three-layered cylinders. An analysis of cylinders' stress state is conducted and the stress intensity factor is evaluated depending on the crack's geometry, its location and ratio of the shear modulus. Advantages of the proposed method include reduction of the solution constants' number regardless of the number of layers, and presentation of the mechanical characteristics in a form of uniformly convergent series.     

Torsion of a long circular cylinder having a spherical cavity with a peripheral edge crack

The singular stress problem of a peripheral edge crack around a spherical cavity in a long circular cylinder under torsion is investigated. The problem is solved by using integral transforms and is reduced to the solution of two integral equations. The solution of these equations is obtained numerically by the method due to Erdogan, Gupta, and Cook, and the stress intensity factors, and crack opening displacements are displayed graphically.     

Stress state of a cylindrical composite panel weakened by a circular hole

The paper studies the stress-strain state of a deep cylindrical panel weakened by a hole and subjected to a tensile load at the outer boundary. A variational difference method is used. A numerical analysis is carried out for an orthotropic panel with low shear stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 73–78, May 2006.     

Torsion of a cylinder with a shallow external crack

The torsional problem of a finite elastic cylinder with a circumferential edge crack is studied in this paper. An efficient solution to the problem is achieved by using a new form of regularization applied to dual Dini series equations. Unlike the Srivastav approach, this regularization transforms dual equations into a Fredholm integral equation of the second kind given on the crack surface. Hence, exact asymptotic expansions of the Fredholm equation solution, the stress intensity factor and the torque are derived for the case of a shallow crack. The asymptotic expansions are certain power-logarithmic series of the normalized crack depth. Coefficients of these series are found from recurrent relations. Calculations for a shallow crack manifest that the stress intensity factor exhibits the rather weak dependence upon the cylinder length when the torque is fixed and the triple length is larger than the diameter.     

Bending of a circular cylinder containing a crack

The study of bending of cracked circular cylinders is of more significance. The bending of cylinders containing radical crack or cracks was discussed by refs. [1]–[4] and that of concentrically craked circular cylinders was studied by [5]. Continuing [6] and using complex variable methods in elasticity, this paper deals with the bending problems of a circular cylinder, containing an internal linear crack at any position under an acting force perpendicular to the crack. The general forms of displacements, stresses, and stressintensity factors, expressed in terms of series, are obtained and to this bending problems with small Ah are presented good approximate formulas for the stress-intensity factors whose variations with the center of the crack are analysed. Finally, the twist angle per unit length and the center of bending for the radically cracked circular cylinder, one of whose crack-tips is located at the origin, have been computed and the results are almost the same as that calculated in [1].     

Evaluating the strength of circular cylindrical shells weakened by a longitudinal crack under static loading by an axial force and internal pressure

Institute of Mechanics of the Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 11, pp. 60–64, November, 1992.     

Torsion of a sectorially composite hollow circular cylindrical beam

Summary In the first part solution of torsion problem of a sectorially composite hollow circular cylindrical beam has been obtained by a potential method involving use of a Green's identity and Green's function. At first a composition of two isotropic media is considered, then it is shown that the procedure can be successfully applied to the case of a composition of any finite number of isotropic media. A special feature of this St.- Venant-type problem is the multiplicity of the cross-sectional region. In later part the problem of torsion of a sectorially cut out beam is dealt with and solved.

---

Übersicht Im ersten Teil wird eine Lösung für die Torsion eines aus Sektoren zusammengesetzten kreiszylindrischen Balkens angegeben. Dabei wird eine Potentialmethode verwendet, zu der von der Greenschen Identität und der Greenschen Funktion Gebrauch gemacht wird. Zunächst wird ein Balken untersucht, der aus zwei isotropen Materialien zusammengesetzt ist; danach wird gezeigt, daß das Verfahren auch auf den Fall einer endlichen Zahl isotroper Materialien angewendet werden kann. Als Besonderheit dieses Problems vom Saint-Venant-Type ist ein Multiplikationsgesetz für die Spannungen in den Querschnittsbereichen zu erwähnen. Im letzten Teil wird das Problem der Torsion eines sektionsweise ausgeschnittenen Balkens behandelt und gelöst.

     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

Torsion of an elastic cylinder slackened by an external circular notch II. The case of a finite cylinder

The axisymmetric torsion problem of the boundary-free finite cylinder with external notch is considered. The problem is reduced to a regular Fredholm integral equation of the second kind having symmetric kernel. Simple asymptotics are worked out for the case of a long cylinder. Numerical results are adduced for the problem symmetrical with respect to the axial coordinate.     

The indentation of a Newtonian fluid in a finite cylindrical container by a right circular cylinder

The indentation of the free surface of a Newtonian fluid in a finite cylindrical container by a right circular cylinder is considered. It is assumed that weight and inertia effects are negligible compared to viscous effects. A finite difference technique is used to obtain approximate values for initial velocities, pressures, and stresses at any point in the fluid as well as an estimate of the force required to indent the fluid with a given velocity. The solution obtained forms the basis for a primary indenter viscometer for very viscous fluids which have viscosities in the range of 10⁴–10¹⁰ poises.     

Torsion of a thick-walled cylinder with an external crack: boundary collocation method

The boundary collocation method is used to obtain the torsional rigidity and Mode III stress intensity factor of a thick-walled cylinder with an external radial crack. When the internal radius of the cylinder is very small, the results agree well with those obtained previously from other methods for an edge crack in a solid cylindrical bar. The present method is shown to be expedient when applied to obtain results for different ratios of the internal and external radii of the cracked cylinder.     

Stresses in bonded half-plates weakened by a circular hole

Summary The problem is solved by the well established method of using a dislocation distribution on the perimeter of the hole to reduce it to a singular integral equation. Appropriate numerical techniques are applied and accurate evaluation of the stresses can be effected anywhere in the region of the bonded plates. As examples a constant uniaxial tension applied at infinity and an internal pressure within the hole are considered for selected material pairs. For these examples the stresses on the perimeter of the circular hole and on the interface are reported for a range of values for the geometric parameters of the problem.

---

Die spannungen in zusammengefügten halbscheiben mit kreisloch

Übersicht Zur Lösung wird eine Versetzungsverteilung auf dem Umfang des Lochs eingeführt, wodurch das Problem auf eine singuläre Integralgleichung zurückgeführt wird. Bei Anwendung geeigneter numerischer Verfahren können genaue Spannungswerte an beliebigen Punkten der verbundenen Scheiben ermittelt werden. Als Anwendungsbeispiele werden die Fälle konstanter einachsiger Zugspannung als Fernfeld sowie von Innendruck im Loch für verschiedene Materialparameter betrachtet. Für eine Reihe geometrischer Parameter des Problems werden die Umfangsspannungen am Loch und die Spannungen in der Verbundfuge angegeben.