Stress analysis of a strip with a step and a crack

Stress analysis for a strip of which widths are different at the right and left handsides is carried out for before and after occurrence of a crack at a corner of a step. The strip is analyzed as a thin plate bending problem subject to transverse bending and torsion, and as a plane eleastic problem subject to bending in the plane and uniaxial tension. The rational mapping function of a sum of fractional expressions and complex variable method are used. Stress distribution and stress intensity factors are obtained.     

Dispersion of a solute in a Poiseuille flow of a viscoelastic fluid

Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls is extended to the flow of non-Newtonian viscoelastic fluids (known as Phan-Thein-Tanner (PTT)). Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficient K_i(t) is obtained exactly and numerically for linearized and exponential forms of the PTT fluids, respectively. The analysis leads to the novel result for K₁ and K₂(t) (which is a measure of the longitudinal dispersion coefficient of the solute). It is found that the value of K₂(t) depends on the value of Deborah number (De=a measure of the level of elasticity in the fluid) whereas the value of K₁ is constant in both cases. Finally, the effect of the Deborah number on the axial distribution of the mean concentration θ_m is investigated in detail.     

Strength analysis of a split sleeve in a pipe containing a defect

We study the decrease in the strength of a pipe containing an artificial defect. On the basis of the analytic and numerical models, we consider the influence of the structural features of a split sleeve on its load-carrying ability. We also analyze the joint operation of a sleeve and a pipe containing an artificially made axial surface defect. The results of the numerical analysis are compared with the experimental data. Translated from Problemy Prochnosti, No. 2, pp. 102–111, March–April, 2009.     

Interaction between a liquid and a cylindrical body touching a wall

An exact solution is obtained for the problem of interaction between the ideal liquid homogeneously moving at infinity and streamlining a round cylinder touching a solid wall.     

Imaging a point to a line with a single spherical mirror

Methods for imaging a single point source to a line image are discussed, and a design study of single spherical mirror systems that form aberration-free line images is presented. An expression forthe ray density along the line image is derived for such systems in the cases of (i) uniform beam profiles and (ii) Gaussian beam profiles. The resulting ray density profiles are illustrated for single spherical mirror systems over a wide range of design parameters.     

Calculation of a transient in a two-pole network with a thermistor

An analytical expression is derived which describes the variation of the thermistor temperature during a relay-effect transient process following an instantaneous change in the supply voltage in an R — R_T two-pole network.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 3, pp. 465–472, March, 1980.     

Influence lines for bending under a ring load of a free shell,a shell embedded in a soft medium and a shell containing a soft core

Summary Theoretical expressions for stresses and displacements have been derived for bending under a ring load of a free shell, a shell embedded in a soft medium, and a shell containing a soft core. Numerical work has been done for typical cases with anElliot 803 Digital Computer and influence lines are drawn therefrom.

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Einflußlinien für die Biegung einer freien Schale, einer Schale in einer weichen Bettung und einer Schale mit weichem Kern

Zusammenfassung Für die Biegung einer freien Schale, einer weich gebetteten Schale und einer Schale mit weichem Kern unter einer Ringlast werden Ausdrücke für die Spannungen und Verschiebungen hergeleitet. Die Ergebnisse wurden für einige typische Fälle mit einem DigitalrechnerElliot 803 numerisch ausgewertet. Die sich ergebenden Einflußlinien wurden graphisch dargestellt.

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Nomenclature A (),B () Functions of - a, t Mean radius and thickness of the shell - E _S , _S Young's modulus andPoisson's ratio of the shell - G _c , _c Shear modulus andPoisson's ratio of the casting or core - I ₀ (r),I ₁ (r) ModifiedBessel functions of the first kind and order zero and one respectively - K ₀ (r),K ₁ (r) ModifiedBessel functions of the second kind and order zero and one respectively - p Ring load, lb/in - U, W Displacement components in the casing or core in thez andr direction - u, w Displacement components of a middle surface point in the shell - _r , _rz Radial and shearing stress components - Independent variable of infinite integrals - k [3(1–S ²)a ²/t ²]^1/4 With 13 Figures     

聚醚砜四元制膜液体系的相图计算

以Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ理论为基础，对ＰＥＳ－ＰＧ－ＮＭＰ＿Ｈ２Ｏ＿）聚醚砜丙二醇－Ｎ－甲基－２－哟咯烷酮水）四元制液体系的相图进行了计算，利用三元相图考察Ｈ２Ｏ和ＰＧ对液－液相分离的影响，在三元的理论的基础上提出了低分子量添加剂的卤元改性Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ理论，并提出了一种获得四元相图的方法，利用四元相图能较争地描述四元体系，利用改性的四元理论，能了地理解该种体系的液－液相分离行为。     

Interaction of a characteristic shock with a weak discontinuity in a relaxing gas

The evolution of a characteristic shock in a relaxing gas is investigated and its interaction with a weak discontinuity is studied. A particular solution to the governing system, which exhibits space–time dependence, is used to study the evolutionary behaviour of the characteristic shock; the properties of incident, reflected and transmitted waves, influenced by the relaxation mechanism, together with the geometry of the fluid flow and the background state at the rear of the shock, are studied.     

Analysis of a Premature Failure of a Hub from a Diesel Generator of a High-Speed Motor Ship

Failure analysis is carried out on a fractured hub obtained from a diesel generator of a high-speed motor ship. Macrofractography, microfractography, standard optical metallography, material characterization techniques, and numerical modeling were used to verify the findings of the current investigation. Cracking initiation is attributed to fretting fatigue caused by a modification performed in the vicinity of the fractured hub. Operational vibrations contributed to the propagation of the cracks as typical fatigue cracks until final fracture.     

Piercing a metallic barrier with a jet of a dilute polymer solution

Results are shown pertaining to the action of jets of dilute polymer solutions on solid barriers. The piercing of a barrier is explained by the viscoelastic properties of aggregates which, during an impact, behave like solid particles.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 6, pp. 1090–1094, December, 1973.     

Flow of a Casson fluid in a narrow tube with a side branch

Development of a mathematical model suitable for studying the mass-flux and hematocrit reduction due to plasma skimming in a capillary emerging from an artery making an angle with the parent artery is of primary concern in the paper. The flow is considered to have three phases – the peripheral plasma layer, the cell depleted middle layer and the core region where the concentration of erythrocytes is highest. Both steady and pulsatile flow situation are studied. The analysis for pulsatile flow has been carried out by considering the pressure gradient as a periodic function of time and the inertial effects as negligibly small. A perturbation technique is employed to solve the resulting quasi-steady non-linear system of equations that are considered to govern the flow. Basing upon relevant experimental data available for coronary arteries as well as very small vessels of the circulatory system, the study has been performed by considering Womeresely parameter to be small (less than unity). The theoretical estimates computed under the purview of the present mathematical analysis reveal that hematocrit in the branch capillary decreases with an increase in the yield stress of blood, both in steady and pulsatile flows for any branching angle. Further, erythrocytes entrainment from the parent artery to the branch capillary is least when the branch is perpendicular to the parent artery.     

Diffusion of a dissolved gas in a flow with a stationary cavity

An exact solution is obtained for the plane problem of the diffusion of a gas from a solution into a stationary cavity behind a symmetric profile for a zero cavitation number in an ideal liquid, and its approximate generalizations are indicated.     

Mixing of a jet array with a transverse stream in a channel

Universal empirical formulas are proposed for calculating, from the trajectories, the attenuation of velocity and temperature along the axis of a jet through a transverse stream in a channel.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 3, pp. 541–544, September, 1972.     

Sliding of a body over a melting surface at a high velocity

A mathematical model of thermal processes in the motion of one body over the melting surface of another is considered. A simple analytical solution to the problem, applicable in a wide range of velocities, is obtained.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 60, No. 6, pp. 964–968, June, 1991.     

Bending of a thin plate containing a rigid inclusion and a crack

The bending of a thin infinite plate with a line crack and an arbitrarily shaped rigid inclusion is analyzed. The superposition principle is used to reduce the original formulation to two subsidiary problems. A distribution of dislocation is assumed along the crack line. The solution is obtained in an integral form by using the Green function of a point dislocation. The stress functions for both subsidiary problems are obtained by employing the rational mapping function technique. The stress intensity factors are obtained in terms of the dislocation density function. Numerical results are demonstrated for the plate containing a square rigid inclusion and a line crack.     

Linear heat transfer in a flow around a cylinder or a sphere

It is shown that the relation between the Nusselt and Reynolds numbers determined by the Reynolds analogy is linear with self-similarity of the hydrodynamic resistance coefficient.Special Design and Technology Office Element, Odessa, Ukraine. translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, May–June, pp. 395–396, 1995.