The problem of axisymmetric deformation of a thin cylindrical shell under the action of a local temperature field acting on the annular part of its lateral surface is approximately solved. The solution is based on the use of classical shell theory and the application of generalized functions. Due to the latter, an exact solution to the problem is impossible, and a solution using the Bubnov method in high approximations is employed. A variant of studying the inverse problem is also considered, where the permissible temperature regimes for heat treatment can be established from the known displacements of the shell. Examples are given. The results can be used to predict the stress-strain state of thin-walled structures under conditions of unsteady aerodynamic heating of their individual sections, caused by both convective heat transfer and the heat of chemical reactions (oxidation, catalysis).

Using instrumental means of recording vibration acceleration amplitudes, a methodology for experimental study of forced bending vibrations of a cantilevered rod-strip connected on one of its frontal surfaces to a support element of finite dimensions in the fixation zone under the action of an axial harmonic force applied to the end of the fixed section is developed. A refined model of deformation of the fixed section is constructed based on the refined shear model of S.P. Timoshenko, taking into account transverse compression deformations and specified displacements of the support element. The deformation process of the unfixed (cantilever) part of the rod is described by the classical Kirchhoff-Love model. Kinematic conjugation conditions for the fixed and unfixed parts of the rod are formulated. Taking these conditions into account, the equations of motion for the unfixed and fixed parts of the rod-strip, the corresponding boundary conditions, and the force conjugation conditions for the fixed and unfixed sections of the rod are obtained based on the Hamilton-Ostrogradsky variational equation. An exact analytical solution to the problem of forced vibrations of the rod under loading by a harmonic axial force applied to the end section of the fixed part, as well as by a harmonic transverse force at the end of the unfixed part, is found. Computational experiments are carried out for a rod-strip made of aluminum alloy D16AT, taking into account the specified displacements of the support element in the form of a steel channel. It is established that under the action of an axial force applied at the end of the fixed section, the vibrations of the unfixed part of the rod are almost completely determined by the specified displacements of the support element, while under the action of an external transverse force at the end of the unfixed part, they are practically independent of them.

In a three-dimensional (3D) formulation, we consider the problem of impact fragmentation of two identical aluminum spheres, sensitive to strain rate, moving towards each other along the line connecting their centers with equal velocity V in the laboratory frame of reference. We use dimensional analysis and numerical simulation of the full system of equations of solid mechanics using the Smoothed Particle Hydrodynamics (SPH) method with the Johnson-Cook viscoplastic model to study the problem. An assumption is made about the complete self-similarity of the problem with respect to the dimensionless effective strain rate parameter eff ε, which is verified by numerical simulation. As a result, we consider and compare two cases corresponding to high-speed loading 1eff>> ε and low-speed loading 1eff<< ε. The size of each sphere is characterized by the total number totN of SPH particles approximating the sphere with a cubic lattice. The assumption of complete self-similarity with respect to the parameter eff ε is confirmed by numerical simulation, at least at the physical level of rigor. It is shown that for a finite totN, the threshold fragmentation velocity under high-speed loading cV∞ exceeds that under low-speed loading 0cV, i.e., 0ccVV∞>. Calculations show a slight difference between 0cV and cV∞, amounting to only 1-3%. Furthermore, we find that the cumulative mass distributions under low-speed and high-speed loading practically coincide in the region of small and medium masses, and differ only in the region of large masses. Thus, it can be argued that viscoplasticity has a weak effect on sphere fragmentation.

A coupled problem of non-isothermal elastoplastic dynamic deformation of flexible circular cylindrical shells reinforced with fibers along arbitrary trajectories is formulated. The poor resistance of such composite structures to transverse shear and wave processes in them are modeled within the framework of Ambartsumyan’s bending theory. Shell compression is taken into account. The geometric nonlinearity of the problem is considered in the Karman approximation. The plastic deformation of the composite materials is described by the constitutive equations of the flow theory with isotropic hardening. The loading functions of the composite components depend on both the hardening parameter and temperature. The temperature sensitivity of the elastic and thermophysical characteristics of these materials is also taken into account. The temperature across the shell thickness is specified by a high-order polynomial. Two-dimensional heat balance equations for the thin-walled composite structure, corresponding to such a temperature representation, are presented. An explicit numerical scheme is developed to integrate the formulated nonlinear two-dimensional problem. The elastoplastic and thermoelastoplastic axisymmetric deformation of long flexible cylindrical shells reinforced in the longitudinal and circumferential directions is investigated. The structures are loaded by internal pressure similar to that of an air blast wave. It is demonstrated that for a practically acceptable calculation of the thermal response in dynamically bent reinforced shells, the temperature across their thickness must be approximated by a 7th-order polynomial. It is shown that fiberglass shells under the specified loading are additionally heated by no more than 10-12°C, and they can be calculated without considering the thermal response. Metal-composite shells can be additionally heated by 40°C, and the calculation of their inelastic dynamic behavior must be performed taking into account the resulting temperature fields. Otherwise, the calculated deformed state of the metal-composite components may be significantly (by several tens of percent) distorted.

The results of computational and experimental studies on the influence of impact energy on the residual strength of load-bearing wing panels are presented. The objects of study were two-stringer panels of the wing load-bearing box made of polymer composite materials with skin damage obtained at various impact energies. During the tests, the residual strength of the panels under axial compression and the stress-strain state of the impact damage zone were evaluated using strain gauge measurements. The obtained results made it possible to determine the dependence of the residual strength of the panel on the impact energy. It is shown that there is a threshold value of impact energy, after which a sharp decrease in the residual strength of the panel occurs in a relatively narrow range of impact energy variation. A further increase in energy does not significantly affect the residual strength of the panel. The experimental results allowed us to compare the critical stresses of local stability loss of the damage zone with the degree of damage to the composite matrix at different impact energy levels. The obtained data provide a potential opportunity to model impact damage of composites in large power units of the aircraft airframe structure without resorting to complex and time-consuming mathematical models. In general, the results of the experimental work confirmed the assumption that the fracture mechanism of a composite in the presence of impact damage is associated with its local stability loss due to a decrease in the transverse shear stiffness characteristics of the laminate.

To determine the elastic and strength characteristics of polymer composite materials under shear, both in the reinforcement plane and in the transverse direction, various experimental methods are used, based, in particular, on the tension of a strip sample at an angle of 45° to the reinforcement direction, three-point bending of a beam sample with different span-to-thickness ratios, short beam bending, or shear of a sample with V-shaped notches. In these methods, it is quite difficult to assess the influence on the test results of factors such as fiber rotation, complex stress state in the working part of the samples, degree of anisotropy, and local contact deformations. In this regard, this study conducted a comprehensive investigation to evaluate the shear elastic and strength characteristics of a fabric carbon-fiber reinforced plastic using the above-mentioned methods. Analysis of the results showed that tests of Iosipescu samples for in-plane shear and tests of strip samples under tension at an angle of 45° to the reinforcement direction yield almost identical values of shear characteristics, but only in the strain range limited to 5-6%. The failure strains under shear in these experiments differ significantly: tension of strip samples gives 30% lower values. It was also found that, despite the differences in deformation methods during Iosipescu sample tests for transverse shear and beam sample bending tests, the values of elastic and strength shear characteristics of fabric carbon-fiber reinforced plastics differ insignificantly.

In this work, the model of a space-time transversely isotropic continuum is used to develop the most complete version of a variational model for coupled reversible dynamic processes of heat transfer and thermomechanics of deformable media, and to most fully account for coupled effects concerning spatial and temporal effects. The time axis is the axis of transverse isotropy. When describing temperature fields and thermomechanical processes, the applied 4D space-time continuum model allows for the natural introduction of a thermal potential, which is considered as the fourth component of the 4D displacement vector. To determine the force model, the principle of virtual displacements is used, assuming that the list of arguments is determined by the generalized distortion tensor and the 4D displacement vector. The problem of identifying the physical constants of the model for reversible processes is solved. For this purpose, physically justified hypotheses are formulated: the hypothesis of pairing of spatial shear stresses, the hypothesis of the classical dependence of momentum on velocity, and the hypothesis of the potentiality of heat flux (a weakened Fourier hypothesis). It is also assumed that the Duhamel-Neumann law has the form of the classical Duhamel-Neumann law, generalized by taking into account relaxation effects in temperature, pressure, and the spherical strain tensor. It is noted that the use of the space-time continuum model made it possible to obtain a generalization of the Maxwell-Cattaneo heat conduction law for heat flux for reversible processes. A distinctive aspect of the proposed modeling method is that within the framework of the considered models, the generalized Maxwell-Cattaneo and Duhamel-Neumann laws are not introduced phenomenologically but are obtained as compatibility equations when eliminating the thermal potential from the equations of Hooke’s law for temperature, heat flux, and pressure.

The bending of a three-layer plate under direct and repeated alternating loading by a circular line load is investigated. The physical equations of state for the materials of the thin outer load-bearing layers take into account the occurring small elastoplastic deformations. The material of the thicker rigid core is nonlinearly elastic. It is assumed that the deformation of the asymmetric plate follows Kirchhoff’s hypotheses in the load-bearing layers and Timoshenko’s hypothesis in the core. This leads to a linear distribution of radial displacements across the layer thickness. The plate is subjected to a heat flux falling perpendicularly on its upper layer. The end face of the plate and the outer surface of the lower load-bearing layer are thermally insulated. To calculate the temperature field, a formula obtained by averaging the thermophysical characteristics over the package thickness is used. The influence of temperature on the elastic moduli and plasticity functions and the physical nonlinearity of the materials is taken into account. The boundary value problem is formulated using variational methods. A corresponding system of equilibrium equations and force boundary conditions for the considered three-layer plate is obtained. The work of tangential stresses in the core is taken into account. Kinematic boundary conditions are formulated, and the boundedness of the solution at the center of the plate is used. When constructing the solution to the bending problem of the corresponding elastic plate under a line load, a known solution for a uniformly distributed annular load is used. A limit transition is applied as the thickness of the load ring approaches zero. The solution of the boundary value problem for loading an elastoplastic plate from the natural state is carried out using Ilyushin’s method of elastic solutions. The analytical iterative solution is expressed in terms of Bessel functions. For repeated alternating loading, Moskvitin’s variable loading theory is used. Cyclic hardening of the material in the load-bearing layers is taken into account. A numerical analysis of the obtained analytical solutions is carried out, and the dependence of displacements on the physically nonlinear properties of the layer materials, temperature, and boundary conditions is investigated.