Том 58, № 3 (2017)

A supersonic compressible flow over a 60° swept delta wing with a sharp leading edge undergoing pitching oscillations is computationally studied. Numerical simulations are performed by the finite volume method with the use of the k−ω turbulence model for various Mach numbers and angles of attack. Variations of flow patterns in a crossflow plane, hysteresis loops associated with the vortex core location, and vortex breakdown positions during a pitching cycle are investigated. Trends for various Mach numbers, mean angles of attack, pitching amplitudes, and pitching frequencies are illustrated.

The prime objective of this article is to study the axisymmetric flow and heat transfer of the Carreau fluid over a radially stretching sheet. The Carreau constitutive model is used to discuss the characteristics of both shear-thinning and shear-thickening fluids. The momentum equations for the two-dimensional flow field are first modeled for the Carreau fluid with the aid of the boundary layer approximations. The essential equations of the problem are reduced to a set of nonlinear ordinary differential equations by using local similarity transformations. Numerical solutions of the governing differential equations are obtained for the velocity and temperature fields by using the fifth-order Runge–Kutta method along with the shooting technique. These solutions are obtained for various values of physical parameters. The results indicate substantial reduction of the flow velocity as well as the thermal boundary layer thickness for the shear-thinning fluid with an increase in the Weissenberg number, and the opposite behavior is noted for the shear-thickening fluid. Numerical results are validated by comparisons with already published results.

The influence of the mesh size of the displacement vector field on the strain estimate in the digital image correlation method is considered. The reasons for the emergence and the magnitude of the strain estimate error in processing optical images of material surfaces with different textures are analyzed. The dependence of the mesh size for strain estimation on the magnitude of displacements and also on the presence and size of the discontinuity region in the strain field is studied. An adaptive algorithm for choosing the mesh size is proposed, which allows the strain calculation error to be reduced by a factor of 1.9 with simultaneous reduction of computational expenses by a factor of 2.1.

The history of stresses and creep strains of a rotating composite cylinder made of an aluminum matrix reinforced by silicon carbide particles is investigated. The effect of uniformly distributed SiC micro- and nanoparticles on the initial thermo-elastic and time-dependent creep deformation is studied. The material creep behavior is described by Sherby’s constitutive model where the creep parameters are functions of temperature and the particle sizes vary from 50 nm to 45.9 μm. Loading is composed of a temperature field due to outward steady-state heat conduction and an inertia body force due to cylinder rotation. Based on the equilibrium equation and also stress-strain and strain-displacement relations, a constitutive second-order differential equation for displacements with variable and time-dependent coefficients is obtained. By solving this differential equation together with the Prandtl–Reuss relation and the material creep constitutive model, the history of stresses and creep strains is obtained. It is found that the minimum effective stresses are reached in a material reinforced by uniformly distributed SiC particles with the volume fraction of 20% and particle size of 50 nm. It is also found that the effective and tangential stresses increase with time at the inner surface of the composite cylinder; however, their variation at the outer surface is insignificant.

This paper presents the results of a finite-element study of elastic-plastic deformation and damage accumulation in structural materials under various cyclic loading conditions. Material behavior is described by the relations of damage mechanics using thermoplastic model which takes into account the plastic deformation of material under cyclic loading and the kinetic equations of the energy theory of damage accumulation. The basic laws of plastic deformation and development of damage in materials under hard, soft, symmetric, and asymmetric low-cycle loading are established.

This paper studies the chaotic dynamics of two cylindrical shells nested into each other with a gap and their reinforcing beam, also with a gap, which is subjected to a distributed alternating load. The problem is solved using methods of nonlinear dynamics and the qualitative theory of differential equations. The Novozhilov equations for geometrically nonlinear structures are used as the governing equations. Contact pressure is determined by Kantor’s method. Using finite elements in spatial variables, the partial differential equations for the beam and shells are reduced to the Cauchy problem, which is solved by explicit integration (Euler’s method). The chaotic synchronization of this system is studied.

This paper describes the experimental implementation of the laser-ultrasonic method for diagnosing mechanical compression and tensile stresses in steel structures, based on the acoustoelasticity effect. The special laser-ultrasonic transducer that provides the laser excitation and highly sensitive piezoelectric detection of head (longitudinal subsurface) ultrasonic waves is developed. It is shown on the example of R65 rail samples of various quality that, regardless of the structural phase state of the rail, there is one and the same linear relationship between the relative variation of the velocity of head ultrasonic waves and the absolute value of uniaxial compression and tensile stresses acting in the rail.

The flexural vibrations of D16AT Duralumin specimens have been investigated, showing that the dynamic elastic modulus of D16AT Duralumin is significantly dependent on frequency. It has been found that the dynamic elastic modulus significantly reduces in the frequency range 0–20 Hz, and at high frequencies, it is practically constant. A general method has been developed to determine the modes and frequency of free vibrations of a structure taking into account the dependence of the dynamic elastic modulus of the material on its deformation frequency. Numerical experiments on impulsive loading of an elongated plate have been performed, showing that the frequency dependence of the dynamic elastic modulus of Duralumin should be taken into account in structural analysis.

This paper touches upon the computer simulation of the propagation of elastic waves in three-dimensional multilayer fractured media. The dynamic processes are described using the defining system of equations in the partial derivatives of the deformed solid mechanics. The numerical solution of this system is carried out via the grid-characteristic method on curvilinear structural grids. The fractured nature of the medium is accounted for by explicitly selecting the boundaries of individual cracks and setting special boundary conditions in them. Various models of heterogeneous deformed media with a fractured structures are considered: a homogeneous medium, a medium with horizontal boundaries, a medium with inclined boundaries, and a medium curvilinear boundaries. The wave fields detected on the surface are obtained, and their structures are analyzed. It is demonstrated that it is possible to detect the waves scattered from fractured media even in the case of nonparallel (inclined and curvilinear) boundaries of geological layers.

An analytical simulation of an elastically restrained tapered cantilever beam is performed. Five different analytical methods are applied to solve the dynamic model of the nonlinear oscillation equation. Analytical relationships between the natural frequency and the initial amplitude are obtained. The present solutions are compared with the exact solution, and excellent agreement is noted.

A fluid flow through an isotropic porous medium with randomly arranged elliptical particles is simulated by the lattice Boltzmann method. The dimensionless pressure drop and the dimensionless permeability are evaluated as functions of the Reynolds number. The effect of the aspect ratio of the major to minor semi-axis of the ellipse on the dimensionless permeability is considered for different values of porosity. The pressure drop is thoroughly investigated as a function of fluid viscosity for different values of the aspect ratio and porosity. The influence of various parameters of the problem on the mean tortuosity of the medium is considered.