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An explicit asymptotic model extracting the contribution of a surface wave to the dynamic response of a viscoelastic half-space is derived. Fractional exponential Rabotnov’s integral operators are used for describing of material properties. The model is derived by extracting the principal part of the poles corresponding to the surface waves after applying Laplace and Fourier transforms. The simplified equations for the originals are written by using power series expansions. Padè approximation is constructed to unite short-time and long-time models. The form of this approximation allows to formulate the explicit model using a fractional exponential Rabotnov’s integral operator with parameters depending on the properties of surface wave. The applicability of derived models is studied by comparing with the exact solutions of a model problem. It is revealed that the model based on Padè approximation is highly effective for all the possible time domains. [ABSTRACT FROM AUTHOR]

Indentation of an elastic half-space with functionally graded coating by a rigid flat punch is studied. The half-plane is additionally subjected to distributed tangential stresses. Tangential stresses are represented in a form of Fourier series. The problem is reduced to the solution of two dual integral equations over even and odd functions describing distribution of unknown normal contact stresses. The solutions of these dual integral equations are constructed by the bilateral asymptotic method. Approximated analytical expressions for contact normal stresses are provided. [ABSTRACT FROM AUTHOR]

The 2-D problem of an infinite elastic solid with a nanoinclusion of a different from circular shape is solved. The interfacial stresses are acting at the interface. Contact of the inclusion with the matrix satisfies the ideal conditions of cohesion. The generalized Laplace – Young law defines conditions at the interface. To solve the problem, Gurtin – Murdoch surface elasticity model, Goursat – Kolosov complex potentials and the boundary perturbation method are used. The problem is reduced to the solution of two independent Riemann – Hilbert’s boundary problems. For the circular inclusion, hypersingular integral equation in an unknown interfacial stress is derived. The algorithm of solving this equation is constructed. The influence of the interfacial stress and the dimension of the circular inclusion on the stress distribution and stress concentration at the interface are analyzed. [ABSTRACT FROM AUTHOR]

The paper presents an analysis of the effect of the heat transfer process in metals on the parameters of thermal stresses under pulsed laser action. The dynamic problem of thermoelasticity is considered as a two-stage process. The first stage is determined by the time of action of the radiation pulse. The second stage is caused by the dynamics of the heat transfer process after the end of the laser pulse. For showing the continuity of thermoelastic and thermoelectric processes, the analysis of the electronic mechanism for the propagation of heat in metals and the results of experimental studies of these processes are presented. The results of the experiments demonstrate the high sensitivity of the parameters of thermoelastic and thermoelectric pulses to the microstructure of metals. [ABSTRACT FROM AUTHOR]

The problem of mechanochemical corrosion of a vertically standing or hanging elastic tube under its own weight is considered. The influence of a local smooth reduction in the initial thickness of the tube (up to 12.5%) on its durability and manifestation of the mechanochemical effect is studied. The numerical analysis revealed that despite the fact that the presence of a defect reduces the service life of the tube, it only slightly intensifies the mechanochemical effect compared to the same initially perfect tube; therefore, for relatively short, both initially perfect and defective tubes this effect can be ignored. For relatively short tubes, a permissible initial thinning of the tube wall can be taken into account by consideration of the same initially perfect tube with the ultimate residual thickness increased by the depth of the defect. However, for long tubes this approach gives a slightly overstated durability. The effect of the initial thickness of the tube was also investigated. [ABSTRACT FROM AUTHOR]

This work presents studies the effect of ultrafine-grained (UFG) structure on impact toughness and dynamic compression of pure copper M1 (99.9%). The UFG structure was provided by means of equal-channel angular pressing (ECAP) on the Conform scheme with four and eight passes. Impact toughness tests on samples with U-shaped notch were performed using a drop weight impact machine. Dynamic compression test of cylindrical samples were performed with a setup with the Split-Hopkinson pressure bar (SHPB-20) by the Kolsky method. The results showed that the impact toughness of the UFG copper states was not less than that of the coarse-grained (CG) counterpart. Moreover, the fracture process of the UFG material requires more energy. An increase of compression strain rate by 6 orders resulted in the well-known strain-rate dependence of the yield strength for the CG material and the UFG material after eight ECAP passes. The yield strength of the material after four ECAP passes remained at the level corresponding to a quasi-static loading. [ABSTRACT FROM AUTHOR]

A thin-walled spherical shell subjected to simultaneous action of internal and external pressure, nonuniform heating and outside mechanochemical corrosion is considered. It is assumed that the shell is homogeneous, isotropic and linearly elastic. The rate of corrosion is linearly dependent on the equivalent stress, which is the sum of mechanical and temperature stress components. Paper presents a new analytical solution, which takes into account the effect of the internal and external pressure values themselves, not only their difference. At the same time, the new solution has a rather simple form as compared to the results based on the solution to the Lame problem for a thick-walled sphere under pressure. The solution obtained can serve as a benchmark for numerical analysis and for a qualitative forecast of durability of the vessel. [ABSTRACT FROM AUTHOR]

The paper suggests mathematical models of decaying vibrations in layered anisotropic plates and orthotropic rods based on Hamilton variation principle, first-order shear deformation laminated plate theory (FSDT), as well as on the viscous-elastic correspondence principle of the linear viscoelasticity theory. In the description of the physical relationships between the materials of the layers forming stiff polymeric composites, the effect of vibration frequency and ambient temperature is assumed as negligible, whereas for the viscous-elastic polymer layer, temperature-frequency relationship of elastic dissipation and stiffness properties is considered by means of the experimentally determined generalized curves. Mitigation of Hamilton functional makes it possible to describe decaying vibration of anisotropic structures by an algebraic problem of complex eigenvalues. The system of algebraic equation is generated through Ritz method using Legendre polynomials as coordinate functions. First, real solutions are found. To find complex natural frequencies of the system, the obtained real natural frequencies are taken as input values, and then, by means of the 3rd order iteration method, complex natural frequencies are calculated. The paper provides convergence estimates for the numerical procedures. Reliability of the obtained results is confirmed by a good correlation between analytical and experimental values of natural frequencies and loss factors in the lower vibration tones for the two series of unsupported orthotropic rods formed by stiff GRP and CRP layers and a viscoelastic polymer layer. Analysis of the numerical test data has shown the dissipation & stiffness properties of heterogeneous composite plates and rods to considerably depend on relative thickness of the viscoelastic polymer layer, orientation of stiff composite layers, vibration frequency and ambient temperature. [ABSTRACT FROM AUTHOR]

The paper discusses the possibility to control coupled bending-twisting vibrations of anisotropic composite wing by means of the monoclinic structures in the reinforcement of the plating. Decomposing the potential straining energy and kinetic energy of natural vibration modes into interacting and non-interacting parts, it became possible to introduce the two coefficients that integrally consider the effect of geometry and reinforcement structure upon the dynamic response parameters of the wing. The first of these coefficients describes the elastic coupling of the natural vibration modes, the second coefficient describes the inertial one. The paper describes the numerical studies showing how the orientation of considerably anisotropic CRP layers in the plating affects natural frequencies, loss factors, coefficients of elastic and inertial coupling for several lower tones of natural bending-twisting vibrations of the wing. Besides, for each vibration mode, partial values of the above mentioned dynamic response parameters were determined by means of the relationships for orthotropic structures where instead of “free” shearing modulus in the reinforcement plant, “pure” shearing modulus is used. Joint analysis of the obtained results has shown that each pair of bending-twisting vibration modes has its orientation angle ranges of the reinforcing layers where the inertial coupling caused by asymmetry of the cross-section profile with respect to the main axes of inertia decreases, down to the complete extinction, due to the generation of the elastic coupling in the plating material. These ranges are characterized by the two main features: 1) the difference in the natural frequencies of the investigated pair of bending-twisting vibration modes is the minimum and 2) natural frequencies of bending-twisting vibrations belong to a stretch restricted by corresponding partial natural frequencies of the investigated pair of vibration modes. This result is of practical importance because it enables approximate analysis of real composite wings with complex geometry in the existing commercial software packages. [ABSTRACT FROM AUTHOR]

The additive process of forming a semicircular arched structure by means of layer-by-layer addition of material to its inner surface is simulated. The impact of this process running mode on the development of the technological stresses fields in the structure being formed under the action of gravity under properties of the material creep and aging is examined. In the framework of the linear mechanics of accreted solids a mathematical model of the process under study is offered and numerical experiments are conducted. It is shown that the stress-strain state of the additively formed heavy objects decisively depends on their formation mode. Various practically important trends and features of this dependence are studied. [ABSTRACT FROM AUTHOR]

A criterion is proposed that determines the moment when the growth pattern of the monotonic numerical sequence varies from the linear to the parabolic one. The criterion is based on the comparison of squares of errors for the linear and the incomplete quadratic approximation. The approximating functions are constructed locally, only at those points that are located near a possible change in nature of the increase in the sequence. [ABSTRACT FROM AUTHOR]

The problem of vibrations of a thin-walled elastic cylindrical shell reinforced by frames of different rigidity is investigated. The solution for the case of the clamped shell edges was obtained by asymptotic methods and refined by the finite element method. Rings with zero eccentricity and stiffness varying along the generatrix of the shell cylinder are considered. Varying the optimal coefficients of the distribution functions of the rigidity of the frames and finding more precise parameters makes it possible to find correction factors for analytical formulas of approximate calculation. [ABSTRACT FROM AUTHOR]

Deformation of reinforced square plate under external pressure is considered. The averaged fourth-order partial differential equation for the plate deflection w is obtained. The new mathematical model of the plate is offered. Asymptotic averaging and Finite Elements Method (ANSYS) are used to get the values of normal deflections of the plate surface. The comparison of numerical and asymptotic results is performed. [ABSTRACT FROM AUTHOR]

The present study is devoted to the problem of formulation of conservation laws in divergent form for hyperbolic thermoelastic continua. The field formalism is applied to study the problem. A natural density of thermoelastic action and the corresponding variational least action principle are formulated. A special form of the first variation of the action is employed to obtain 4-covariant divergent conservation laws. Differential field equations and constitutive laws are derived from a special form of the first variation of the action integral. The objectivity of constitutive equations is provided by the rotationally invariant forms of the Lagrangian employed. [ABSTRACT FROM AUTHOR]

Conventional drilling of rocks can generate significant damage in the drilled material; a material layer is often split off a back surface of a sample during drilling, negatively affecting its strength. To improve finish quality, ultrasonically assisted drilling (UAD) was employed in two rocks - sandstone and marble. Damage areas in both materials were reduced in UAD when compared to conventional drilling. Reductions in a thrust force and a torque reduction were observed only for UAD in marble; ultrasonic assistance in sandstone drilling did not result in improvements in this regard. [ABSTRACT FROM AUTHOR]

The axisymmetric contact problem with fretting wear for an elastic foundation with a longitudinally nonuniform (surface nonuniform) coating and a rigid punch with a rough foundation has been solved for the first time. The case of linear wear is considered. The nonuniformity of the coating and punch roughness are described by a different rapidly changing functions. This strong nonuniformity arises when coatings are deposited using modern additive manufacturing technologies. The problem is reduced the solution of an integral equation with two different integral operators: a compact self-adjoint positively defined operator with respect to the coordinate and the non-self-adjoint integral Volterra operator with respect to time. The solution is obtained in series using the projection method of the authors. The efficiency of the proposed approach for constructing a high-accuracy approximate solution to the problem (with only a few expansion terms retained) is demonstrated. [ABSTRACT FROM AUTHOR]

The exact analytical solution of nonlinear problem of elasticity (plane stress and plane strain) for a plane with elastic elliptic inclusion is obtained. The external constant nominal (Piola) stresses are given at infinity of a plane. The continuity conditions for the stress and displacement are satisfied on the boundary of the inclusion. The mechanical properties of the plane and inclusion are described by a model of semi-linear material. For this material methods of the theory of functions of a complex variable are using for solving nonlinear plane problems. The stresses and displacements are expressed through two analytic functions of a complex variable, which are defined from the nonlinear boundary conditions on a boundary of inclusion. The assumption is made that the stress state of the inclusion is homogeneous (the tensor of nominal stresses is constant). The hypothesis has allowed to reduce a difficult nonlinear problem of elliptic inclusion to the solution of two simpler problems (first and second) for a plane with an elliptic hole. The validity of this hypothesis has proven to that obtained solution precisely satisfies to all equations and boundary conditions of a problem. The similar hypothesis was used earlier for solving linear and nonlinear problems of elliptic inclusion. Using general solution, the solutions of some particular nonlinear problems are obtained: a plane with a free elliptic hole and a plane with a rigid inclusion. The stresses are calculated on the contour of inclusion for different material parameters. [ABSTRACT FROM AUTHOR]

The main purpose of this work was the development of an experimental technique for search and analysis of pore formation in the presented material. Geometry of the samples, the procedure of experiment and processing the samples for investigation were developed. [ABSTRACT FROM AUTHOR]

The unconventional approach to the plane elasticity problem for a crack near the curved surface is presented. The solution of the problem is considered in the form of the sum of solutions of two auxiliary problems. The first one describes the plane with a crack, whose surfaces are loaded by some unknown self-balanced force p(x). The second problem is dealing with the semi-infinite region with the boundary conditions equal to the difference of boundary conditions of the problem to be sought and the solution of the first problem on the region border. The unknown function p(x) is supposed to be approximated with the sufficient level of accuracy by N order polynomial with complex coefficients. This paper is aimed to determine the critical loads causing the spontaneous growth of cracks. The angles of propagation of the stationary cracks located in the region with a ledge or a cut are found. The influence of length of a crack on the bearing ability of an elastic body with the curved surface is investigated. The effect of a form of the concentrator and orientation of a crack to the fracture load subject to the different combinations of forces acting both on a surface of a crack and at infinity is analysed. The results of this research can be applied for calculation of the durability of thin-walled vessels of pressure, e.g., chemical reactors, in order to ensure their ecological safety. [ABSTRACT FROM AUTHOR]

The study of a deformation features of metal alloys which are sensitive to tension or compression loading is an important technical challenge in the design and creation of a new shipbuilding and aircraft constructions. We use a mathematical model for the elastic-plastic bending of such material where SD(strength-different) parameter is taken into account. The problem is solved analytically and numerically. As an example of the material with the SD-effect the steel alloy is considered. [ABSTRACT FROM AUTHOR]

The present paper is devoted to mathematical modelling of complex continua deformations considered as immersed in an external plane space. The complex continuum is defined as a differential manifold supplied with metrics induced by the external space. A systematic derivation of strain tensors by notion of isometric immersion of the complex continuum into a plane space of a higher dimension is proposed. Problem of establishing complete systems of irreducible objective strain and extrastrain tensors for complex continuum immersed in an external plane space is resolved. The solution to the problem is obtained by methods of the field theory and the theory of rational algebraic invariants. Strain tensors of the complex continuum are derived as irreducible algebraic invariants of contravariant vectors of the external space emerging as functional arguments in the complex continuum action density. Present analysis is restricted to rational algebraic invariants. Completeness of the considered systems of rational algebraic invariants is established for micropolar elastic continua. Rational syzygies for non-quadratic invariants are discussed. Objective strain tensors (indifferent to frame rotations in the external plane space) for micropolar continuum are alternatively obtained by properly combining multipliers of polar decompositions of deformation and extra-deformation gradients. The latter is realized only for continua immersed in a plane space of the equal mathematical dimension. [ABSTRACT FROM AUTHOR]

In this paper, we present an approach to the stress concentration analysis of an isotropic ultra-thin film coating with thickness from hundreds to a few nanometers coherently bonded to a substrate through an undulated interphase region. To capture the size dependence of the mechanical properties observed in nanostructured materials, we use Gurtin-Murdoch model in which surface and interphase domains are represented as negligibly thin layers ideally adhering to the bulk phases. This model is characterized by traction discontinuities at the surface and interface where the additional surface and interface stresses appear due to different bond lengths, angles and charge distribution of surface and interface atoms. In the case of plane strain conditions, the elasticity solution for a four-phase system is derived in the terms of the Goursat-Kolosovs complex potentials. [ABSTRACT FROM AUTHOR]

Here, we use the theory of surface elasticity to extend the morphological instability analysis of stressed solids developed in the works of Asaro, Tiller, Grinfeld, Srolovitz and many others. Within the framework of Gurtin-Murdoch model, the surface phase is assumed to be a negligibly thin layer with the elastic properties which differ from those of the bulk material. We consider the mass transport mechanism driven by the variation of surface and bulk energy along undulated surface of stressed solid. The linearized surface evolution equation is derived in the case of plane strain conditions and describes the amplitude change of surface perturbations with time. A parametric analysis of this equation leads to the definition of critical conditions which depend on undulation wavelength, residual surface stress, applied loading, surface and bulk elastic constants and predict the surface morphological stability. [ABSTRACT FROM AUTHOR]

The paper considers the stability problem of an arch shock absorber made of a rubber-like material. As a model, the nonlinear theory of thin shells from elastomers K.F. Chernykh is used. The case of symmetrical and asymmetrical deformation of an arch shock absorber under symmetrical compression is investigated. The possibility of asymmetric bifurcation is evaluated depending on the boundary conditions. [ABSTRACT FROM AUTHOR]

The 2-D problem of elasticity for bimaterial with planar interface under the periodic set of point forces is considered at the nanoscale. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation, are used. The solution of this equation and explicit formulas for stress field (Green functions) are derived in terms of Fourier series. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distances from the interface. [ABSTRACT FROM AUTHOR]

A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method. [ABSTRACT FROM AUTHOR]

Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green’s function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points. [ABSTRACT FROM AUTHOR]

Small free low-frequency vibrations of a rotating closed cylindrical shell which is in a contact with rigid cylindrical rollers are considered. Assumptions of semi-momentless shell theory are used. By means of the expansion of solutions in truncated Fourier series in circumference coordinate the system of the algebraic equations for the approximate calculation of the vibration frequencies and the mode shapes is obtained. The algorithm for the evaluation of frequencies and vibration modes based on analytical solution is developed. In particular, the lowest frequencies of thin cylindrical shell, representing greatest interest for applications, were found. Approximate results are compared with results of numerical calculations carried out by the Finite Elements Analysis. It is shown that the semi-momentless theory can be used for the evaluation of the low frequencies of a cylindrical shell rotating on rollers. [ABSTRACT FROM AUTHOR]

The choice of Gibbs’ potential for microstructural modeling of FCC ↔ HCP martensitic transformation in FeMn-based shape memory alloys is discussed. Threefold symmetry of the HCP phase is taken into account on specifying internal variables characterizing volume fractions of martensite variants. Constraints imposed on model constants by thermodynamic equilibrium conditions are formulated. [ABSTRACT FROM AUTHOR]

The singular plane problems of nonlinear elasticity (plane strain and plane stress) are considered for bi-material infinite plane with interface crack. The plane is formed of two half-planes. Mechanical properties of half-planes are described by the model of semi-linear material. Using model of this harmonic material has allowed to apply the theory of complex functions and to obtain exact analytical global solutions of some nonlinear problems. Among them the problem of bi-material plane with the stresses and strains jumps at an interface is considered. As an application of the problem of jumps, the problem of interface crack is solved. The values of nominal (Piola) and Cauchy stresses and displacements are founded. Based on the global solutions the asymptotic expansions are constructed for stresses and displacements in a vicinity of crack tip. As an example the case of a free crack in bi-material plane subjected to constant stresses at infinity is studied. As a special case, the analytical solution of the problem of a crack in a homogeneous plane is obtained from the problem for bi-material plane with interface crack. [ABSTRACT FROM AUTHOR]

The present study is devoted to the problem of residual stresses calculation in AM fabricated ball during heating. Strains of the ball are assumed to be small, which allows to use the apparatus of the theory of thermoelastoplastic akin to Prandtl and Reuss. The problem of the evolution of the field of residual stresses in the ball at a given temperature on its external border is solved. The heat conduction equation and the equilibrium equations may be independently integrated when the hypothesis of the insignificance of the coupled effects of thermal and mechanical processes is adopted. The fields of residual stresses and displacements are computed. [ABSTRACT FROM AUTHOR]

This paper considers the constitutive relations of the nanoplate theory with surface stresses taken into account according to the original or complete Gurtin–Murdoch (GM) model and according to the simplified strain-consistent GM model (which does not include any non-strain terms in the surface stress–strain relation). It is shown that the potential energy of a deformed nanoplate according to both GM models preserves the classical structure using the redefined elastic moduli (effective tangential and flexural elastic properties, which contain the characteristics of bulk phase and a surface). This allows to apply the known solutions and methods from macroplates to nanoplates. As example, it is shown that the critical load of the compressive buckling of a nanoplate according to the complete and strain-consistent GM models has the difference between two solutions no more than 1.5%. [ABSTRACT FROM AUTHOR]

The formulation and analysis of ecological problems involves the mathematical modeling, when some assumptions concerning the nature of the processes are introduced. These assumptions must be justified. In the present paper the effect of the form of the initial domain occupied with a diffusing substance on the process of diffusion is studied. It’s shown that the form of the initial domain plays unimportant role and it may be modeled as semi-sphere, for which the problem has analytical solution. That solution may serves as the zeroth approximation in modeling of actual ecological problem taking into account the relief of the bottom and the bottom currents. [ABSTRACT FROM AUTHOR]

A vibration protection system under consideration consists of a payload connected to a vibrating housing by shape memory alloy (SMA) slotted springs. To provide an arrest function two permanent magnets are inserted into the system. The slotted SMA elements are preliminary deformed in the martensitic state. Activation of one element by heating initiates force and displacement generation, which provide an arrest of the payload by magnets. The magnets also secure the arrest mode after cooling of the SMA element. Activation of the other element results in uncaging of the payload and switching to the vibration isolation mode. Computer simulations of arrest and uncaging when the housing is quiescent or producing sine-wave displacements were carried out. Functional-mechanical behavior of SMA parts was described by means of a microstructural model. [ABSTRACT FROM AUTHOR]

Microstructural simulation of mechanical behavior of shape memory alloy samples at cyclic loading in the pseudoelastic state has been carried out. Evolution of the oriented and scattered deformation defects leading to damage accumulation and resulting in the fatigue fracture has been taken into account. Simulations were performed for the regime of loading imitating that for endovascular stents: preliminary straining, unloading, deformation up to some mean level of the strain and subsequent mechanical cycling at specified strain amplitude. Dependence of the fatigue life on the loading parameters (pre-strain, mean and amplitude values of strain) has been obtained. The results show a good agreement with available experimental data. [ABSTRACT FROM AUTHOR]

A microstructural model of shape memory alloys (SMA) describing their deformation and fatigue fracture is presented. A new criterion of fracture has been developed which takes into account the effect of hydrostatic pressure, deformation defects and material damage. It is shown that the model can describe the fatigue fracture of SMA under various thermomechanical cycling regimes. Results of calculating the number of cycles to failure at thermocycling under a constant stress, at symmetric two-sided cyclic deformation, at straining-unloading cycles, at cycling in the regime of the thermodynamic cycles of a SMA working body in the hard (strain controlled) and soft (stress controlled) working cycles, is studied. Results of calculating the number of cycles to failure are presented for different parameters of these cycles. [ABSTRACT FROM AUTHOR]

The paper deals with the main positions of strict continuum model of compositions of shells of revolution smoothly connected with each other. Solutions of singular equations of the membrane conduct thermoelasticity for different species of compositions obtained in a closed form. The ability to eliminate discontinuities of the first kind of one of the tangential force on the lines of the distortion has been proved by using the additional local force impact or temperature. [ABSTRACT FROM AUTHOR]

This work analyzes buckling under action of external lateral pressure of a thin cylindrical shell with a curvelinear edge stiffened by identical rings. It is assumed that the rings may be considered as circular beams. A combination of asymptotic methods is applied to get approximate formulas for the critical pressure. The usage of asymptotic formulas for critical pressure allows obtaining the approximate relations for calculation of optimal stiffened shell parameters corresponding to the minimal value of its weight. [ABSTRACT FROM AUTHOR]

Vibrationally non-equilibrium flows of chemically homogeneous diatomic gases are considered under the conditions that the distribution of the molecules over vibrational levels differs significantly from the Boltzmann distribution. In such flows, molecular collisions can be divided into two groups: the first group corresponds to “rapid” microscopic processes whereas the second one corresponds to “slow” microscopic processes (their rate is comparable to or larger than that of gasdynamic parameters variation). The collisions of the first group form quasi-stationary vibrationally non-equilibrium distribution functions. The model kinetic equations are used to study the transport processes under these conditions. In these equations, the BGK-type approximation is used to model only the collision operators of the first group. It allows us to simplify derivation of the transport fluxes and calculation of the kinetic coefficients. Special attention is given to the connection between the formulae for the bulk viscosity coefficient and the sound velocity square. [ABSTRACT FROM AUTHOR]

The features of the nanofluid flows modeling are analyzed. In the first part the thermophysical properties (viscosity and thermal conductivity) of nanofluids are discussed in detailed. It was shown that the transport coefficients of nanofluids depend not only on the volume concentration of the particles but also on their size and material. The viscosity increases with decreasing the particle size while the thermal conductivity increases with increasing the particle size. The heat transfer of nanofluid in cylindrical channel and laminar-turbulent transition in some flows are considered. The heat transfer coefficient is determined by the flow mode (laminar or turbulent) of the nanofluid. However it was shown that adding nanoparticles to the coolant significantly influences the heat transfer coefficient. The laminar-turbulent transition begins in all cases earlier (at smaller Reynolds numbers) than for base fluid. In conclusion the possibility of the use of traditional similarity criteria are discussed. [ABSTRACT FROM AUTHOR]

One-dimensional non-equilibrium air flows in nozzles are studied on the basis of the state-to-state description of vibrational-chemical kinetics. Five-component mixture N2/O2/NO/N/O is considered taking into account Zeldovich exchange reactions of NO formation, dissociation, recombination and vibrational energy transitions. The equations for vibrational and chem-ical kinetics in a flow are coupled to the conservation equations of momentum and total energy and solved numerically for different conditions in a nozzle throat. The vibrational distributions of nitrogen and oxygen molecules, number densities of species as well as the gas temperature and flow velocity along a nozzle axis are analysed using the detailed state-to-state flow description and in the frame of the simplified one-temperature thermal equilibrium kinetic model. The comparison of the results showed the influence of non-equilibrium kinetics on macroscopic nozzle flow parameters. In the state-to-state approach, non-Boltzmann vibrational dis-tributions of N2 and O2 molecules with a plateau part at intermediate levels are found. The results are found with the use of the complete and simplified schemes of reactions and the impact of exchange reactions, dissociation and recombination on variation of vibrational level populations, mixture composition, gas velocity and temperature along a nozzle axis is shown. [ABSTRACT FROM AUTHOR]

The aim of this paper is to set a correct analytical calculation algorithm for molecule pair distribution function within a shock wave. Another purpose is to explain analytical nature of all fundamental factors of translational non- equilibrium high velocity overshoot effect. The analytical models of high-velocity non-equilibrium phenomenon in binary polyatomic gas mixtures are considered. The main results of numerical study of high velocity overshoot effect in shock-compressed gases are shown. Analytical results of the authors are successively presented. Sufficient conditions of a relative overshoot effect maximum for molecule pair distribution function are given. Analytical estimate of the value of this effect is suggested. [ABSTRACT FROM AUTHOR]

Theoretical models for the vibrational state-resolved Zeldovich reaction are assessed by comparison with the results of quasi-classical trajectory (QCT) calculations. An error in the model of Aliat is corrected; the model is generalized taking into account NO vibrational states. The proposed model is fairly simple and can be easily implemented to the software for non-equilibrium flow modeling. It provides a good agreement with the QCT rate coefficients in the whole range of temperatures and reagent/product vibrational states. The developed models are tested in simulations of vibrational and chemical relaxation of air mixture behind a shock wave. The importance of accounting for excitated NO vibrational states and accurate prediction of Zeldovich reactions rates is shown. [ABSTRACT FROM AUTHOR]

The fixed-time heliocentric trajectory optimization problem is considered for planar solar sail with minimum area. Necessary optimality conditions are derived, a numerical method for solving the problem is developed, and numerical examples of optimal trajectories to Mars, Venus and Mercury are presented. The dependences of the minimum area of the solar sail from the date of departure from the Earth, the time of flight and the departing hyperbolic excess of velocity are analyzed. In particular, for the rendezvous problem (approaching a target planet with zero relative velocity) with zero departing hyperbolic excess of velocity for a flight duration of 1200 days it was found that the minimum area-to-mass ratio should be about 12 m2/kg for trajectory to Venus, 23.5 m2/kg for the trajectory to Mercury and 25 m2/kg for trajectory to Mars. [ABSTRACT FROM AUTHOR]

An experimental facility for modeling of icing processes in various conditions (supercooled droplets, ice crystals and mixed-phase) is described and experimental results are presented. Some methods of icing processes characterization with non-dimensional coefficients are suggested. Theoretical model of a liquid film dynamics, mass and heat transfer during its movement on the model surface is presented. The numerical calculations of liquid film freezing and run-back ice evolution on the surface are performed. [ABSTRACT FROM AUTHOR]

The local equilibrium flows of five-component air mixtures are considered. Gas dynamic equations are derived from the kinetic equations for aggregate values of collision invariants. It is shown that the traditional formula for sound velocity is true in air mixtures considered with the chemical reactions and the internal degrees of freedom. This formula connects the square of sound velocity with pressure and density. However, the adiabatic coefficient is not constant under existing conditions. The analytical expression for this coefficient is obtained. The examples of its calculation in air mixtures of various densities are presented. [ABSTRACT FROM AUTHOR]

Shock wave structure in carbon dioxide is studied using different continuum models within the framework of one-temperature thermal equilibrium flow description. Navier-Stokes and Euler equations as well as commonly used Rankine-Hugoniot equations with different specific heat ratios are used to find the gas-dynamic parameters behind the shock wave. The accuracy of the Rankine-Hugoniot relations in polyatomic gases is assessed, and it is shown that they give a considerable error in the predicted values of fluid-dynamic variables. The effect of bulk viscosity on the shock wave structure in CO2 is evaluated. Taking into account bulk viscosity yields a significant increase in the shock wave width; for the complete model, the shock wave thickness varies non-monotonically with the Mach number. [ABSTRACT FROM AUTHOR]

Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established. [ABSTRACT FROM AUTHOR]

Results of the direct simulation Monte Carlo of 1D spherical and 2D axisymmetric expansions into vacuum of condens-ing water vapor are presented. Two models based on the kinetic approach and the size-corrected classical nucleation theory are employed for simulations. The difference in obtained results is discussed and advantages of the kinetic approach in comparison with the modified classical theory are demonstrated. The impact of clusterization on flow parameters is observed when volume fraction of clusters in the expansion region exceeds 5%. Comparison of the simulation data with the experimental results demonstrates good agreement. [ABSTRACT FROM AUTHOR]

The 3D turbulent supersonic flow over a body of revolution at various angles of attack α is studied numerically and experimentally. The body surface incorporates a forward-facing step near its midpart and a nose cone. Experiments were conducted in a wind tunnel of the Research Institute of Mechanics, Moscow State University, at the Mach number of 3 for various lengths L of the distance between the step and nose cone. Numerical simulations were performed with a finite-volume solver ANSYS CFX-15. The study reveals bands of α and L in which the pressure on the leeward side of step abruptly increases and exceeds the pressure on the windward side. [ABSTRACT FROM AUTHOR]