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An experimental and numerical analysis was performed to investigate the laminar regimes of conjugate thermogravitational convection in a closed parallelepiped with heat-conducting walls of finite thickness in the presence of a local energy source with convective heat exchange with the environment. The numerical studies were performed using the Fluent software. The experimental data and numerical results agree well each other.

The Eulerian and Lagrangian approaches are used to perform a numerical study of the disperse phase dynamics, turbulence, and heat transfer in a turbulent gas–droplet flow in a tube with sudden expansion with the following ranges of two-phase flow parameters: initial droplet size d₁ = 0–200 μm and mass fraction of droplets M_L1 = 0–0.1. The main difference between the Eulerian and Lagrangian approaches is the difference in the predictions of the droplet mass fraction: the Eulerian approach predicts a smaller value of M_L both in the recirculation region and in the flow core (the difference reaches 15–20%). It is demonstrated that the disperse phase mass fraction calculated by the Lagrangian approach agrees better with measured data than the corresponding value predicted by the Eulerian approach.

Using the equation of living forces averaged over the volume of the filter and obtained from the Navier–Stokes equations of an incompressible fluid, an analytical formula for the permeability coefficient in the classical Darcy problem is derived to within the principal terms of the Poiseuille number. It is shown that the resulting permeability coefficient is inversely proportional to the square of the specific surface area and the dimensionless average dissipation rate of the kinetic fluid energy in the filter.

A local-interaction model describing the penetration of axisymmetric projectiles into sandy soil at a constant velocity is studied experimentally and theoretically. Two approaches to the determination of the parameters of the quadratic local-interaction model are considered. The first approach is based on the use of the solution of the problem of spherical-cavity expansion taking into account the dynamic compressibility and shear resistance of soil. In the second approach, model parameters are determined based on the experimental dependence of the resistance to penetration of conical projectiles into a sandy soil on the impact velocity. Good agreement was obtained between the results of experiments, two-dimensional numerical calculations, and calculations for the local interaction model based on the solution of the spherical-cavity expansion problem and used to determine the maximum resistance to penetration of conical and spherical projectiles.

The resonant frequency of flexural vibrations for a double tapered atomic force microscope (AFM) cantilever has been investigated by using the Timoshenko beam theory. In this paper, the effects of various parameters on the dimensionless frequency of vibrations of the AFM cantilever have been studied. The differential quadrature method (DQM) is employed to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when the Timoshenko beam parameter or the cantilever thickness increases, and high-order modes are more sensitive to it. The first frequency is sensitive only in the lower range of contact stiffness, but the higher-order modes are sensitive to the contact stiffness in a larger range. Increasing the tip height increases the sensitivity of the vibrational modes in a limited range of normal contact stiffness. Furthermore, with increasing the breadth taper ratio, the frequency increases. The DQM results are compared with the exact solution for a rectangular AFM cantilever.

A method is developed for determining the load-bearing capacity of ice plates, which are modeled by an ideal rigid-plastic plate located on an incompressible foundation. The plate with a simply supported or clamped arbitrary smooth curvilinear contour is subjected to a load uniformly distributed over an arbitrarily shaped reinforced local central region. An analytical expression for the ultimate load is derived. A plate shaped as an ellipse is considered as an example.

A method is proposed to study the distribution of residual stresses in a semicircular notch in a hollow cylindrical specimen after advanced surface plastic deformation. The initial information used in the method is one or two experimentally determined components of the residual stress tensor in the hardened layer of the smooth specimen. The problem is solved using a finite element technique taking into account initial plastic strains, which are set in correspondence to the residual stresses according to the laws of elasticity. The effect of the hardening technology and notch depth on the distribution of residual stresses is studied. Experimental verification of the method showed that the calculated and experimental data on the stress distribution over the depth of the layer are in good agreement.

The problem of the interaction of surface and flexural-gravity waves with a vertical barrier is solved in a two-dimensional formulation. It is assumed that the fluid is ideal and incompressible, has infinite depth, and is partially covered with ice. The ice cover is modeled by an elastic plate of constant thickness. The eigenfrequencies and eigenmodes of oscillation of the floating elastic ice plate, the deflection and deformation of ice, and the forces acting on the wall are determined.

The condition of mutual nonpenetration of the crack faces is proposed for a Timoshenko plate with an oblique crack, whose initial state is defined by a surface the normal to which makes a small angle with the middle plane. Unique solvability of the variational problem of plate equilibrium with the nonpenetration conditions for the crack faces specified on the curve describing the crack is proved. A differential formulation of the problem equivalent to the original formulation for sufficiently smooth solutions is proposed. For the one-dimensional case (beam with a cut), an analytical solution is obtained, and the cases of longitudinal tension and compression are examined.

The mechanical properties of notched samples of St.10 steel under tension at different strain rates were studied. Fracture surfaces of the notched samples after the dynamic bending were investigated, the mechanisms of plastic deformation and fracture were determined, and the fractal dimension of the fracture contours were obtained.