In earlier works the authors have constructed a model of the starting earthquake from the preliminary stage and up to the earthquake itself. The model is based on the boundary problem formulation accepted in a number of works and represents two semi-infinite lithospheric plates with straight boundaries modeled by Kirchhoff plates slowly moving towards each other. The plates are placed on a three-dimensional linearly deformable foundation. It is assumed that the foundation surface is a Conrad boundary separating the top granite and bottom basalt structures of the Earth's crust. For such a boundary problem, we have studied the change in the contact stresses concentration under the lithospheric plates for the cases with and without a distance between the plates and the change in the contact stresses concentration in the convergence zone of the lithospheric plates. When the plates are close to each other, the concentration of stresses in the convergence zone, which is a fault, is singular. According to the experience of solving boundary problems for linear elastic materials, this means the destruction of a zone with such stresses concentration, i.e. the occurrence of an earthquake. For this model, different effects from the impact on the lithospheric plates have been studied. As a result, it was found that the same effects were characteristic for faulting and breaking earthquakes which had actually occurred. The study was carried out for the static problem with vertical external effects on the lithospheric plates assuming no boundary stresses at the ends. The study based on the block element method executed in the present work is aimed at building a more complex model, assuming the presence of stresses, i.e. shearing forces and bending moments, at the ends of the plates, that is, the end fault boundaries. Ratios that take into account the presence of different variants of the mentioned boundary conditions on the banks of the faults were built, and their effect on an earthquake possibility was studied.

The paper presents a model development related to the longitudinal oscillations of the rod string inthe deep-well pumping unit taking into account the compressibility of the gas-liquid mixture in the cylinder of the pump. The approach which uses the problem formulation in the form of quasi-variational inequalities was applied to solve this problem. The solution of this problem can be reduced to a sequence of non-smooth minimization problems. This approach is quite versatile and can be used for columns in highly deviated wells. In this model, the gas component of the mixture is subject to Boyle's law. This model does not consider the compressibility of the liquid components, the dilution of gas in a liquid and extraction of gas from the fluid. On the basis of the proposed model, we considered the influence of the gas content in the mixture which fills the pump cylinder on the dynagraph of the rod string in the upper section. Besides, different behaviors of the rod string in two cases are considered. In the first case the gas is uniformly distributed (but not dissolved) in a liquid which fills the pump cylinder. In the second case the gas fills a localized volume in the pump cylinder. If the gas is distributed in the pumped mixture, the dynagraph segments which correspond to the compression phase have a weaker inclination than the ones of the extension phase. It can be explained by the fact that the mass of the gas and, thus the compressibility of the mixture in the phase of compression is higher than the one in the extension phase. This fact also explains the weakening of free oscillations which is much more significant for that phase when the plunger moves down, rather than the phase when the plunger moves upward. If the gas occupies the localized volume in the pump cylinder, then it has the same shape both in the compression and extension phases. When the plunger moves downward, no excessive weakening of oscillations is found.

The paper considers the problem of holding a torn blade of a turbojet fan to ensure safety for passengers and crews. It is concerned with one of the main trends in designing fans satisfying this requirement. The experimental and computational analysis of strength for several fan case designs is given. A difference between the calculation results and experimental data for metals with different plasticity is presented. We outlined and described the well-known procedures of calculating metal armoured protection, specified its common disadvantage which is neglecting the material ultimate strain. We suggested the calculation procedure for the metal case which takes the material ultimate strain in account including the boundary value of the material ultimate strain dividing metals on rigid and flexible ones with the calculated formulas of the armoured wall. A good convergence is revealed between the calculation data based on the proposed correlations and the experimental results for Ti and Al alloys. We described the structural design, analyzed strength and the rate of impact absorption by a separated blade using a specially developed goffered hood (a cover) made of the high-strength cloth which can be installed on any fan case made of either metal or polymer composite materials (PCM) without principal changes in the structural configuration. The calculated advantages of using the developed goffered hood design in comparison with the conventional one have been shown. The efficiency has been estimated with respect to applying aluminum alloys as a production material for a fan case being an alternative to the titanium ones. Experimental equipment for testing full-size cases is proposed. The disadvantages of the testing equipment for model cases have been outlined. We analyzed the problem of PCM application for a load-carrying case which is cut by fan blades when one blade is torn away. The engineering estimation of using PCM in a fan case and the solutions aiming to increase the ballistic resistance of PCM cases have been presented.

The current work presents a qualitative and quantitative assessment of microdamage occurring in the structure as a result of different loading tests by the example of the "U"-shaped bulkhead segment made of carbon fiber reinforced plastic (CFRP) using microfocus X-radiography. The resin transfer molding (RTM) technology was used to manufacture this structure. X-ray images with the fixed tensile force were made during the sample tests. These images were analyzed in order to reveal a delamination as the basic damage type occurring in the tested part. The areas of interlayer cracks localization and their estimated sizes were identified at the various load levels. It was noted that the cracks were completely closed after unloading; and it was difficult to identify them by any non-destructive testing methods. The three-dimensional computer model was created to carry out the stress-strain analysis of the sample. A detailed ply-by-ply analysis allowed us to estimate the interlaminar normal and shear stresses which determine the structural failure. The numerical simulation of this problem was carried out using the finite element method (FEM) with ANSYS Workbench software. Due to a high dimensionality of the FE model, the high-performance computing complex was used. The numerical simulations results with regard to the mechanical tests of the bulkhead segment were compared with the X-ray radiography results, and a good qualitative correlation was found. Thus, it was shown that the areas of maximal interlaminar stresses are localized in the part’s bending areas. The difference between the experimental and numerical values of the bearing strength was about 23% but it could be corrected after testing a series of similar samples and refining the material interlaminar gap strength.

The dynamic axisymmetric problem for a round bimorph structure consisting of the metal substrate and the axially polarized piezoceramic plate is considered. Its bending modes are caused by the action of the mechanical loading (normal tension) on the side surface; the loading is a function of the radial coordinate and time. The rigid and hinge supports of the plate are considered. The initial design relations are formulated for the piezoceramic material with the hexagonal crystal lattice of the 6 mm class. In order to solve the problem of the theory of electrodynamics in a three-dimensional formulation, the finite integral Hankel transformations along the axial coordinate and a generalized transformation (FIT) over the radial variable is used. At each stage, the standardization is carried out which allows implementing an appropriate transformation algorithm. In the first case the boundary conditions are presented in a mixed form; and in the second case they are homogeneous by introducing auxiliary functions. This approach allows gaining precise (within the used models) calculated ratios in a most general form. The built closed solution allows defining the frequency range of the axisymmetric oscillations, the stress-strain state and the nature of the changing induced electric field of the bimorph plate. This makes it possible to establish the conventional solutions of the designed devices, determine a way of fixing the electrical signal, pick up all the geometrical and physical characteristics of the typical elements of the piezoceramic transducers Also, the developed solution allows solving the problems of the elasticity and electroelasticity theory for circular thick and thin plates with an arbitrary number of layers under most general loading conditions without the use of kinematic hypotheses.

The paper presents the results of studying inelastic deformation and fracture of microscopic regions of porous brittle materials under triaxial compression using the movable cellular automaton method. The study is focused on analyzing the applicability of the classical macroscopic criteria of plasticity and strength for the integral description of the mechanical response of microscopic representative volumes. We analyzed the dependence of the parameters of the integral mechanical response of the microscopic regions on the value of porosity, spatial distribution of pores and strength of the material in the skeleton walls. Main stages of the process of damage accumulation and growth in the skeleton walls and its manifestation in the integral inelastic response of the considered microscopic region are investigated by the example of the axial compression of the samples under constant lateral pressure. It is shown that the increase in the value of the lateral pressure leads to a change in the fracture type of the porous material from the elastic-brittle fracture to the formation of the shear localization zone (shear band) and then (at higher lateral pressures) to the spatially distributed cataclastic flow. The characteristic threshold values of the lateral pressure at which the failure mechanism starts to change, mostly depend on the sensitivity of the skeleton wall strength to the local pressure. The analysis of the simulation results showed that the conventional plasticity conditions (criteria) which take into account the contribution of the local average stress in the linear approximation, are able to adequately describe the response of the microscopic representative volumes of brittle porous materials under constrained conditions only from the beginning of inelastic deformation to the stage of the formation of the system of non-interacting relatively short cracks. It is important to note that the softening of the representative microvolumes of brittle porous materials under constrained conditions is concerned not with the loss of integrity of the sample, but with subsequent processes of forming the localized shear bands and pore collapse in the already fragmented material. This gives reason to believe that the experimentally determined strength of the constrained sample as the maximum resistance force may be significantly overestimated in comparison to the true value (corresponding to the fragmentation of the material). It is established that the conditions for the loss of integrity of brittle porous materials under constrained conditions are adequately described using the "linear" failure criteria with the parameters determined not by standard uniaxial compression/tension tests but by multiaxial compression tests.