In the present article, we propose the model of in-plane oscillations of inhomogeneous prestressed plates, both solid ones and those containing a set of holes and inclusions made of different materials. We treat the plates’ mechanical properties and the prestress tensor components in the considered 2D problem statement as functions of two coordinates. In order to formulate the boundary value problems of steady-state in-plane vibrations of plates, we employ the general linearized formulation for an elastic body under conditions of an initial stress-strain state. The developed vibration model makes it possible to specify an arbitrary type of prestress state in the plate in the form of analytical dependences, as well as numerically, by solving the corresponding static problem, in which prestresses arise as a result of applying some initial load. To implement the finite element (FE) approach to solving the problems, we formulated the weak problem statement by projecting the original governing equations on the field of test displacements satisfying the essential boundary conditions. To increase the accuracy of calculations for plates with holes and inclusions, the local refinement of FE meshes are used. The proposed approach to calculating plate vibrations is implemented as a software package via FreeFem++. A method for assessing the effect of prestress on dynamic plates’ characteristics under various types of loads is described; a comprehensive analysis is carried out to identify the probing modes, frequency ranges and response pickup areas, most sensitive to the prestress changes, for each of the plates. We systematize and generalize the results obtained during the analysis, give a few practical recommendations on the choice of probing modes for each type of the plates considered, allowing to perform the most efficient schemes for identifying the prestress components.

The aim of this study is the approach to the optimal design of structurally-anisotropic aircraft bearing surface panels with the restrictions according to the refined buckling theory for the optimal size-weight design implementation. The panels are subjected to the distributed constant compressive loading applied to the edges in the skin plane in the longitudinal direction. The panel contour boundary conditions are assumed to be the particular case with conformable boundary restrictions for the plane problem and problem of bending. The optimal design problem statement and analytical solution are formulated to determine the geometry parameters of a flat rectangular multilayer panel made from composite materials with the eccentric longitudinal and lateral stiffening set being of minimal mass. The equal-buckling condition is the optimal design base. The general bending mode of buckling and multi-wave torsion mode of buckling must have the same occurrence probability while the buckling margin tends to one. The optimal design problem is reduced to the mathematic conditional extremum investigation of the goal weight function with multiple variables using the analytical and numerical methods. New mathematic model relations for the buckling problem investigation of structurally-anisotropic composite panels are presented. The primary scientific novelty of this research is the further development of the thin-walled elastic rib theory related to the contact problem for the skin and rib with an improved rib model. The analytical solution is reduced to determine the displacements of a base neutral surface that may be select arbitrarily. The schematization of the panel as structurally-anisotropic one has been proposed as a design model when the critical forces of total bending mode of buckling are determined. For a multi-wave torsion buckling study, one should use the generalized function techniques for the discrete stringer stiffness. The solution of the strained surface differential equation of an eighth order is designed by a trigonometric series in the closed form. The results of the optimal design with the refined buckling restrictions based on refined buckling analysis calculations offer opportunities to reduce and optimize the weight characteristics of aircraft elements.

The article considers non-contact deformation during surface plastic deformation based on the reverse rotation of the deforming tool. Using software for 3D design (Solid work 2019) and computational modeling (Ansys workbench 19.2), calculations were made to determine the size of an elastic-plastic wave depending on the main parameters of reverse surface plastic deformation (SPD) and the physical and mechanical properties of the material. The stress state in elastoplastic waves generated in the direction of feed (A1) and in the direction of the main movement (A2) is also established. It has been established that the linear dimensions of elastoplastic waves reach a maximum at a preload value of t = 0.4 mm. The main parameters of the reversible PPD, which characterize the kinematics of the working tool (reverse speed of the working tool, the speed of the workpiece, the initial angle of the working tool and the amplitude of the angle of the reverse rotation of the working tool) have a significant impact on the change in the size of the elastoplastic wave in the direction of the longitudinal feed and slightly affect the change in the size of the elastic-plastic wave in the direction of the main movement. The change in the stress state of the surface layer is shown depending on the physical and mechanical properties of the material: large sizes of the elastic-plastic wave during elastic-plastic deformation are formed in the material with a reduced yield strength and elastic modulus. It was also found that the larger the size of the elastic-plastic wave, the higher the maximum tensile stresses at their vertices. The resulting stress state of the wave allows us to conclude that maximum tensile stresses are formed at their tops, the value of which reaches 202–271 MPa (2,4–3,2 times less than the ultimate strength of the material), which practically does not cause strength failure hardened surfaces.

An actual problem of modern engineering about destruction of a pipeline as a result of influence of hydrogen contained in the transported products is considered. Hydrogen changes the mechanical properties of metal, affecting the stress-strain state of the pipe, which, in turn, affects the distribution of hydrogen in the pipe. The hypotheses about the nature of this relationship accepted in the paper allowed to explain the reason of circum-ferential crack formation in the pipe under the influence of hydrogen. An algorithm for iterative calculation of the stress-strain state of a tube containing a hydrogen-containing mixture inside the tube has been developed. The coupled problem of the theory of elasticity and diffusion in the planar axisymmetric formulation is solved. Since the interaction process of hydrogen and metal is very slow, it is considered in sequential static formulations. First, the Lame-type problem for a tube with the modulus of elasticity depending on the radial coordinate is solved. By the finite difference method the stress and strain fields of the pressurized pipe are found. Further, the concentration of free hydrogen in the pipe caused by its content on the pipe surfaces and its stress state is determined. The accepted hypothesis about the condition of hydrogen atoms embedding into the crystal lattice of metal allows to estimate the influence of hydrogen on mechanical properties of the pipe material at the next stage of the calculation. The calculation of stress and concentration fields is repeated again with already modified mechanical properties. The iteration process is stopped when the stresses in the tube reach critical values according to Mises criterion or when the mechanical properties of the pipe mate-rial stop changing. The calculations show that at some combination of hydrogen concentration and pressure on the pipe wall, zones of plastic deformation arise in the pipe, which can lead to delamination of the material in the circumferential direction. This result is consistent with known experimental data.

This paper explores the optimization macrostructure to reach a stable low coefficient of thermal expansion αx of a composite with carbon fibers. To limit the search area, a necessary condition for the existence of αx local minima is proposed, expressed in terms of the radii of hyperspheres in the design space of the angular orientation of the layers transformed by the PСA algorithm. The analysis of the structure variants characterized by low αx shows different sustainability to lamina properties variability. Multi-criteria optimization was carried out. The objective functions are expectation E(αx) and variance Var(αx). The analysis of Pareto fronts and probability density functions make it possible to estimate the reachability of the calculated αx under given conditions of lamina properties variability. The reduction variance opportunity of αx distribution by modifying the polymer matrix with MWCNTs under conditions of reinforcing fibers disorientation and lamina properties variability is investigated. The microstructure modification of the polymer composite material allows to reduce the Var(αx) by 91.61 % with a volume ratio of MWCNTs up to 1 %. Requirement thermomechanical properties are reached by determining the orientation of anisotropic layers. Based on the obtained optimal structures, specimens of CFRP with 0, 1 and 2 vol.% MWCNTs were made. Scanning electron microscopy using FE–SEM Hitachi S–5500 was performed to check the uniformity of distribution and compatibility of the epoxy matrix and MWCNTs. The measurement of αx is determined using a TAInstrumentsQ400 thermomechanical analyzer. Measured αx of specimens is in the range from 6.2·10-8 to 1.98·10-7 1/K. The structure optimization approach proposed in this paper makes it possible to obtain a set of solutions with a consistently low αx in the range up to 1·10-7 1/K. The transformation of the design space of the layers’ orientation angles and the limitation of the search area allowed to reduce the range of solutions under consideration by 83.9 %.

One of the most important tasks in the development of aircraft structures from polymer composite materials is to ensure fatigue strength. It is known that the behaviour under cyclic loading of parts and standard samples is not the same. The problem of transferring the results of standard tests to a full-scale product is especially acute due to the variety of reinforcement schemes, the influence of technological and design factors. This forces us to test full-scale products or structurally similar elements. This work is devoted to the study of the patterns of fatigue failure of a typical element of shell aircraft structures – an L-shaped flange made of laminated carbon fibre. A method of fatigue testing of the critical zone of the flange has been developed. It reproduces the operational conditions of flange loading. The fatigue loading of the sample is carried out by the inertia forces of the load attached to it. The tests were carried out with resonant harmonic vibrations on a vibration stand in a bending shape. The experimental setup ensures constant maintenance of the resonant mode. The experimental setup ensures continuous monitoring of deformation, the resonant frequency of vibrations of the sample and the temperature field on its surface. The characteristic patterns of the development of fatigue damage of the flange are established. The main mechanism of destruction is the appearance and development of delaminations in the flange and in the area of its connection with the shell. Fatigue failure is accompanied by a drop in the resonant frequency of vibrations of the sample, due to a decrease in its rigidity. The typical dependences of the resonant frequency drop on the relative fatigue time reflect an abrupt change in the stiffness of the sample. The established regularities of the fatigue damage accumulation process are confirmed by the analysis of the thermal state of the sample during testing, which changes as a result of its self-heating during cyclic loading. The experimental data can be used in the development of the design of flanges made of CFRP and in the development of models for predicting their fatigue life.