Initial stage of the collision of blast waves

The collision of two blast waves is analyzed for the case of variable parameters of the gas behind the wave front and wave reflection at a plane, a cylindrical, and a spherical obstacle. The reflection of a blast wave from a nonmoving obstacle is investigated in detail. The problem of the collision of two shock waves with constant parameters behind the front is solved both in the symmetrical case (reflection from a nonmoving wall) and in the case of waves of different amplitudes by a system of algebraic relations for the compression shocks. The reflection of a strong point-source spherical shock wave from a wall has been treated in [1, 2]. The present article examines the initial stage of wave collision for an arbitrary distribution of the parameters behind the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–48, September–October, 1971.The authors are grateful to V. P. Korobeinikov for a discussion of the results and to V. P. Kolgan for furnishing the numerical solutions.     

Simulation of hydroforming of steel tube made of metastable stainless steel

The Olson–Cohen model for strain-induced deformation, further developed by Stringfellow and others, has been calibrated together with a flow stress model for the plastic deformation of metastable stainless steel. Special validation tests for checking one of the limitations of the model have also been carried out. The model has been implemented into a commercial finite element code using a staggered approach for integrating the stress–strain relations with the microstructure model. Results from a thermo-mechanical coupled simulation of hydroforming of a tube have been compared with corresponding experiments. The agreement between experimental results of radial expansion and martensite fraction and the corresponding computed results is good.     

Analysis of shifting performance of power shuttle transmission

This study was conducted to investigate the effects on the shifting performance of the design parameters of a power shuttle tractor using a computer simulation technique. The EASY 5 models of the hydraulic control system and power shuttle transmission were developed, and combined with a tractor model to complete a simulation model for a power shuttle tractor. The models for the hydraulic control system and power shuttle transmission were verified using an experimental power train constructed for the validation purpose.The design parameters included the terminal pressure and time for the modulation of the hydraulic control system, and forward speed, weight, shuttle gear ratio and torsional damping of the tractor. The shift performance was evaluated in term of the peak torques of the input shaft of the transmission and tractor axles, and power transmitted per unit area of the clutch and the time required for the power transmission.     

Stability of the in-plane bending mode of thin-walled framed structures

The paper outlines an approach to solving the stability problem for framed structures under arbitrary transverse loading. The available methods are limited by one law of variation in the bending moment responsible for loss of stability. The equilibrium equations for a thin-walled bar are integrated assuming that the bending moment is constant. The solution of the Cauchy problem is given in normal form. The arbitrary varying bending moment is approximated by a piecewise-constant function, which will be a little different from the original if the bar is partitioned into a great number of segments. The equations of the boundary-value problem for a discretized framed structure are derived using the boundary-element method. The critical forces and moments are determined from a transcendent equation. Numerical solutions are presented to demonstrate the high accuracy and efficiency of the approach. The solutions of test problems are in agreement with those obtained by Timoshenko     

Motion of bed-loads under the influence of flow of a liquid

Equations are obtained for the motion of a water-soil mixture in the layer next to the base. The water-soil mixture is modeled by means of a viscous-friable medium, and the acceleration of the mixture is assumed to be small and is not taken into account. The validity of the equations is confirmed by the experimental data for the following characteristics of uniform motion of a flow: for the speed of the start of particles touching on an even bed and with allowance for inclines of a bed, and also for the flow rate of loads on an even bed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 182–185.The author is grateful to A. G. Kulikovskii, V. Ya. Shkadov, and M. É. Églit for discussing the results of the study.     

On the theory of transverse bending of elastic plates

Departing from a self-contained two-dimensional formulation of the linear-theory problem of transverse bending of plates, three distinct topics are considered.The first of these concerns the integration problem for the case of orthotropy, specifically in regard to the factorization of a certain sixth-order master-equation.The second topic concerns the boundary layer aspects of contracted or reduced boundary conditions for the interior solution contribution for the case of isotropic plates. The analysis of this is based on a new form of the well-known general solution in terms of a deflection and a stress function variable, with this new form making it possible to distinguish between first- and second-order transverse shear deformation effects; the former being associated with the edge zone and the latter with the interior domain of the plate, with the shear correction terms for the interior being generalizations of the Timoshenko shear correction terms for beams.The third topic is a new system of contracted boundary conditions, both for the stress and for the displacement boundary value problem, in such a way that first-order transverse shear deformation effects are explicitly incorporated in the interior-domain solution contribution.     

Disintegration of axisymmetric body of revolution made of a material of complex chemical composition in a high-enthalpy airflow

We present a numerical solution of the problem of the disintegration in a high enthalpy airflow of an axisymmetric body of revolution made of a plastic of complex chemical composition. The system of partial differential equations for the laminar multicomponent boundary layer is solved by the pivotal method. The use of an experimental kinetic condition for the disintegration in place of the vapor pressure curve, which is usually used for single-component subliming materials, permits the use of a single technique for calculating both coking and noncoking materials of complex composition. Calculated is the composition of the products of combustion of materials consisting of the chemical elements, H, C, N, O. As an example the results are presented of the calculation of the disintegration of a sphere made from a material similar to textolite in composition.The author wishes to thank G. A. Tirskii for guidance in this study and E. A. Gershbeyn for discussions of the solution scheme.     

Draft of a nozzle with the circulating outflow of a vortical flow of gas

The presence of circulation in an outflowing gas leads to a change in the working parameters of a nozzle. The question of the mass flow rate and the draft of a nozzle without a diffusor (a point) for twisted flows has been studied theoretically and experimentally [1–6]. The use of nozzles with a supersonic part introduces a considerable degree of complication into the method for the analytical calculation of the draft characteristics and the program for their experimental investigation. In [2, 7], a theory of a nozzle is formulated for a model of a potential circulating flow of gas; in [5, 8], an electronic computer was used to solve the complete system of the equations of gasdynamics for the motion of a rotating flow along a nozzle; in [7, 9], an investigation was made of a variational problem of the shaping of a diffusor for a circulation flow. The calculation of the draft, carried out in the above-mentioned communications (with the exception of [2], in which a study was made of a partial model of an eddyless rotational motion), is bound up with labor-consuming computer calculations. In the present article, in a development of [3, 6], a quasi-one-dimensional theory of a supersonic nozzle for a vortical flow of gas is formulated and verified experimentally.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–149, September–October, 1975.     

The theoretical study of the efficiency of diffusion deposition of nanoaerosols in the extended range of the Peclet numbers

The efficiencies of the diffusion deposition of nanoaerosols for a single fiber for the models of aerosol filter and wire mesh screen are studied numerically in the extended range of the Peclet number Pe. The rectangular periodic cell model for fluid flow and convective-diffusive transport of small aerosol particles is used. Most of the previous theoretical and experimental studies of single fiber diffusion deposition efficiency were for the case of Pe > 1. The array with uniform square or chess grid of fibers and of a row of circular cylindrical fibers are considered as the filter and wire mesh screen models. The flow and particles transport equations are solved numerically using the Boundary Element Method.The obtained numerical data are used to derive the approximate formulas for the deposition efficiency in the entire range of the Peclet number for the various porosities of the filter medium or distances between fibers in a wire mesh screen. The derived dependencies take into account nonlinearity of the deposition efficiency at the low Peclet numbers. The obtained analytical dependencies compare well with the numerical and experimental data.     

A lattice-based model of the kinetics of twin boundary motion

In this paper we derive a macroscopic kinetic law for twin boundary motion from a lattice dynamical model. The model is developed for compound and type-1 twins and it is explicitly illustrated for a Cu-Al-Ni shape memory alloy. The governing multiple-well energy is calculated using an effective interatomic potential; a Frenkel-Kontorowa type model is developed for the dynamics at the lattice scale; and a quasi-continuum approximation is used to determine the continuum-scale kinetics. The model predicts that compound twins in the Cu-Al-Ni shape memory alloy are an order of magnitude more mobile than type-1 twins which is consistent with experimental observations.     

Some Properties of the Boundary Value Problem of Linear Elasticity in Terms of Stresses

The relation between the classical formulation of linear elastic problems in displacements and the stress formulation proposed by Pobedria is studied. It is shown that if the Navier and Pobedria differential operators are elliptic then corresponding boundary value problems are equivalent. The values of parameters for which Pobedria's boundary value problem has the Fredholm property are found. The homogeneous Pobedria's system is considered as a spectral problem with Poisson's ratio as a spectral parameter. The points of the essential spectrum are found and classified. The example of solving Pobedria's system for the Lamé problem for a spherical shell is presented.     

Application of a microprocessor for acquisition of load,strain and acoustic-emission data

This paper describes an automatic system for acquisition, logging and analysis of stress, strain and acoustic-emission data. The complete system is a combination of several standard items of equipment and a newly developed intelligent data logger which has the capability to send data directly to a large-scale computer for reduction and plotting. The data logging and all interfacing with peripheral equipment are accomplished using digital electronics. The heart of the system is a four-bit microprocessor and digital cassette-tape unit. The system, which is controlled by instructions from a cathode-ray-tube terminal, has the capability to transmit data from the cassette unit to a large computer via a time-sharing aption. Typical results are presented for acoustic-emission count rate and total-count curves superimposed on stress-strain diagrams for boron/epoxy advanced composites.     

Experimental study of the aerodynamic characteristics of a low-aspect-ratio flat plate array in a configuration of interest for a tidal energy converter

Wind tunnel experiments were conducted for the flow around a single flat plate and through an array of three parallel flat plates at different angles of incidence to compare their lift and drag coefficients for several values of the Reynolds number around 10⁵ and for three aspect ratio values. The selected cascade configuration is of interest for a particular type of tidal hydrokinetic energy converter. The main differences in the lift and drag forces are discussed, finding that for a plate in a cascade the maximum lift coefficient takes place at a quite different angle of attack, depending on the aspect ratio. The optimal conditions for extracting power from a tidal current are analyzed.     

On the fundamental equations of piezoelasticity of quasicrystal media

The three-dimensional fundamental equations of elasticity of quasicrystals with extension to quasi-static electric effect are expresses in both differential and variational invariant forms for a regular region of quasicrystal material. The principle of conservation of energy is stated for the regular region and the constitutive relations are obtained for the piezoelasticity of material. A theorem is proved for the uniqueness in solutions of the fundamental equations by means of the energy argument. The sufficient boundary and initial conditions are enumerated for the uniqueness. Hamilton’s principle is stated for the regular region and a three-field variational principle is obtained under some constraint conditions. The constraint conditions, which are generally undesirable in computation, are removed by applying an involutory transformation. Then, a unified variational principle is obtained for the regular region, with one or more fixed internal surface of discontinuity. The variational principle operating on all the field variables generates all the fundamental equations of piezoelasticity of quasicrystals under the symmetry conditions of the phonon stress tensor and the initial conditions. The resulting equations, which are expressible in any system of coordinates and may be used through simultaneous approximation upon all the field variables in a direct method of solutions, pave the way to the study of important dislocation, fracture and interface problems of both elasticity and piezoelasticity of quasicrystal materials.     

Slow rotation of a sphere in a confined volume of a dilute gas

The axially symmetric motion of a gas in a volume confined between an external immobile surface of rotation and a coaxial surface of a rotating sphere is considered. A solution is obtained by the moment method based on the Boltzmann equation with a collision integral of Maxwellian molecules. The gas-velocity distribution and an expression for the friction torque exerted on the sphere are obtained for arbitrary Knudsen numbers and for an arbitrary shape of the outer surface. The proportionality of the gas slip velocity over the surface of the sphere to the friction strain is shown. The friction torque is investigated for specific shapes of the outer surface. The motion of a gas filling the space between concentric spheres, each of which rotates about an arbitrary axis, is treated. In the limiting case of small Knudsen numbers the expressions obtained are compared with the corresponding results for a continuous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–124, July–August, 1978.The authors are grateful to the participants of the seminars guided by G. I. Petrov and A. M. Golovnyi for discussions concerning this work.     

Determination of the size of the representative volume element for random composites: statistical and numerical approach

The representative volume element (RVE) plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties. A quantitative definition of its size is proposed in this work. A RVE size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume V of microstructure that one is able to consider. It is shown to depend on the investigated morphological or physical property, the contrast in the properties of the constituents, and their volume fractions. The methodology is applied to a specific random microstructure, namely a two-phase three-dimensional Voronoı̈ mosaic. Finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity. The volumes are subjected to homogeneous strain, stress or periodic boundary conditions. The effective properties can be determined for large volumes and a small number of realizations. Conversely, smaller volumes can be used providing that a sufficient number of realizations are considered. A bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions. The variance of computed apparent properties for each volume size is used to define the precision of the estimation. The key-notion of integral range is introduced to relate this error estimation and the definition of the RVE size. For given wanted precision and number of realizations, one is able to provide a minimal volume size for the computation of effective properties. The results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision. The RVE sizes found for elastic and thermal properties, but also for a geometrical property like volume fraction, are compared.     

Theory of Short-Term Microdamageability of Granular Composite Materials

The theory of microdamageability of granular composites is outlined through the simulation of microdamages in the components by pores filled with compression-resisting particles of a destroyed material. The damage criterion for a microvolume of a component is taken in the Schleicher–Nadai form, which allows for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of Weibull-distributed coordinates. The stress–strain state and the efficient properties of the material are determined from the stochastic equations of elastic theory for a granular composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the components. Nonlinear diagrams of the concurrent processes of deformation in the granular material and microdamage in the matrix are plotted. The effect of the physical and geometrical parameters on them is studied     

Steady motion of a rigid disk of finite thickness on a horizontal plane

The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady-state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of ground and it is shown that the possible steady motion of a disk is either on a straight line or in a circle. Oscillations about steady state are discussed and conditions for stable motion established. The bifurcations of steady motions on a smooth surface are also considered.     

Asymptotic form of the problem of nonsymmetrical proper vibrations of a circular-conic al shell

The problem concerning nonsymmetric proper vibrations of a circular-conical shell with a vertex is separated into two parts, one being the determination of an edge-effect type of solution, and the other being the determination of a more slowly varying solution. The ranges of wavelengths for which the separation in question becomes asymptotically accurate as the thickness of the shell tends to zero are indicated. The first solution is written down explicitly; the second is obtained for a free and for a swivel-supported boundary by numerical methods. The numerical solution indicates that the system of equations governing the slowly varying part of the solution has a winding point of a rather complicated structure.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 135–142, March–April, 1973.