Lift Force of an Airfoil in the Form of an Arc with a Sink

The problem of maximizing the lift force of an airfoil in the form of an arc with a sink modeling flow removal is studied within the framework of the classical model of a steady ideal incompressible liquid flow. For a sink with a fixed flow rate, an optimal position on the upper surface of the arc is found, which ensures the greatest increase in the lift force. It is shown that, in the presence of a sink, the optimal shape of the arc with a limited curvature and chord length coincides with the optimal shape of the arc without a sink, which was designed by M. A. Lavrent'ev (an arc of a circle). The flow rate corresponding to the maximum lift force is determined, and the mechanism of the influence of flow removal on the lift force is examined.     

On the transformation toughening of a crack along an interface between a shape memory alloy and an isotropic medium

In this study, a bilinear cohesive zone model is employed to describe the transformation toughening behavior of a slowly propagating crack along an interface between a shape memory alloy and a linear elastic or elasto-plastic isotropic material. Small scale transformation zones and plane strain conditions are assumed. The crack growth is numerically simulated within a finite element scheme and its transformation toughening is obtained by means of resistance curves. It is found that the choice of the cohesive strength t₀ and the stress intensity factor phase angle φ greatly influence the toughening behavior of the bimaterial. The presented methodology is generalized for the case of an interface crack between a fiber reinforced shape memory alloy composite and a linear elastic, isotropic material. The effect of the cohesive strength t₀, as well as the fiber volume fraction are examined.     

Oscillations of an infinite plate on an elastic base under the influence of a rotating load

International Applied Mechanics -     

Selection of an initial approximation in an asymptotic representation of the solution of the problem of a point-source thermal explosion in a nonlinearly heat-conducting gas

Qualitative analysis shows [1] that the initial stage of a point-source thermal explosion in a homogeneous stationary gas is characterized by the predominance of radiative heat transfer. This finding is related to the nonlinear dependence of the coefficient of radiative heat transfer on the temperature of the gas T. The function (T) can be assigned in power form =/n T^n–1, where is a dimensional constant and n>1 is the nonlinearity exponent. In complete agreement with the qualitative conclusions in [1], the author of [2] found by the asymptotic method that for short periods of time after the explosion, radiative heat transfer occurs independently of the motion of the gas and completely determines it. Here, the occurrence of the shock wave in [2] is connected with the convergence of the asymptotic solution on the well-known self-similar solution for a thermal explosion in a non-heat-conducting gas [3]. Conversely, the experimental findings and qualitative analysis of the problem in [1, 4] indicate that an isothermal shock wave can occur within a finite period of time after a thermal explosion. The shock then separated from the region heated by radiation [1], while radiative heat transfer turns out to have a diminishing effect on its motion. The role of heat transfer is negligible far from the site of the explosion, and the motion of the shock becomes self-similar [3]. Using the example of a plane thermal explosion in a nonlinearly heat-conducting ideal gas for the case n1, here we propose an asymptotic representation of the solution of the above problem which will make it possible to analyze the generation of an isothermal shock wave.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 3, pp. 84–90, May–June, 1986.We thank K. B. Pavlov for his constant attention to the work and his critical observations.     

Example of an exact solution of the problem of the distribution of an ionized impurity in the surface region of a semiconductor

An exact solution of the nonlinear problem of determining the electrostatic potential and the distribution profile of an ionized impurity in the surface region of a semiconductor is constructed. Altai State University, Barnaul 656099. Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 17–24, July–August, 1998.     

Influence of the capillarity on a creeping film flow down an inclined plane with an edge

Summary In creeping flows of thin films, the capillarity can play a dominant role. In this paper, the creeping film flow down an inclined plane with an edge is considered. The influence of the capillarity on the velocity and the film surface is studied analytically, numerically and experimentally. Received 12 April 1999; accepted for publication 9 May 1999     

Influence of a flat wall on the motion of an aerosol particle in an inhomogeneous temperature field

The method of successive approximation is used to investigate the influence of a flat wall on the thermophoretic force acting on an aerosol particle of radius R at distance1 from the wall and moving in the direction normal to it. The problem is solved in the first approximation in R/1 1.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 185–188, September–October, 1980.We are grateful to Yu. I. Yalamov for suggesting the problem, for discussing the results, and for constant interest in the work.     

Construction of an approximate solution of the problem of a cavitational flow around a disk

An approach to analytical analysis of a steady axisymmetric cavitation flow of a potential ideal incompressible fluid is developed. An approximate analytical solution of Ryabushinskii’s problem for a disk-shaped cavitator is constructed. All integral and local characteristics of the flow calculated by the proposed approximation formulas in a wide range of cavitation numbers are demonstrated to differ insignificantly from the numerical solution of the problem in the exact nonlinear formulation.     

Identification of an open crack in a beam using an a posteriori error estimator of the frequency response functions with noisy measurements

This paper presents a robust damage assessment technique for the nondestructive detection and size estimation of open cracks in beams. The damage detection, based on the constitutive relation error updating method, is used for the identification of the crack's location and size in a simply-supported beam. The transverse open crack is modeled through the introduction of the flexibility due to the presence of the crack, i.e. by reducing the second moment of area of the element at the crack's location.This identification algorithm is illustrated through numerical examples involving different positions and sizes of a transverse open crack. We show that the detection of damage and the identification of the crack's size and position can be achieved with satisfactory precision, even if 20% noise has been added to the simulations and less than 5% of all displacements have been measured.     

Computation of the pressure on the surface of a fuselage with a wing in an ideal fluid

The flows around complex three-dimensional bodies by an ideal fluid are computed by methods [1–3] using approximation of the surface by a set of plane elements. A layer of surface singularities, whose intensity is found by solving a system of linear algebraic equations of very high order, is distributed continuously over each element. Evaluation of the system coefficients and its solution require significant machine time expenditures on powerful electronic computers. If in the method of [2] the total system of equations is separated successfully into several subsystems by simplifications and an approximate solution of the problem is obtained more rapidly than by the method in [1], then the same author practically used the method in [1] to design specific fuselages in [3]. A method [4] developed for a fuselage is expanded in this paper to design a wing-fuselage combination. This method turns out to be less tedious, without being inferior in accuracy, by being different from the method in [1] in the means of solving the fundamental integral equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–115, May–June, 1977.     

Modeling the motion of a vapor bubble in a tube in an ascending flow

The steady rise of a vapor bubble in a liquid moving in a vertical tube is modeled by means of the Navier-Stokes equations. The shape of the vapor bubble (drop) and the structure of the flow are determined by numerically solving the equations inside and outside the drop. The calculations are made on the interval of intermediate values of the dimensionless parameters and describe the transition to piston-type motion. The solutions obtained are compared with the existing experimental and approximate data for creeping flows. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 76–86, July–August, 1994.