Том 57, № 5 (2016)

Publications dealing with the study of methods of reducing a three-dimensional problem of the elasticity theory to a two-dimensional problem of the theory of plates and shells are reviewed. Two approaches are considered: the use of kinematic and force hypotheses and expansion of solutions of the three-dimensional elasticity theory in terms of the complete system of functions. Papers where a three-dimensional problem is reduced to a two-dimensional problem with the use of several approximations of each sought function (stresses and displacements) by segments of Legendre polynomials are also reviewed.

Various approaches to determining the load-carrying capacity of beams and shells under elastoplastic deformation and creep deformation conditions are analyzed.

The creep rupture strength of tensile bars in a corrosive medium is studied. The time to failure of the bars is analyzed as a function of their cross-sectional shape. It is shown that the influence of the corrosive medium on the creep rupture strength of the bars is determined by the diffusion of its elements into the bar material, resulting in a decrease in its creep rupture strength. The diffusion of the corrosive medium into a bar is studied using an approximate method for solving the diffusion equation taking into account the motion of the diffusion front. Bars with different cross-sectional shapes are considered using Rabotnov kinetic theory. It is shown that at the same tensile stress, the bar with a circular cross-section has minimum time to failure.

The generalized rheological method is used to construct a mathematical model of small deformations of a porous media with open pores. Changes in the resistance of the material to external mechanical impact at the moment of collapse of the pores is described using the von Mises–Schleicher strength condition. The irreversible deformation is accounted for with the help of the classic versions of the von Mises–Tresca–Saint-Venant yield condition and the condition that simulates the plastic loss of stability of the porous skeleton. Within the framework of the constructed model, this paper describes the analysis of the propagation of plane longitudinal compression waves in a homogeneous medium accompanied with plastic strain of the skeleton and densification of the material. A parallel computational algorithm is developed for the study of the elastoplastic deformation of the porous medium under external dynamics loads. The algorithm and the program are tested by calculating the propagation of plane longitudinal compression shock waves and the extension of the cylindrical cavity in an infinite porous medium. The calculation results are compared with exact solutions, and it is shown that they are in good agreement.

A mathematical model is developed for an inhomogeneous thermoelastic prestressed half-space consisting of a stack of homogeneous or functionally graded layers rigidly attached to a homogeneous base. Each component of the inhomogeneous medium is subjected to initial mechanical stresses and temperature. Successive linearization of the constitutive relations of the nonlinear mechanics of a thermoelastic medium is performed using the theory of superposition of small deformations on finite deformations with the inhomogeneity of the medium taken into account. Integral formulas are derived to explore dynamic processes in inhomogeneous prestressed thermoelastic media.

The electromagnetoviscoelastic problem is solved for piecewise-homogeneous plates. The problem is reduced to solving a sequence of electromagnetoelastic problems with complex potentials. General representations of approximation functions for multiply connected domains and boundary conditions for their determination are given. An analytical solution of the problem for a plate with one inclusion and an approximate solution for a plate with a finite number of inclusions are obtained. The change in the electromagnetoelastic state is investigated numerically as a function of time, the properties of the plate and inclusion materials, and the distance between the inclusions.

A mathematical model is proposed which describes the interrelated processes of unsteady elastoplastic deformation of stacks of woven metal wire mesh and wave processes in pore gas in a two-dimensional axisymmetric approximation. The nonlinear equations of the dynamics of two interpenetrating continua are solved numerically using a modified Godunov’s scheme. The problem of explosive loading of a multilayer shell with an internal permeable deformable layer is solved. The results of numerical solutions are compared with experimental data. The influence of the gas-permeable layer on shell deformation is determined.

The structure of a swirl flow in a vortex chamber is studied. Distributions of the azimuthal and axial components of velocity are obtained almost in the entire volume of the chamber. A pattern of streamlines of this flow is constructed, and the mechanism of the emergence of a reverse flow directed toward the closed end face of the chamber is identified.

The effect of the arc-cone liner configuration parameters on explosively formed projectile (EFP) flight stability is studied experimentally. The effect of the liner edge structure on the EFP formation is computed numerically. The results show that an EFP formed by a liner whose thickness is 0.046 times the charge caliber has improved flight stability and can perforate a steel armor 0.5 times the charge caliber thick in the case of large stand-off distances. A good tail skirt EFP can be formed by choosing appropriate parameters: the liner-to-charge diameter ratio in the interval 0.96–0.98, the liner edge thickness equal to 0.0020–0.0025 times the charge caliber, and the liner edge chamfer of 45–50°.

The goal of the present paper is to examine the magnetohydrodynamic effects on the boundary layer flow of the Jeffrey fluid model for a non-Newtonian nanofluid past a stretching sheet with considering the effects of a heat source/sink. The governing partial differential equations are reduced to a set of coupled nonlinear ordinary differential equations by using suitable similarity transformations. These equations are then solved by the variational finite element method. The profiles of the velocity, temperature, and nanoparticle volume fraction are presented graphically, and the values of the Nusselt and Sherwood numbers are tabulated. The present results are compared with previously published works and are found to be in good agreement with them.

A numerical study of a steady two-dimensional double-diffusive free convection boundary layer flow over a vertical surface embedded in a porous medium with slip flow and convective boundary conditions, heat generation/absorption, and solar radiation effects is performed. A scaling group of transformations is used to obtain the governing boundary layer equations and the boundary conditions. The transformed equations are then solved by the fourth- and fifth-order Runge–Kutta–Fehlberg numerical method with Maple 13. The results for the velocity, temperature, and concentration profiles, as well as the skin friction coefficient, the Nusselt number, and the Sherwood number are presented and discussed.

Heat transfer characteristics of an incompressible viscous fluid past a plate embedded into a porous medium with a convective boundary condition are obtained by using the Darcy–Forchheimer–Brinkman model. The governing partial differential equations are reduced to nonlinear ordinary differential equations, and similarity solutions are obtained. The similarity equations are solved numerically. With increasing convective parameter, the surface temperature increases. The rate of heat transfer increases as the Prandtl number increases.