Vol 59, No 7 (2018)

The onset of convection in a system of horizontal layers of a binary solution and an inhomogeneous porous medium saturated with the solution is studied. The system is subjected to high-frequency transverse vibrations in the gravity field. It is assumed that the porosity of the medium depends linearly on the vertical coordinate. The permeability is estimated by the Karman–Kozeny formula for different values of the dimensionless gradient of the porosity, m_z. The convection of the fluid under the action of high-frequency vibrations in the gravity field is described using the averaging method. The linear problem of the stability of the mechanical equilibrium of the fluid is solved numerically by the shooting method. The values of the critical parameters corresponding to the convection initiation threshold are determined for the system heated from below or from above. The heating from below is distinguished by a sharp change in the character of the instability with a variation in the porosity gradient or the vibration intensity. It is shown that, when the porosity increases with depth, at m_z =–0.2, the instability is caused by the development of long-wave perturbations involving the fluid and the porous layers. When the porosity decreases with depth, at m_z = 0.2, the most dangerous perturbations are short-wave perturbations localized in the fluid layer. For intermediate values of the porosity gradient,–0.2< m_z < 0.2, the values of the minimum Rayleigh–Darcy critical numbers, which determine the equilibrium stability threshold with respect to short-wave and long-wave disturbances, approach one another. The neutral curves are bimodal. Upon heating from below, vertical vibrations effectively suppress convection in the fluid layer; therefore, with an increase in their intensity, the transition from short-wave vibrations, which are most dangerous, to long-wave perturbations is observed. A noticeable increase in the stability threshold is observed when the porosity decreases with depth. Upon heating from above, vibrations destabilize the equilibrium in the system and lead to a reduction in the wavelength of the critical perturbations. The wavelength decreases monotonically. Its maximum change is detected in layers whose porosity increases with depth.

Mechanisms of plastic strain localization under the dynamic loading of specially shaped specimens made of the AMg6 aluminum alloy and intended for tests under conditions close to a pure shear on a split Hopkinson–Kolsky pressure bar are studied theoretically and experimentally. The mechanisms of plastic flow instability are related to collective effects in the ensemble of microdefects in spatially localized regions visualized in situ using a CEDIP Silver 450M high-speed infrared camera. The calculation corresponding to the experimental loading scheme is implemented using wide range constitutive equations reflecting the dependence of structural relaxation mechanisms—manifestation of the collective behavior of microdefects—on the evolution of the localized flow shear instability. Microstructure analysis of deformed specimens included the study of the spatial relief (porosity) scaling by the data of a NewView-5010 microscope-interferometer in regions of plastic strain localization. An increase in the structural scaling exponent (Hurst exponent) reflected the degree of the multiscale correlated behavior of defects and the porosity induced by them in regions of localized plasticity. Infrared scanning of the strain localization region and numerical simulation followed by an estimate of the defect structure corroborated the hypothesis that effects of thermal softening do not play a decisive role in the process of plastic shear localization in the tested material under the considered loading regimes. A new, one of the possible ones, mechanism of plastic strain localization under dynamic loading is justified. It is caused by the multiscale collective behavior of mesodefects—structure-scaling transitions—and establishes the stadiality of the localized shear evolution.

The one-dimensional boundary problem of the theory of thermal stresses that simulates the shrink fit assembly of cylindrical parts is used to discuss a computational approach to predicting the evolution of the thermal stresses under piecewise-linear plasticity conditions. The solution of the problem is based on the classical maximum shear stress criterion (Tresca–Saint Venant yield criterion), and the maximum reduced shear stress criterion (Ishlinsky–Ivlev yield criterion) is only used to compare the calculation results. The application of piecewise-linear potentials in the theory of plastic flow is shown to allow equilibrium equations to be integrated in both the region of reversible deformation and various parts of a plastic flow region. The dependences thus obtained are important for a time-step calculation algorithm. This algorithm can trace the site and time of both nucleation and completion of plastic flows at each time step. The calculations demonstrate that, following temperature, the stresses in the assembly element materials can pass from correspondence to a certain face of a loading surface to correspondence to its edge and, then, to another face. This circumstance implies the division of the irreversible deformation region into parts, where a plastic flow obeys different sets of equations, which take into account the assignment of the state of stress to various faces and edges of the loading surface. The computational algorithm also makes it possible to trace the beginning of division of a flow region into parts and the motion of the part boundaries through irreversibly deformed materials, including the times of their coincidence (i.e., the disappearance of the parts of the calculation region). A repeated plastic flow is shown to appear. This flow nucleates when an assembly is cooled, i.e., when the assembly element materials return to reversible deformation conditions due to the evolution of the state of stress. Taking into account the change in plastic flow conditions that is caused by the use of piecewise-linear plastic potentials is found to substantially affect the level and the distribution of residual stresses and the final tightness of the assembly.

When using local fracture criteria, it is usually assumed that a fracture begins when the maximum equivalent stress reaches the limit value at least at one point of the body. However, under conditions of an inhomogeneous stress state, it is suitable to use nonlocal failure criteria which take into account the nonuniformity of the stress distribution and yield limit load estimates that are closer to the experimental data. An algorithm of the joint use of the boundary element method (in the version of the fictitious stress method) and gradient fracture criterion for calculations of the strength of plane construction elements is composed. The computations are carried out using a program written in FORTRAN. Results on the limit loading obtained numerically and analytically based on the local criterion of maximum stress and nonlocal fracture criteria (gradient criterion and Nuismer criterion) are compared both among themselves and with the experimental data on the failure of ebonite specimens. A brittle fracture of ebonite cylinders with a hole under diametric compression is studied experimentally. It is shown that nonlocal criteria lead to limit loading values which are closer to the experimental ones than the local criterion. The estimates obtained by the local maximum stress criterion are significantly less than the experimental ones. The estimates found for limit loads by the Nuismer criterion are greater than similar ones determined by the local criterion; nevertheless, they are less than the experimental ones, while the limit load values according to the gradient criterion are closest to the experimental values. Using the nonlocal fracture criteria in designing constructions with stress concentrators will allow us to increase the design values of the limit loads.

The free vibrations of a circular cylindrical shell resting on a two-parameter Pasternak elastic foundation are investigated. The elastic medium is inhomogeneous along the shell length, and the inhomogeneity represents an alternation of areas with and without the medium. The behavior of the shell is considered in the framework of the classical shell theory based on the Kirchhoff–Love hypotheses. The corresponding geometric and physical relations, together with the equations of motion, are reduced to a system of eight ordinary differential equations for new unknowns. The problem is solved by applying the Godunov orthogonal sweep method, and the differential equations are integrated using the fourth-order Runge–Kutta method. The natural frequencies are calculated by applying a stepwise iterative procedure, followed by a further refinement based on the bisection method. The results are validated by comparing them with available numerical-analytical solutions. For simply supported, clamped-clamped, and clamped-free cylindrical shells, the numerical results reveal that the lowest vibration frequencies depend on the elastic medium characteristics and the type of the inhomogeneity. It is shown that a violation in the smoothness of the curves is caused by variations in the lowest frequency mode, the ratio of the size of the elastic foundation to the total length of the shell, and its stiffness, as well as by a combination of the boundary conditions specified at the ends of the shell.

Composite materials, due to their properties (high specific strength and low weight), are currently among the most demanded materials used in creating objects for many purposes. The strict modern safety standards require timely monitoring of the occurrence and development of defects, in particular, delaminations. In this respect, considerable attention is paid to the development and improvement of methods of flaw detection. This paper presents a numerical study of the possibility of detecting and localizing delaminations in structures made of laminated composite materials by using vibrational approaches. The approach proposed is based on the excitation of vibrations with an increased amplitude in the region of the defect. This is possible due to the rise of natural vibration frequencies, the maximum amplitude of which is localized exactly in this place. In the first stage of numerical experiments, it was found that such natural frequencies depend weakly on the location of the defect but are strongly correlated with the size of the delamination. In the next stage, for an adequate description of the vibrational processes in the structure, forced steady-state vibrations were simulated taking into account the necessary dissipative parameters of the composite material. The frequency of the external action was chosen in accordance with the natural vibration frequency corresponding to the defect obtained from the modal analysis. The calculation results showed a significant increase in the vibration amplitude in the delamination region in comparison with the defectless structure if the frequency of the external action is chosen correctly. The effectiveness of the approach depending on the distance from the place of the application of the forced oscillation to the delamination region was tested. The method of defect monitoring proposed in the paper makes it possible to justify the possibility of developing, based on the vibtrational processes, a system for detecting delaminations in composite materials and to determine the main parameters of such a system.

The problem of taking into account the influence of turbulence comes up while solving both fundamental questions of geo- and astrophysics and applied problems arising in the development of new engineering solutions. Difficulties in applying the standard propositions of the theory appear when considering flows with a special spatial structure, for example, helical flows. The flow helicity determines the topology of vortices and is conserved in the process of energy transfer in a turbulent flow. In this paper we suggest an approach for numerical simulation of homogeneous isotropic helical turbulence aimed at detecting characteristic signatures of the inertial range and finding the distributions of the spectral energy and helicity densities. In this approach we use the TARANG code designed to numerically solve various problems of fluid dynamics in the regime of a developed turbulent flow and to study hydrodynamic instability phenomena of a different physical nature (thermal convection, advection of passive and active scalars, magnetohydrodynamics, and the influence of Coriolis forces). TARANG is an open source code written in the object-oriented C++ language with a high efficiency of computation on multiprocessor computers. Particular attention in the paper is given to the application of the tool kit from the package to analyze the solutions obtained. The spectral distributions and fluxes of energy and helicity have been computed for Reynolds numbers of 5700 and 14 000 on 512³ and 1024³ grids, respectively. We have checked whether the –5/3 spectral law is realizable and estimated the universal Kolmogorov and Batchelor constants in the inertial range. An analysis of the energy and helicity transfer functions between the selected scales (shell-to-shell transfer) shows a significant contribution of nonlocal interactions to the cascade process.