The study is focused on a structure represented by a multimass elastic cantilever rod with dry friction seismic isolation elements in the support part under a horizontal random impact of a seismic type. The paper aims at investigating the seismic reaction and selecting optimal parameters of the seismic isolation system involving random impact characteristics, limit parameters of the structure, and the seismic isolation system. The researches are based on dynamic computations; the impacts and fluctuations of the system are random processes. The dynamic model of the structure with the considered seismic isolation is presented in the form of a cantilever rod with concentrated masses; a system of differential equations describing the displacement of the structure with the seismic-isolating sliding elements at the level of the top of the foundations is compiled; and a seismic impact is modeled in the form of a nonstationary random process. An algorithm is developed to integrate the system of differential equations of motion and to determine the statistical characteristics of the seismic reaction and reliability indicators of the structures with the seismic isolation. A method aimed at evaluating effectiveness of the seismic isolation system and selecting its rational parameters is suggested. We developed the computational dynamic model of the structure with the seismic-isolating sliding elements installed at the top level of the foundations, and elastic and rigid limiters for the movement of the sliding supports. This model is made in the form of a multimass cantilever rod that takes into account the relative movements of the masses and the stops of the system on the movement limiters. The structure’s movement under a seismic impact is described by a system of differential equations that takes into account the conditions of transitions of the structure from the state of sticking to the state of sliding and vice versa. The statistical characteristics of the seismic reaction and the reliability indicators of the structure in the process of vibrations are determined for different values of the maximum acceleration of the ground vibration, the prevailing period of impact, the number of masses in the calculated model and the coefficient of friction-sliding of the support elements. The influence of the impact parameters and the system on the efficiency of the seismic isolation of the structures with sliding elements is estimated. The proposed approach to selecting the optimal parameters of the seismic isolation system can be used as a research method aimed at improving efficiency of systems with different design options for seismic isolation of structures.

Numerical simulation of defect healing process in the field of previously created compressive stresses is performed. Isotropic cylinders with small axisymmetrically located defects are used as samples. The pressure created the initial field of compressive stresses inside the cylinder. The defects were modeled as a small blind closed annular cavity or as a through annular cut located around the cylinder axis. In the first case, a numerical three-dimensional solution is considered. For the second defect, the plane stress state model was used. The problems were solved in both elastic and elastoplastic formulations with an ideally elastoplastic behavior of the material. The external pressure was varied from values significantly lower than the yield strength to the yield strength and (for the first problem) for values slightly exceeding it. Based on the results of the numerical solution, the radial displacements of the cavity sides parallel to the cylinder axis are obtained depending on the external pressure. We found the values of pressure at which the cylindrical surfaces of the void defect were in contact. For the blind cavity, at any external pressure, there were unhealed areas. Healing was assessed by the volume of the material filling the initial cavity at the initial residual stresses. The value of the newly formed contact pressure at a certain value of the compressive stresses was determined by the ratio of the height of the healed area to the cavity height. The evaluation of the healing effect for a through cut in the cylinder was performed by varying the size of the gap formed by the cut between the inner cylinder and the outer ring depending on the applied external pressure. When the gap is completely healed, the values of the maximal contact pressure in the notch zone are determined.

The loading of a strip with a crack-like defect according to mode I is considered. In contrast to the classical representation of a crack in the form of a mathematical section, the proposed model defines a crack as a physical cut with a characteristic linear size. The mental continuation of a physical cut in a solid forms an interaction layer (IL). It is important that the stress-strain state of the layer at a finite value of the linear parameter does not introduce a singularity into the crack model. The process of elastoplastic deformation with a constant layer length is considered. We obtained a simplified analytical solution to the problem of deformation of two elastic bodies connected by a thin layer with elastoplastic properties. The dependence of the displacement and stress fields on the length and thickness of the interaction layer has been found. It is shown that, under the classical plasticity condition, the range of variation of the external load leading to a purely elastic behavior is possible only for a finite layer thickness. As the layer thickness tends to zero, as in the Dugdale model, the plasticity region is formed at an arbitrarily small external load. For small layer thicknesses, a local plasticity criterion is proposed, by using which it is possible to distinguish the intervals of the external load variations associated with elastic and plastic deformations. The local plasticity condition, determined by the critical value of the energy product, makes it possible to reflect the stage of elastic deformation at an arbitrarily small finite thickness of the interaction layer. An asymptotic dependence of the external load on the IL thickness and the reduced length of the plastic zone is obtained. At the same time, the separation of the external load into elastic and plastic components is preserved. From the analysis of the experimental data, an estimate of the elastic limit of the energy product for the AV138 adhesive was obtained.

The paper presents results of studying mechanical properties of polymer composites depending on types of filler particles (granular - carbon black, nanodiamonds; layered - graphene plates; fibrous - single-walled nanotubes). These nanofillers differ greatly from each other in their structure and geometry. A significant difference in behavior of nanocomposites was revealed even with little introduction of particles into the elastomer. The highest level of reinforcement of the matrix was obtained when single-wall nanotubes and detonation nanodiamonds were used as fillers. The viscoelastic properties and the Mullins softening effect [1-4] were investigated in experiments performed with material samples subjected to complex uniaxial cyclic deformation. In these experiments, the amplitude of deformations was changed step by step; and at each step a time delay was specified to complete rearrangement processes of the material structure. It was found that a pronounced softening effect after the first cycle of deformation and significant hysteresis losses occur in the material filled with single-walled nanotubes. These characteristics are insignificant for the rest of nanocomposites until elongation increases twofold. In accordance with the obtained results, a new version of the mathematical model to describe properties of the viscoelastic polymer materials was proposed. The constants of the constitutive relations were calculated for each material; the theoretical and experimental load curves were compared. As a result, the introduced model is able to describe the behavior of elastomeric nanocomposites with a high accuracy. Moreover, this model is relatively easy to use, suitable for a wide range of strain rates and stretch ratios and does not require the entire history of deformation as needed for integral models of viscoelasticity.

It has been for the first time that an analytical solution to the problem of free vibrations of a cantilevered thick orthotropic plate is presented. This problem is quite cumbersome for using the exact methods of the theory of elasticity; therefore, methods based on the variational approach were developed to solve it. The paper suggests using the superposition method to construct a general solution of the vibration equations of a plate in the series form of particular solutions obtained with the help of a variables separation. The particular solutions of one of the coordinates are built in the form of trigonometric functions of a special type (modified trigonometric system). The constructed solution, in contrast to the solutions known in the literature on the basis of the variational approach, accurately satisfies the equations of vibrations. The use of a modified trigonometric system of functions makes it possible to obtain uniform formulas for even and odd vibration shapes and to reduce the quantity of boundary conditions on the plate sides from twelve to nine ones, while five of the nine boundary conditions are also accurately satisfied. The structure of the presented solution on the plate boundary is such that, each of the kinematic or force characteristics of the plate is represented as a sum of two series, i.e. a trigonometric series and a series in hyperbolic functions. Remaining boundary conditions make it possible to obtain an infinite system of linear algebraic equations with respect to the unknown coefficients of the series representing the solution. The convergence of the solution by the reduction method of the infinite system is investigated numerically. Examples of the numerical implementation are given; numerical studies of the spectrum of natural frequencies of the cantilevered thick plate were carried out based on the obtained solution, both with varying elastic characteristics of the material and with varying geometric parameters.

The paper proposes a mathematical model aimed at calculating the effective elastic moduli of a micro-inhomogeneous two-component isotropic composite material, which components are connected randomly depending on the level of their relative volumetric contents. A stochastic equation is formulated for the connectivity parameter of the constituent components, according to which, with an increase in the volumetric content of the filler, individual inclusions build the structures of the matrix mixture in the form of interpenetrating frameworks, and then turn into a new binding matrix with individual inclusions from the material of the rest of the old matrix. The algorithm for the numerical solution of this stochastic differential equation is constructed in accordance with the Euler-Maruyama method. For each implementation of this algorithm, the corresponding stochastic trajectories are constructed for the random connectivity function of the constituent components of the composite material. A variant of the method aimed at calculating the mathematical expectation of a random connectivity function of the constituent components has been developed and the corresponding differential equation has been obtained for it. It is shown that the numerical solution of this equation and the average value of the production factor function calculated for all realizations of stochastic trajectories give close numerical values. New macroscopic constitutive relations are found for microinhomogeneous materials with a variable microstructure and their effective elastic moduli are calculated. It is noted that the formulas for these effective elastic moduli generalize the known results for isotropic composite materials. The values of the effective elastic moduli, constructed according to the expressions obtained in the paper, lie within the Khashin-Shtrikman range for the lower and upper bounds of the effective elastic moduli of the composite materials. The numerical analysis of the developed models showed a good agreement with the known experimental data.

It was experimentally observed that in polycrystalline materials under low macro loading of the specimen the first sites of failure initiation take place in the specific clusters of few grains. In some grains of these extreme clusters, the local (meso-) strains and stresses are high enough to cause first damages or plastic slips. In the stochastic microstructure of polycrystals, the formation of an extreme cluster is random and rare. Nevertheless, they govern the failure process initiation and can severely affect the reliability of polycrystalline machine parts. It is time and resource consuming to search and investigate extreme clusters on the real specimens of polycrystalline materials experimentally. A theoretical tool is desirable. Here we present the powerful computational method to look for extreme clusters, to investigate their possible patterns, and to evaluate the absolute maximums of local strains/stresses that can be achieved in these clusters. The experimentally observed clusters consist of few (3-4) preferably oriented neighboring grains or even of one big supergrain. The strain and stress bursts arise due to an interaction of the grains. One can expect that in bigger clusters, larger local bursts of fields can be generated. We found the typical forms of the extreme clusters (small and big) in four different polycrystals with grains of a weak and strong anisotropy for the case of uniaxial tension. In all regarded cases, the extreme clusters have the forms of the symmetrical patterns. In big clusters of highly anisotropic grains, the maximum of mesostrain exceeds the macrostrain by several times. In clusters of weakly anisotropic grains, the local strain concentration is rather moderate (tens of percents).

А new closed-loop solution for the coupled nonstationary problem of thermoelectric elasticity is designed for a long piezoceramic radially polarized cylinder. The case of the nonstationary load acting on its inner cylindrical surface is considered as a function of temperature change at a given law of the convection heat exchange on the outer face wall (boundary conditions of heat conductivity of the 1st and 3rd types). Electrodynamic cylinder surfaces are connected to a measuring device with a high input resistance (electric idling). We investigate the problem where the rate of the temperature load changes does not affect the inertial characteristics of the elastic system. It makes it possible to expand the initial linear computational relations with the equilibrium, electrostatics and heat conductivity equations with respect to the radial component of the displacement vector, electric potential as well as the function of temperature field changes. Hyperbolic LS-theory of the thermal conductivity is used in the computations. The problem is solved with a generalized method of biorthogonal finite integral transformation based on a multicomponent ratio of eigen functions of two homogeneous boundary value problems. The structural algorithm of this approach allows identifying a conjugated operator, without which it is impossible to solve non-self-conjugated linear problems in mathematical physics. The resulted computational relations make it possible to determine the stress-strain state, temperature and electric fields induced in the piezoceramic element under an arbitrary external temperature effect. By connecting the electroelastic system to the measuring tool, we can find voltage. Firstly, the analysis of the numerical results allows identifying the rate of the temperature load changes, at which it is necessary to use the hyperbolic theory of thermal conductivity. Secondly, it allows determining the physical characteristics of the piezoceramic material for the case when the rate of changing the body volume leads to a redistribution of the temperature field. The developed computational algorithm can be used to design non-resonant piezoelectric temperature sensors.

The paper presents the experimental results of growing surface cracks in the turbine disk of a gas turbine engine (GTE) under cyclic tension at room and elevated temperatures. The geometry of the imitation model of the GTE turbine disk with a stress concentration zone in the form of a bolt hole was justified. In order to ensure the similarity of the initial damage of the imitation model and the GTE turbine disc in the plane of symmetry of the stress concentration zone, a semi-elliptical notch was made. The loading conditions of the imitation model were developed based on results of a comparative stress-strain state (SSS) analysis of the stress concentration zone of the imitation model and the GTE turbine disc. As a result of the fatigue test of the imitation model at room and elevated temperatures, the experimental positions and sizes of the crack fronts with respect to the drop potential signal on the crack edges were obtained. The fixed positions and sizes of the crack fronts were used as the basis for the numerical calculation of the fracture resistance parameters. For the numerical studies, ten three-dimensional finite element models with different positions and sizes of the crack fronts were considered. The numerical calculation results based on the finite element method were used to determine the distributions of the elastic stress intensity factors along each crack front. The crack growth rate characteristics both on the free surface and at the deepest point of the crack front were obtained at room and elevated temperature conditions. A technique for the automation tests that simulate the block-type loading of the disk material at elevated temperatures was proposed.