Method to Calculate Bending Center and Stress Intensity Factors of Cracked Cylinder Under Saint-Venant Bending

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｓｔｒｅｎｇｔｈｏｆｍａｔｅｒｉａｌｓ[1],ｉｎｏｒｄｅｒｔｏｅｌｉｍｉｎａｔｅｔｈｅａｄｄｉｔｉｏｎａｌｔｏｒｓｉｏｎｉｎａｔｈｉｎ＿ｗａｌｌｅｄｃｙｌｉｎｄｅｒｗｉｔｈｏｐｅｎｃｒｏｓｓ＿ｓｅｃｔｉｏｎｕｎｄｅｒｂｅｎｄｉｎｇｂｙａｔｒａｎｓｖｅｒｓｅｆｏｒｃｅ,ｉｔｉｓｓｕｆｆｉｃｉｅｎｔｔｏｒｅｍｏｖｅｔｈｅｔｒａｎｓｖｅｒｓｅｆｏｒｃｅａｔｔｈｅｂｅｎｄｉｎｇｃｅｎｔｅｒ.Ｔｈｅｒｅｆｏｒｅａｎａｐｐｒｏｘｉｍａｔｅｍｅｔｈｏｄｔｏｃａｌｃｕｌａｔｅｔｈｅ…     

Stress intensity factors of a crack in a composedcircular cylinder

A composed circular cylinder, formed by a core circular cylinder, containing a crackand enclosed by a layered hollow circular cylinder, is investigated in regard to the evaluation ofstress intensity factors. Analytic solutions to the problem are provided, with which the upper andlower bounds of stress intensity factors in a cracked circular cylinder, the stress distribution in alayered hollow circular cylinder, and the stress intensity factors for a crack in the composedcircular cylinder can precisely be determined. Numerical materials, demonstrating the discretevalues of the stress intensity factors, as well as the general pattern according to which the stressintensity factors vary with the material and geometric constants, are presented. The solutions aredeveloped based on a simplified and modified solution to the Hilbert problem, and the matrixpresentation and manipulation of functions and variables, used in the circuit theory.     

Aerodynamic pressure on a wall due to movement of a high-speed train

The questions of train aerodynamics have taken on great practical importance in connection with the rapid increase of the speeds of the modern trains. In particular, of very great importance is the aerodynamic effect of trains on people and structures located near the tracks.The present article makes an attempt to evaluate the pressure of a train on a long wall parallel to a moving train.Similar problems have been considered for circular cylinders and for spheres. Literature on the subject and the initial discussion of the question may be found in the classical hydrodynamics courses [1,2]. A more exact solution of the problem of the motion of a circular cylinder in the presence of a wall has been given by Mazur [3]. The problems of the motion of an ellipsoid and certain other bodies have been examined recently to determine the suction force acting on a ship [4–6] In these studies bodies were considered whose slenderness ratio is much less than that of trains. Particular note should be taken of the article of Blokh and Ginevskii [5] which gives an approximate method which may be used also for very elongated bodies, if account is taken of the transverse velocities which they generate.The methods of thin wing theory are used in the present study.     

Small oscillations of a liquid in a partitioned cylindrical vessel

The equations of motion of a rigid body whose cavity is partially filled with an ideal fluid have been obtained in works of Moiseev [1, 2, 3], Okhotsimskii [4], Narimanov [5], and Rabinovich [6]. All the equation coefficients have been calculated for a cavity in the form of a circular cylinder or two concentric cylinders.The problem of fluid motion in a partitioned cylindrical cavity was considered by Rabinovich [7]. It was also considered by Bauer [8], who analyzed the particular case of vessel motion in the plane of one of the partitions.In the following we consider the two-dimensional motion of a cylinder with radial and annular baffles, and a definition is given of the velocity potential in the case of arbitrary positioning of the radial baffles with respect to the motion plane. Formulas are obtained for determining the parameters of a mechanical analog of the wave oscillations, which consists of two mathematical pendulum subsystems.     

Rotating Variable-thickness Orthotropic Cylinder Containing a Solid Core of Uniform-thickness

This paper presents accurate elastic solutions for the rotating variable-thickness and/or uniform-thickness orthotropic circular cylinders. The present circular cylinder may contain a uniform-thickness solid core of rigid or homogeneously isotropic material. Different cases of rotating cylinders of various cores are investigated. These cylinders include completely isotropic solid cylinder, uniform-thickness orthotropic cylinder containing an isotropic core, variable-thickness orthotropic cylinder containing an isotropic core, uniform-thickness orthotropic cylinder containing a rigid core, and variable-thickness orthotropic cylinder containing a rigid core. For all cases studied, exact elastic solutions are obtained and numerical results are presented. The results include the radial, hoop, and axial stresses and radial displacement of the five cylinder configurations. The distributions of displacement and stresses through the radial direction of the rotating cylinder are obtained and comparisons between different cases are made at the same angular velocity.     

An effective boundary element method for analysis of crack problems in a plane elastic plate

A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.     

Bending integral expressions of a cylinder with cracks

ＢＥＮＤＩＮＧＩＮＴＥＧＲＡＬＥＸＰＲＥＳＳＩＯＮＳＯＦＡＣＹＬＩＮＤＥＲＷＩＴＨＣＲＡＣＫＳＷａｎｇＸｉａｏ－ｃｈｕｎ（王晓春）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｃｈａｎｉｃｓ,ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ,Ｂｅｉｊｉｎｇ）（ＲｅｃｅｉｖｅｄＮｏｔ...     

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.     

Rectangular tensile sheet with a center notch root crack

This paper deals with the rectangular tensile sheet with a center notch crack. Such a crack problem is called a center notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, two center notch models are analyzed in detail. By changing the geometrical forms and parameters of the center notch, and by comparing the SIFs of the center notch crack problem with those of the center cracked plate tension specimen (CCT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the center notch on the stress intensity factors (SIFs) of the center cracked plate tension specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the center cracked plate tension specimen. So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the center cracked plate tension specimen. In addition, the numerical investigation proves that the conventional angular notched specimen is much less sensitive to the size of notch than is the circular notched specimen.     

On a semi-infinite crack penetrating a piezoelectric circular inhomogeneity with a viscous interface

We investigate a semi-infinite crack penetrating a piezoelectric circular inhomogeneity bonded to an infinite piezoelectric matrix through a linear viscous interface. The tip of the crack is at the center of the circular inhomogeneity. By means of the complex variable and conformal mapping methods, exact closed-form solutions in terms of elementary functions are derived for the following three loading cases: (i) nominal Mode-III stress and electric displacement intensity factors at infinity; (ii) a piezoelectric screw dislocation located in the unbounded matrix; and (iii) a piezoelectric screw dislocation located in the inhomogeneity. The time-dependent electroelastic field in the cracked composite system is obtained. Particularly the time-dependent stress and electric displacement intensity factors at the crack tip, jumps in the displacement and electric potential across the crack surfaces, displacement jump across the viscous interface, and image force acting on the piezoelectric screw dislocation are all derived. It is found that the value of the relaxation (or characteristic) time for this cracked composite system is just twice as that for the same fibrous composite system without crack. Finally, we extend the methods to the more general scenario where a semi-infinite wedge crack is within the inhomogeneity/matrix composite system with a viscous interface.     

On applications of the microlocal parameter method in modelling of temperature distributions in composite cylinders

Summary The problems of transient heat conduction in a periodically stratified medium consisting of a large number of alternating concentric cylinders of two homogeneous isotropic rigid materials and in a rotationally periodic cylinder consisting of a large number of circular homogeneous isotropic rigid sectors are considered. The equations of the homogenized models with microlocal parameters are derived by using the homogenization procedure given in [17]. The obtained models take into account certain microlocal effects connected with the microperiodic structure of the considered composites. Some examples of the application of the presented models to the problems of temperature distributions in composite cylinders are detailed. Received 10 March 1997; accepted for publication 23 October 1997     

Effect of irregular gravitational waves on a vertical circular cylinder

We examine the question of three-dimensional irregular waves acting on a vertical circular cylinder. Pilings in the form of circular cylinders are used as support elements for such hydrotechnical structures as offshore piers and stationary moorings.A theoretical-empirical approach to the solution of the problem for the action of swells was developed in [1].The account for irregularity is based on the hypotheses which are adopted in spectral theory of waves. Examples are presented for particular cases of the sea-state spectral density.     

The solution of integral equations with strongly singular kernels applied to the torsion of cracked circular cylinder

In this paper,the functions of warping displacement interruption defined on the crack lines are taken for the fundamental unknown functions.The torsion problem of cracked circular cylinder is reduced to solving a system of integral equations with strongly singular kernels.Using the numerical method of these equations,the torsional rigidities and the stress intensity factors are calculated to solve the torsion problem of circular cylinder with star-type and other different types of cracks.The numerical results are satisfactory.     

Diffusion toward a cylinder in the case of an arbitrary viscous flow. Diffusive boundary layer approximation

Steady convective diffusion of a dissolved substance toward the surface of a cylinder (optionally circular) in a viscous flow is examined. An analytical solution is obtained in [1, 2] for the case of laminar flow around a curved cylinder when the freestream flow is straight and uniform. More complex hydrodynamical problems are examined in [3, 4]. In the present work an approximate analytical expression is obtained for diffusive flow of a substance toward the surface of a solid cylinder in the case of an arbitrary two-dimensional flow. Formulas are given for calculating the mass transfer at a circular cylinder in some shear flows of a viscous, incompressible fluid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 163–166, September–October, 1976.The authors thank Yu. P. Gupalo and Yu. S. Ryazantseva for formulating the problem and their attention to the work.     

残余应力下厚壁筒表面裂纹的应力强度因子计算

本文首先介绍了边界元法计算裂纹尖端应力强度因子的基本理论,接着利用边界元法计算了在残余应力下不同厚壁筒内表面椭圆裂纹的应力强度因子,研究了其大不随椭圆裂纹不同而变化的规律,为厚壁筒结构的设计,制造以及疲劳寿命分析提供了许多有价值的参考资料。     

Calculation of the scattering of elastic waves from a penny-shaped crack by the method of optimal truncation

The method of optimal truncation (MOOT) [1, 2], a least-squares boundary-residual method [3] for solving scattering problems, is applied to the plane circular crack. An equatorially cloven spherical inclusion is used to model the crack. Numerical advantages of this model are discussed and demonstrated. Results are given for cross sections for longitudinal waves incident on the crack at arbitrary angles. Both clear cracks and fluid-filled cracks are considered. A refinement of the method which would allow accurate calculation of dynamic stress-intensity factors is developed.     

Three-dimensional computation for flow-induced vibrations of an upstream circular cylinder in two tandem circular cylinders

It is well known from a lot of experimental data that fluid forces acting on two tandem circular cylinders are quite different from those acting on a single circular cylinder. Therefore, we first present numerical results for fluid forces acting on two tandem circular cylinders, which are mounted at various spacings in a smooth flow, and second we present numerical results for flow-induced vibrations of the upstream circular cylinder in the tandem arrangement. The two circular cylinders are arranged at close spacing in a flow field. The upstream circular cylinder is elastically placed by damper-spring systems and moves in both the in-line and cross-flow directions. In such models, each circular cylinder is assumed as a rigid body. On the other hand, we do not introduce a turbulent model such as the Large Eddy Simulation (LES) or Reynolds Averaged Navier-Stokes (RANS) models into the numerical scheme to compute the fluid flow. Our numerical procedure to capture the flow-induced vibration phenomena of the upstream circular cylinder is treated as a fluid-structure interaction problem in which the ideas of weak coupling is taken into consideration.     

Investigation of turbulent flow past a yawed wavy cylinder

A large eddy simulation (LES) study was conducted to investigate the three-dimensional characteristics of the turbulent flow past wavy cylinders with yaw angles from 0° to 60° at a subcritical Reynolds number of 3900. The relationships between force coefficients and vortex shedding frequency with yaw angles for both wavy cylinders and circular cylinders were investigated. Experimental measurements were also performed for the validation of the present LES results. Comparing with corresponding yawed circular cylinders at similar Reynolds number, significant differences in wake vortex patterns between wavy cylinder and circular cylinder were observed at small yaw angles. The difference in wake pattern becomes insignificant at large yaw angles. The mean drag coefficient and the Strouhal number obey the independence principle for circular cylinders at yaw angle less than 45°, while the independence principle was found to be unsuitable for yawed wavy cylinders. In general, the mean drag coefficients and the fluctuating lift coefficients of a yawed wavy cylinder are less than those of a corresponding yawed circular cylinder at the same flow condition. However, with the increase of the yaw angle, the advantageous effect of wavy cylinder on force and vibration control becomes insignificant.     

Nonsmall liquid oscillations in a right circular cylinder

In this study we consider certain nonlinear effects which occur during oscillations of a liquid partially filling a right circular cylinder. The problem of nonlinear oscillations of a liquid in a circular cylinder has been considered in [1, 2]. The same problem has been solved in [3, 4] for arbitrary cavities by a somewhat different method.In the present paper we investigate the stability of forced oscillations of a liquid in a cylinder when the latter performs small harmonic oscillations in a plane passing through its axis.