The problem of forced bending vibrations of a rod-strip, which has an unfixed cantilever part and a finite-length fixing section on one of its faces, is solved. It is assumed that a harmonically varying axial force is applied to the end of the fixed section. To describe the deformation process of the unfixed part of the rod, the classical Kirchhoff-Love model is used, taking into account geometric nonlinearity when determining axial strains. The deformation of the fixed part of the rod is described by a refined shear model by S.P. Timoshenko, taking into account transverse compression strains, transformed into another model by accounting for the presence of a stationary fixing section. The conditions for kinematic conjugation of the unfixed and fixed parts of the rod are formulated, taking into account which, based on the Hamilton-Ostrogradsky variational principle, the equations of motion, the corresponding boundary conditions, as well as the force conditions for the conjugation of the introduced rod sections are obtained. Exact analytical solutions of the obtained equations of motion for the fixed and unfixed parts of the rod under the action of a harmonic force on the end are constructed, with integration constants determined from a system of nonlinear equations solved by Newton’s iterative method. Numerical experiments were conducted to study the passage of vibrations through the fixing section during resonant vibrations at the two lowest natural modes of rods made of D16AT duralumin and a unidirectional fibrous composite based on ELUR-P carbon fiber and KhT-118 binder. An effect of a noticeable increase in the vibration amplitudes of the ends of the cantilever parts of the mentioned rods due to transverse compression of the fixed section was revealed compared to the results obtained without considering its transverse compression.

Within the framework of the refined bending theory, a coupled problem of non-isothermal viscoelastoplastic dynamic deformation of reinforced plates is formulated. The simplest version of this theory is the traditional non-classical Ambartsumyan theory. Geometric nonlinearity is modeled in the Karman approximation. The temperature and tangential displacements of points of flexible plates in the transverse direction are approximated by high-order polynomials. The numerical solution of the formulated two-dimensional initial-boundary value problem is obtained using an explicit time-stepping scheme. The non-isothermal viscoelastoplastic behavior of a fiberglass plate with an orthogonal 2D reinforcement structure is investigated; the structure is dynamically bent under the action of excess pressure caused by an air blast wave. It is demonstrated that for an adequate calculation of the thermal response in such a structure, the temperature across its thickness must be approximated by a 7th-order polynomial, rather than a 2nd-order polynomial, as is traditionally done for thin-walled structural elements. It is shown that for an adequate determination of the residual shape of the plate after the cessation of its inelastic oscillations and for an adequate calculation of the residual deformed state of its composition components, the refined bending theory should be used, rather than the Ambartsumyan theory. In the absence of external intense heat sources of non-mechanical origin, the dynamics of fiberglass plates can be calculated without considering the thermal response in them. However, in the presence of a pre-induced and significantly non-uniform temperature field across the plate thickness, the magnitude of the residual deflection depends on which face of the structure the external dynamic load is applied to.

The most well-known methods for repairing contour-forming panels made of polymer composite materials used in small aircraft structures that have sustained low-energy impact damage (up to 35÷70 J) are considered. These include: installation of a reinforcing patch with a mechanical or adhesive-mechanical joint, gluing an insert made of layers of carbon or fiberglass with final pressing, as well as a developed operational repair method using sliding metal inserts, intended for use in airfield conditions. The results of computational and experimental studies of residual strength after repair are obtained, including tests of methodological and structurally similar samples. Using the finite element method and a linear degradation model of composite ply properties, the post-critical behavior of panels repaired by installing metal patches with bolt fasteners, both with and without adhesive in the joint, was simulated in the ABAQUS software package. It is shown that the ultimate load on a panel with an adhesive-bolted joint is higher than with a bolted joint without adhesive. The calculation results are confirmed by strain gauge measurements on the repair patch installed on the damage. A computational justification for the selection of design parameters for the considered repair methods is performed based on the condition of restoring the strength characteristics of the repaired parts. The results of experimental studies on samples confirmed the expected estimates of preliminary calculations for the restoration of residual strength after repair.

A version of the unified model of phase-structural deformation of shape memory alloys (SMAs), which takes into account only isotropic hardening with an integral parameter for the structural deformation mechanism, is extended to account for the influence of the stress state type not only on the deformation processes for both the phase and structural mechanisms, but also on the phase transformation process itself. To account for this influence, a parameter of the stress deviator type is used, proportional to the ratio of the third invariant of the stress deviator to the cube of the stress intensity. When modeling the phase deformation mechanism for the direct thermoelastic transformation, both the process of martensite nucleation and the process of their growth are taken into account. When modeling the reverse thermoelastic phase transformation, only the process of degradation of martensitic mesoelements to zero volume is considered. Explicit expressions for the increments of phase-structural deformations are formulated, including for processes occurring with a change in the stress state type. The position on active processes of proportional loading is established. Conditions are found under which the constitutive equations of the unified model in increments can be integrated before solving the boundary value problem, which leads to finite relations between stresses and phase-structural deformations, and significantly simplifies the solution of boundary value problems. A differential form of the constitutive relation for the phase composition parameter — the volume fraction of the martensitic phase — is presented, suitable for describing direct and reverse thermoelastic phase transformations, both in complete and incomplete cycles, and taking into account the influence of changes in the stress state type on this process.

The paper presents a method for determining the density of thermal protection composite materials (TCM) in the zone of thermal decomposition (pyrolysis) of their binders and the density of the pyrolysis gases formed. When modeling complex heat and mass transfer processes in composite materials, as a rule, a single material is considered, for which a limited number of components undergoing chemical reactions are considered in the pyrolysis region (due to limited knowledge of the chemical composition of the composite material binder). In this work, in mathematical modeling of heat and mass transfer in composite materials under conditions of high-temperature heating, a method is used that allows bypassing complex chemical kinetics in the binder decomposition region and allows its application using only experimentally determined temperatures and densities of the beginning and end of binder decomposition, available in the passport of each TCM for most composite materials. To derive the law of density change of TCM in the pyrolysis zone, a complete mathematical model of heat and mass transfer in three phases is considered — the porous coke residue, the pyrolysis zone, and the material unaffected by decomposition.

A contact problem for a spherical shell resting on an absolutely rigid flat surface is considered. For the shell, a system of equilibrium equations in displacements is used, based on S.P. Timoshenko’s hypotheses, taking into account the influence of shear deformation. To construct a system of governing equations, the superposition principle is used, according to which the normal displacements of the shell are related to the contact pressure through an integral relation. This leads to the main governing integral equation of the Fredholm type of the first kind. The kernel of this equation is the influence function for the shell. The influence function is constructed using series expansions in Legendre and Gegenbauer polynomials. To construct a correct system of governing equations, the problem is reduced to a system of pair series-equations. The method for solving the system of governing equations is based on reducing the pair equations to a regular Fredholm integral equation of the second kind. For this purpose, known expansions of discontinuous functions in Legendre polynomial series are used, as well as an integral representation for Legendre polynomials. As a result, the problem is reduced to a Fredholm integral equation of the second kind with respect to an auxiliary function. The desired coefficients of the series for the contact pressure are expressed through the auxiliary function. To determine the contact region, the equilibrium condition of the shell is additionally used.

A new formulation of the momentless theory of shells with shape memory is proposed, based on a simply connected model of thermoelastic phase transitions and internal kinematic variables. Based on the evolutionary and constitutive equations of the three-dimensional problem of mechanics of materials with memory for a thin shell in a momentless stress state, an incremental equation describing the increment of the volume fraction of the phase composition parameter averaged over the thickness, and an incremental constitutive equation for a small increment of the tangential strain tensor of the shell are obtained, while retaining the zero terms of the Maclaurin series for the martensite volume fraction and the linear strain tensor. Within the framework of the simply connected model, the temperature is a given field. The proposed evolutionary and constitutive equations for a momentless shell account for the different resistance of the material with memory, i.e., the dependence of the exact upper bound of the shape change deformation during the phase transformation on the stress state parameter, expressed in terms of the components of the tangential force tensor. Some static problems for momentless shells of revolution under the action of constant external forces and a time-varying homogeneous temperature field (a spherical shell filled with heated liquid under pressure under the action of vertical overload) are considered, allowing a closed analytical solution of the static equilibrium equations. The distributions of tangential strains of the shell along the generatrix at different temperatures are calculated. It is shown that at low overloads, the influence of the filler weight is small compared to the pressure effect, and neglecting the different resistance of the material under biaxial tension of the shell leads to an unacceptable overestimation of the amplitudes of phase strains.

The paper presents the results of determining the effective elastic moduli of an aluminum matrix composite material reinforced with hollow ceramic microspheres with diameters of 40-80 μm and 100-200 μm. The dependences of the bulk elastic wave velocities and density of the composite material, created on the basis of A6 aluminum alloy, on the volume fraction of hollow ceramic microspheres were studied. Based on measurements of elastic wave velocities, the effective moduli were calculated: Young’s modulus, shear modulus, and bulk compression modulus of the matrix material. In the Voigt approximation, the effective moduli of the reinforcing particles were determined. Taking into account the volume fraction of microspheres, the effective elastic moduli of the reinforcing particles were calculated. A high correlation coefficient between the ultimate strength and the elastic moduli was obtained when changing the volume fraction of reinforcing particles. It was found that the shear moduli of the reinforcing particles differ from the matrix moduli by 33% (particles 40-80 μm) and by 38% for particles 100-200 μm, the bulk compression moduli by 60% and 150%, and Young’s moduli by 37% and 58%, respectively. The strength properties of microspheres and the elastic characteristics of microparticles are interrelated, which affects the ultimate strength of the composite as a whole and its elastic properties. The obtained data show that determining the elastic characteristics by the ultrasonic method will allow assessing the strength properties of the composite without its destruction.