Vol 59, No 2 (2018)

Exact solutions of a nonlinear Boltzmann kinetic equation with a source are constructed in the case of an isotropic distribution function and Maxwell model of isotropic scattering. These solutions are constructed with the use of an equivalence group such that one of its transformations uniquely identifies the class of the source functions that are linear in terms of the distribution function; moreover, the transformed equation has a zero right side. As a result, invariant solutions of the type of the Bobylev–Krook–Wu solutions can be explicitly found, in particular, those that admit physical interpretation.

The nonlinear integral model of a turbulent thermal is extended to the case of the horizontal component of its motion relative to the medium (e.g., thermal floating-up in shear flow). In contrast to traditional models, the possibility of a heat source in the thermal is taken into account. For a piecewise constant vertical profile of the horizontal velocity of the medium and a constant vertical velocity shear, analytical solutions are obtained which describe different modes of dynamics of thermals. The nonlinear interaction between the horizontal and vertical components of thermal motion is studied because each of the components influences the rate of entrainment of the surrounding medium, i.e., the growth rate of the thermal size and, hence, its mobility. It is shown that the enhancement of the entrainment of the medium due to the interaction between the thermal and the cross flow can lead to a significant decrease in the mobility of the thermal.

The dynamics of a heavy cylindrical body in a liquid-filled horizontal cylindrical cavity with a time-varying rotation rate is experimentally investigated. The body is near the cavity boundary under a centrifugal force and undergoes solid-body rotation together with the liquid and the cavity at a fixed rotation rate. The dependence of the body dynamics on the amplitude and frequency of modulation of the rotation rate is investigated. It is found that at a critical amplitude of modulation (at definite frequency), the heavy body repulses from the cavity boundary and comes into a steady state at some distance from the wall. It is found that the average lift force (repulsive one) is generated by the azimuthal oscillation of the body in the rotating frame of reference and manifests itself at a distance comparable to the thickness of the viscous boundary layer. In the experiments, we observed azimuthal drift of the body due to asymmetric azimuthal oscillations of the body. In the limit of high frequency of the rotation rate modulation, the dependence of the lift force coefficient on the gap between the body and the wall is determined.

An invariant submodel of gas dynamics equations constructed on a three-dimensional subalgebra with a projective operator for the case of monatomic gas is under consideration. The submodel is reduced to an Abel equation, with integral curves constructed for it. For a separatrix of a saddle, an approximate solution is studied. Such solutions describe the vortex scattering of gas along plane curves placed on the surface of revolution.

This paper consideres the behavior of a semi-infinite ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a load moving with constant velocity along the edge of the cover at some distance from it. The ice cover is modeled by a thin elastic plate of constant thickness. In a moving coordinate system, the deflection of the plate is assumed to be steady. An analytic solution of the problem is obtained using the Wiener–Hopf technique. The wave forces, the deflection of the plate, and the elevation of the free surface of the fluid at different velocities of the load are investigated.

The problem of unsteady coupled heat and mass transfer in the course of motion of a spherically blunted conical body fabricated with the use of thermal protection materials is considered. Numerical integration is applied to study the characteristics of heat and mass transfer at constant stagnation parameters (Mach number 6, altitude 15 km, and flight time 600 s), which impose severe constraints on the choice of materials for thermal protection. It is demonstrated that the use of advanced ceramic materials ensures an admissible temperature regime and maintaining the initial geometry of the body, including its motion at an angle of attack.

This paper analyzes the effect of the time-dependent shape of a load pulse on the spall strength of materials. Within the framework of a classical one-dimensional scheme, triangular pulses with signal rise and decay portions and with no signal rise portions considered. Calculation results for the threshold characteristics of fracture for rail steel are given. The possibility of optimization of fracture by selecting a loading time with the use of an introduced characteristic of dynamic strength (pulse fracture capacity) is demonstrated. The study is carried out using a structure–time fracture criterion.

The one-dimensional dynamic problem of the theory of large elastic–plastic deformations is considered for the interaction of an unloading wave with an elastic–plastic boundary. It is shown that before the occurrence of the unloading wave, the increasing pressure gradient leads to quasistatic deformation of the elasti©viscoplastic material filling the round tube, which is retained in the tube due to friction on its wall, resulting in the formation of near-wall viscoplastic flow and an elastic core. The unloading wave is initiated at the moment of the onset of slippage of the material along the inner wall of the tube. Calculations were conducted using the ray method of constructing approximate solutions behind strong discontinuity surfaces, and ray expansions of the solutions behind the cylindrical surfaces of discontinuities were obtained.

A closed mathematical model is formulated, which takes into account elastoplastic strains and the medium capability of accumulating the energy of internal self-balanced stresses. Satisfaction of the diffeomorphism postulate (assumption of displacement field smoothness) is not required; as a result, the strains depend on the stresses and second derivatives of the stresses with respect to the coordinates. The model involves a linear structural parameter. Relations that take into account local bending of the elementary volumes of the medium are derived.

A previously developed technique is used to solve problems of strength and stability of discretely reinforced noncircular cylindrical shells made of a composite material with allowance for the moments and nonlinearity of their subcritical stress–strain state. Stability of a reinforced bay of the aircraft fuselage made of a composite material under combined loading with bending and twisting moments is studied. The effects of straining nonlinearity, stiffness of longitudinal ribs, and shell thickness on the critical loads that induce shell buckling are analyzed.

A dynamic problem for an elastic space with a semi-infinite crack which suddenly begins to grow at a constant rate is considered. At the initial time, the crack faces at some distance from the crack tip are subjected to normal concentrated forces stretching the crack. The forces move along the crack faces at a speed different from that of the crack tip. The stress intensity factor is calculated. Various special cases are examined.

In the original publication, the second formula on page 1077 was misspelled. It should read:

In the original publication, there are several misprints.

1. The author’s affilation was misspelled. It should read “V. E. Zalizniak^a,b, O. A. Zolotov^a,b, and I. I. Ryzhkov^a,b” instead of “V. E. Zalizniak^a,b, O. A. Zolotov^a,b, and I. I. Ryzhkov^b.”

2. In Abstract, it should read “It is shown that the calculated parameters of ions hydration shells are in good agreement with the theoretical and experimental data at salt concentrations up to 1 mol/kg” instead of “It is shown that the calculated values of the hydration shells of ions parameters are in good agreement with the theoretical and experimental data at a salt concentration of 1 mol/kg.”

3. In Introduction (page 41, second paragraph), it should read “The intermolecular interaction between two water molecules is computed using the Lennard-Jones potential with just a single interaction point per molecule” instead of “Interaction of water molecules is described by the Lennard-Jones potential.”

4. In Section 3.4 (page 46, second paragraph), it should read “The temperature dependence of salt solutions density was investigated in [26] using the interaction potential based on the SPC/E water model” instead of “The temperature dependence of the density of the salt solutions of was investigated in [26] using the interaction potential based on the SPC/E water model.”

5. In Conclusions (page 49, second paragraph), it should read “The proposed interaction potential can be used in large-scale to model flows of ionic solutions in nanostructures” instead of “The proposed interaction potential can be in large-scale calculations to model flows of ionic solutions in nanostructures.”

6. In third paragraph, it should read “The calculations were performed at the Center of High-Performance Computing of the Siberian Federal University” instead of “The calculations were performed at the Center of High- Performance Calculations of the Siberian Federal University.”