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Numerical modeling of a flow around a symmetrical thick drop-shaped airfoil in a non-stationary formulation was carried out at Reynolds numbers Re = 10⁴ ÷ 10⁵ and in the range of angles of attack α = –10 ÷ 10°. The calculations were performed in the approximation of the unsteady Reynolds-averaged Navier-Stokes equations (URANS) using the implicit large-eddy method (ILES). In the URANS approach, the position of the laminar-turbulent transition was determined based on the models k–kl–ω, k–ω–γ–Re_θ (Menter model) and (k–ω)-SST models with a given laminar flow region. It is shown that the position of the laminar-turbulent transition region has a significant impact on the flow structure and aerodynamic characteristics of the airfoil. Comparison of the results obtained using the ILES approach with experimental data showed that they are in good agreement. URANS calculations did not allow obtaining results consistent with experimental data. Fixing the laminar-turbulent transition point in the URANS calculation in some cases made it possible to correct the results.

Ceramic composites based on B₄C with a mole fraction of CrB₂ 0-30% were obtained by reactive hot pressing of a mixture of B₄C, Cr₂O₃, and nanofibrous carbon at a press force of 17.5 MPa, a temperature of 2000 °C and an exposure time of 10 min. The possibility of the chemical reduction reaction of metal oxide with boron carbide during hot pressing was studied. During the synthesis of CrB₂, the density of B₄C was found to increase due to the formation of the CrB₂-B₄C eutectic liquid phase. The relative density of all B₄C-CrB₂ composites obtained under these conditions exceeds 90%. The dependences of the microhardness and elastic modulus of samples on the concentration of the plastic phase were obtained. The dependence of the elastic modulus of the heterogeneous material on the volume fraction of chromium diboride taking into account porosity was determined by sequentially using the Reuss and Voigt averaging schemes

Uniaxial tension and three-point bending tests were performed for polymer composite samples made of Crystal 85-5 epoxy resin modified with MHG-4E (average particle size 5-15 µ m) and FV-530D (average particle size 25 µ m) photoluminescent powders. The dependence of the elastic modulus on the filler concentration was obtained. The photoluminescent properties of the resulting composites were studied. The dependence of the has been established afterglow intensity on the filler content in the composite was determined.

A new technique has been proposed and implemented that allows for time-frequency analysis of data obtained using the PIV method, taking into account the readings of the surface sensor of a hot-wire anemometer. The technique is based on calculating the correlation coefficients between the data obtained by the PIV method and the data from the hot-wire anemometer sensor, which were previously filtered in a given frequency range. Using this approach makes it possible to obtain data on the unsteady characteristics of flows throughout the entire measurement range in the frequency range, the boundaries of which extend beyond the boundaries of the frequency range of the PIV method. Using the proposed method, a study of non-stationary processes in the region of interaction of a shock wave with a boundary layer at the Mach number M = 1.43 was carried out.

A method of transition from the three-dimensional piezoelastic problem for a composite material to the one-dimensional problem for a piezoelastic beam is presented. This is done using an asymptotic method of homogenization based on the separation of fast and slow variables in the solution. A special feature of the problem is the presence of two small parameters, one of which characterizes the microstructure of the composite material, and the other the cross-sectional size. Averaged relations describing the piezoelastic beam and fast correctors were obtained. Their joint use makes it possible to correctly describe the total stress-strain state of the initial three-dimensional body. The proposed method is suitable for solving the three-dimensional problem of deformation of an extended bodies with an arbitrary periodic structure and new problems (e.g., the torsion problem) that have no analogues in the theory of piezoelastic plates.

The stress-strain elastic field in a square array of N non-overlapping circular inclusions is described by approximate analytical formulas. In particular, soft inclusions are studied by an asymptotic analysis. The case with N = 1 yields a regular square array of disks of radius r embedded in an elastic matrix. The computations of Natanzon and Filshtinsky are based on an infinite system of linear algebraic equations solved by the truncation method. The infinite system determines the Taylor series coefficients of the Kolosov-Muskhelishvili complex potentials. A method of functional equations is used to write the series coefficients in symbolic form up to terms of the order of O ( r ^2s) at a fixed value of s . Approximate analytical formulas for local elastic fields are derived.

A small-sized elastic isotropic strip-beam loaded with variable body and surface forces is considered. On the front surfaces, surface shear stress and inertia are taken into account within the framework of the Gurtin-Murdoch surface elasticity theory. Asymptotically correct equations describing the long-wavelength bending deformation of micro/nano-beams taking into account shears and surface effects are derived by asymptotic integration of the two-dimensional elasticity equations over the strip thickness. The influence of surface stress and inertia on the lower spectrum of natural vibrations of metal micro/nano-beams is studied. It has been shown that surface inertia has the same effect on the spectrum of natural frequencies of bending vibrations as surface stresses.

The process of buckling of the von Mises truss in the case of material instability, i.e., with allowance for the loss of ellipticity, is considered. Strain diagrams are constructed. Results that allow one to study buckling of thin-walled structures (arcs or shells) made of materials for which the loss of ellipticity of equilibrium equations is possible are obtained.

The problems of indentation of a rigid stamp of finite dimensions with a surface microrelief into a multilayer elastic strip are considered. Boundary variational formulations of problems using the Poincare-Steklov operator, which maps contact stresses into displacements, are presented. When approximating this operator, a discrete Fourier transform was used; to calculate the transfer function, an algorithm based on the variational formulation of the boundary value problem for displacement transformants was used. As a result of approximation of the original contact problem, a quadratic programming problem with constraints in the form of equalities and inequalities was obtained, for the numerical solution of which an algorithm based on the conjugate gradient method was used. A number of patterns of contact interaction have been established.

The article begins a series of final author’s publications designed to evaluate Descartes’ contribution to the formation and development of the philosophy of the Modern Era. The subject of concern directly in this article is the totality of the components of Descartes’ worldview, scientific and philosophical positions in its integrity and structural specifics. Ten such components are identified, and six of them are worthy of special mention considering their subsequent primary development in the philosophy of the Modern Era. These are materialistic, objective-idealistic, subjective-idealistic, skeptical and irrationalistic components, as well as one more, which there is no reason to describe as directly and consistently dialectical, but which is nevertheless represented in Descartes by his concrete steps to form one that. Focusing here not only on these six components, but on their totality also makes sense. To be exact, this clearly shows that in Descartes, they form a unity in which at least the first six both exclude and condition each other. Whereas, in subsequent modern European philosophers each of this components is present primarily as a separate line, declared as perhaps the only acceptable and worthy of efforts to develop it. So, focusing on the total picture of Descartes’ views makes clear the structural integrity of the entire modern European philosophy in all the diversity of its main components.