The paper solves the problem of bending a piezo plate in the form of a half-plane with holes and cracks by using the complex potentials of the theory of electro-magneto-elastic bending of thin plates. In this case, functions that are holomorphic outside the contours of the holes and cracks are decomposed into Laurent series, and functions that are holomorphic in the lower half-planes are expressed using Cauchy-type integrals in terms of functions conjugate to these functions. При таком подходе полученные суммарные функции точно удовлетворяют граничным условиям на прямолинейной границе полуплоскости, а для определения неизвестных коэффициентов рядов Лорана используются граничные условия на контурах отверстий и трещин, которые в работе удовлетворяются обобщенным методом наименьших квадратов, приводящим задачу к переопределенной системе линейных алгебраических уравнений, решаемой методом сингулярного разложения. With this approach, the resulting total functions precisely satisfy the boundary conditions on the rectilinear boundary of the half-plane. To determine the unknown coefficients of the Laurent series we use boundary conditions on the contours of the holes and cracks, which are affected by the generalized least squares method, leading the problem to an overridden system of linear algebraic equations solved by the singular value decomposition method. The numerical results of the electro-magneto-elastic state of a half-plane with a circular hole or crack, with a circular hole and an internal crack in the jumper, with a circular hole having an edge crack in the jumper are described. We establish regularities of changes in the electro-magneto-elastic state of the plate depending on its material and geometric characteristics of holes and cracks, their mutual location. It has been found that as the hole or crack approaches the rectilinear boundary, the values of the moments at the points of the bridge increase sharply and change insignificantly in other zones. A large concentration of moments is also observed at the points of the rectilinear boundary near the jumper. The values of these moments are especially high in the problem for a half-plane with a circular hole having an edge crack in the jumper. The values of bending moments are significantly affected by taking into account the piezo properties of the material, especially in areas of high concentrations of the bending moments, therefore in these cases it is forbidden to limit ourselves to solving the problem of elasticity theory of plate bending, and it is necessary to solve the problem of electro-magneto-elasticity. Keywords: thin piezo plate, half-plane, holes, cracks, complex potentials, Cauchy type integrals, generalized least squares method, concentration of bending moments, moment intensity factors.

The paper presents numerical and experimental studies of deformation and fracture processes of 10G2FBU and St35 steels under various types of quasi-static and dynamic loadings: tension of a solid rod and M8 bolts with smooth and threaded working parts, as well as compression of compact cylindrical specimens. The developed experimental-calculation techniques are described in detail and shown schematically for quasi-static and dynamic true strain diagrams in tensile and compression experiments. Application of these techniques made it possible to determine quasi-static and dynamic true strain diagrams for steels 10G2FBU and St35. The obtained quasi-static deformation diagrams of 10G2FBU steel in tension and compression practically coincide. It was found that in the construction of true strain diagrams for 10G2FBU steel, the strain rate at values above 500 1/s has a significant influence. A coupled fracture model based on the kinetic equation of damage accumulation in combination with the strength criterion of the Pisarenko-Lebedev type is proposed and implemented to investigate and describe the deformation and fracture processes of elastoplastic materials. Based on the experimental-calculation approach, a new methodology for fitting material parameters for the proposed fracture model is developed. Accordingly, the material parameters of the coupled fracture model for St35 steel are determined. The results of numerical modeling of the fracture process of M8 bolts with smooth and threaded working part under quasi-static tension show a quantitative and qualitative correspondence of the type and character of fracture with the experiment. The joint application of the experimental-calculation approach and the proposed coupled fracture model allows a more accurate description of the deformation and fracture processes of elastic-plastic materials.

The article considers plates with stiffeners, the two opposite ends of which are fixed rigidly, and the other two are free. The stiffeners are located in the same direction, parallel to the free edges of the plate. The paper proposes a method for analyzing such structures by combining the reduction of the dimensionality of the problem using the L. V. Kantorovich method and the Ritz method with discrete approximation of displacements. The methods of defining stiffeners using unit column functions are considered. It is revealed that unit column functions are a convenient way to model stiffeners, even when it is necessary to consider stiffeners in boundary conditions. The stiffeners in the shapes of a box, a T-beam, an I-beam and a solid rectangular section are considered. Their geometric characteristics are given, which are used when constructing the functional of the total potential energy taking into account their discrete location. The calculation results obtained by the proposed method are compared with the solution obtained using the structural anisotropy method for the solution of the boundary value problem for ordinary differential equations. In a numerical experiment, the number of finite elements along the stiffener’s width is established, which is necessary and sufficient to solve the problem. Graphs of displacements of plate middle zones are printed, on the basis of which it is concluded that the proposed method has a fairly good convergence with the method of structural anisotropy. However, the plates calculated by these two methods deform differently and the Ritz method with discrete approximation gives a more accurate form of deformation: the plate deforms less in the area of the stiffeners and more between them. From the calculation results, it can be concluded that the presented method is the most optimal in terms of labor complexity and accuracy. However, if the ratio of the total width of the stiffeners to the width of the plate is 1:3 or more, the structural anisotropy method can be used as a simpler one.

The main provisions and equations of the modified theory of inelasticity, which belongs to the class of theories of flow during combined hardening, are considered. The modified theory of inelasticity is the simplest version of the theory of inelasticity, which is integrated into a finite element complex for calculations of the exhausted and residual life of structural materials under conditions of repetition and duration of the thermomechanical loads. The strain tensor is represented as the sum of elastic and inelastic strain tensors, i.e. there is no conventional division of irreversible (inelastic) deformation into plasticity and creep deformation. Elastic deformation follows Hooke's law which is generalized to non-isothermal loading. In the space of stress tensor components, a loading surface is introduced, which expands or contracts isotropically and shifts during loading. For the radius of the loading surface (isotropic hardening), an evolutionary equation is formulated, generalized to non-isothermal loading and recovery of mechanical properties during annealing. The displacement of the loading surface (anisotropic hardening) is described on the basis of an evolutionary equation with a three-term structure, generalized to non-isothermal loading and microstress relief (displacement) during annealing. To separate the monotonic and cyclic deformation in the space of the inelastic deformation tensor, a memory surface is introduced that limits the region of cyclic deformation. To describe placing and ratcheting of an inelastic deformation loop under asymmetrical cyclic loading, a modification of the theory of inelasticity is introduced. The modification of the theory of inelasticity comes down to the fact that when formulating the evolutionary equation for microstresses, the constitutive (material) parameter of the equation for microstresses of the first type is taken to depend on the accumulated inelastic deformation based on different relations for both cyclic and monotonic deformation. To determine the inelastic deformation rate tensor, the associated (gradient) flow law is used. Conditions for elastic and inelastic states are formulated. To describe nonlinear processes of damage accumulation, a kinetic equation of damage accumulation is introduced, based on the work of microstresses of the second type on the field of inelastic deformations. The kinetic equation is generalized to non-isothermal loading and embrittlement and healing processes. The material parameters and functions that close the theory are identified; the basic experiment and the method for their determination are formulated. The material parameters and functions of the bronze alloy BrKh08-Sh at temperatures of 20, 400, 500, 600 °C are given. The theory is verified under cyclic isothermal deformation and fracture (low-cycle strength) under high temperature conditions. Creep and long-term strength under isothermal and non-isothermal loads are also considered. The calculation results are compared with the experimental results.

The article analyzes acoustic emissions (AE) aimed at studying changes in the state of the material caused by deformation. It is very difficult to obtain information directly about characteristics of AE sources because of signal distortions caused by dispersion, unequal attenuation at different frequencies, reflections from free surfaces of the sample, distortions created by the sensor, waveguide and amplifier of electrical oscillations. This paper proposes to compare the characteristics of signals obtained from "fresh" (control) samples and samples that have experienced mechanical testing. Differences between signals are identified with a comparative diagram of spectra representing the modulus of the ratio of Fourier images of signals. Another method used in this work for analyzing signals is based on searching for such characteristics that do not change under the influence of many of the listed distortions. The graph of the spectral power density has a complex serrated shape and, thus, can be considered as a fractal curve which important attribute is the fractal dimension. It is affected by the signal formation conditions and, therefore, can serve as a characteristic for their classification. As an example, a sample of steel 20 was studied. It was subjected to cyclic loading from stress σ = 0 to σmax = 1.2σy, (σy is the yield strength) and unloading, with a frequency of f = 20 Hz. The test was stopped at the 8851st cycle, when the "neck" was formed, and the relative elongation was 15%. We compared the AE signals generated during sample indentation in areas located at different distances from the neck. The fractal dimension of the power spectra decreased from 0.72 to 0.62 when approaching the neck zone. Peaks near the frequency of 270 kHz and 680 kHz were distinguished on the comparative diagrams of the spectra. Thus, the considered methods of signal comparison allow us to estimate the degree of change in the state of samples occurred because of mechanical tests.