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.     

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 a circular cylinder weakened by a cylindrical crack

Leningrad Wood Technology Academy. Translated from Prikladnaya Mekhanika, Vol. 25, No. 3, pp. 11–14, March, 1989.     

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.     

Plastic zone correction in a stretched cylinder with an external circumferential crack

The Dugdale hypothesis is adapted to the problem of an external circumferential crack in a stretched cylinder. The lateral surface of the cylinder is stress free and restrained from radial displacements. An external circumferential edge crack in the cylinder which is considered elastic-perfectly plastic is envisaged with the assumption that the plastic zone forms a very thin in-plane layer surrounding the crack. The solution of the problem is reduced to the solution of dual Dini series which, in turn, is reduced to a Fredholm integral equation of the second kind. Solving this integral equation numerically and using the boundedness of the axial stress, the size of the plastic zone correction is obtained.     

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.     

Torsion of an elastic space with a semi-infinite conical crack

The axisymmetric problem of stress concentration near a conical crack in an infinite elastic space with a rotation center is addressed. The problem is reduced to an integro-differential equation. Its exact solution is obtained. An expression for the stress intensity factor in crack neighborhood is derived and numerically analyzed for different positions of the rotation center and the crack opening angles __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 99–107, February 2007. For the centenary of the birth of G. N. Savin.     

Torsion of an elastic cylinder slackened by an external circular notch I. The case of an infinite cylinder

The axisymmetric torsion problem of the boundary-free cylinder with external notch is considered. The method of dual equations is used to reduce the problem to a regular Fredholm integral equation of the second kind with a symmetric kernel. Numerical results worked out for the stress intensity factor are adduced.     

Torsion of hollow cylinder with variable shear moduli

Kiev Institute of Civil Aviation Engineers, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 29, No. 11, pp. 41–46, November, 1993.     

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.     

Torsion of a pre-stressed halfspace with a disk-shaped crack at the surface

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 10, pp. 24–31, October, 1991.     

Flow around a cylinder surrounded by a permeable cylinder in shallow water

The change in flow characteristics downstream of a circular cylinder (inner cylinder) surrounded by an outer permeable cylinder was investigated in shallow water using particle image velocimetry technique. The diameter of the inner cylinder and the water height were kept constant during the experiments as d?=?50?mm and h _w ?=?25?mm, respectively. The depth-averaged free-stream velocity was also kept constant as U?=?170?mm/s which corresponded to a Reynolds number of Re_d?=?8,500 based on the inner cylinder diameter. In order to examine the effect of diameter and porosity of the outer cylinder on flow characteristics of the inner cylinder, five different outer cylinder diameters (D?=?60, 70, 80, 90 and 100?mm) and four different porosities (???=?0.4, 0.5, 0.6 and 0.7) were used. It was shown that both porosity and outer cylinder diameter had a substantial effect on the flow characteristics downstream of the circular cylinder. Turbulent statistics clearly demonstrated that in comparison with the bare cylinder (natural case), turbulent kinetic energy and Reynolds stresses decreased remarkably when an outer cylinder was placed around the inner cylinder. Thereby, the interaction of shear layers of the inner cylinder has been successfully prevented by the presence of outer cylinder. It was suggested by referring to the results that the outer cylinder having 1.6????D/d????2.0 and 0.4????D/d????0.6 should be preferred to have a better flow control in the near wake since the peak magnitude of turbulent kinetic energy was considerably low in comparison with the natural case and it was nearly constant for these mentioned porosities ??, and outer cylinder to inner cylinder diameter ratios D/d.     

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].