Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
№ 6 (2025)
Articles
TIMOSHENKO THEORY OF PLATE BENDING IN A HIGH PRESSURE FIELD
Аннотация
The linear equation of cylindrical dynamic bending of an elastic plate, on the front surfaces of which high pressures act, is derived. In addition to the inertia of rotation and transverse shear, the compression of the plate by thickness and the associated longitudinal force are taken into account. The transverse distributed force, depending on the average pressure and curvature of the middle surface, is specified. The dependence of static bending on the average pressure on the surface of the plate and the rigidity of the supports in the longitudinal direction is considered in detail.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):3–21
3–21
USING A MOVING MASS TO CHANGE THE SPATIAL ORIENTATION OF A RIGID BODY SUBJECT TO TIME-DEPENDENT EXTERNAL FORCES
Аннотация
A mechanical system consisting of a rigid body and a material point is considered. They interact with each other by means of internal forces whose physical nature is not defined. Both objects are affected by external forces specified as functions of time. The task is to construct a trajectory for a point mass such that the solid body, under the action of the force of interaction with this mass, changes its orientation in space according to a predetermined program. Based on the theorem on the change in the relative moment of momentum, a second-order vector differential equation, unresolved with respect to the highest derivative, is obtained that describes the system. A change of variables is found that allows replacing the original equation with a first-order vector differential equation resolved with respect to the derivative. All special cases arising from the use of the new equation are considered. The obtained relationships can be used to control spacecraft and robotic systems.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):22–36
22–36
SCALE EFFECTS OF FIBROUS AND DISPERSED MATERIALS WITH AN INTERFACE LAYER
Аннотация
The paper considers anomalous scale effects for fibrous and dispersed nanomaterials with a gradient interphase layer caused by the dispersion and aggregation of inclusions. To model these effects and evaluate the mechanical properties of dispersed and fibrous composites with interphase layer, an analytical-numerical algorithm has been developed that allows one to obtain an exact solution to the cell problem in the Bakhvalov asymptotic homogenization method. This algorithm is used to evaluate and simulate the effective characteristics of structurally inhomogeneous materials taking into account the aggregation of the filling nanoparticles, when non-classical effects of strengthening occur at ultra-small volume fractions. The obtained solutions also allow one to calculate the stress concentration tensor that reproduces the distribution features of local stresses near inclusions taking into account the gradient properties of the interphase layer. It is of great importance for evaluating the strength characteristics of such materials. Using the developed algorithm a study was conducted of the anomalous properties of polymethyl methacrylate filled with multilayer carbon nanotubes, and for the first time, the presence of two enhancement waves of the mechanical properties for the composite with ultra-low filler fractions was noted, which is confirmed by the similar behavior of metal-matrix composites based on an aluminum matrix and oxide fillers.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):37–60
37–60
ON CONVENTIONAL STABILITY OF STEADY-STATE MOTIONS OF MECHANICAL SYSTEMS WITH A PARTIAL STEKLOV’S INTEGRAL
Аннотация
Investigation of the conditions of conventional stability of steady-state motions of a mechanical system, which assumes existence of an additional partial V.A. Steklov’s integral, has been conducted. Analysis of conventional stability is conducted by Chetayev’s technique with the Lyapunov’s function represented by a full bundle of first integrals of the disturbed motion. It has been ascertained by analytical computations that, in case of a full bundle of integrals, it is possible to formulate sufficient stability conditions, which are the most close to the necessary conditions. It has been demonstrated for the scrutinized system that the boundary conditions of stability may be reached under the limit values of some Langrange multipliers. This allows the researcher to consider the bundles of integrals in the Routh-Lyapunov method and in the Chetayev’s technique differently.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):61–74
61–74
On the extrusion of an elastic-viscoplastic material in a rectangular matrix due to a changing pressure difference
Аннотация
Algorithms for solving and calculation results for the problem of the movement of material in a rectangular pipe under the action of an increasing pressure drop in the frame of theory of finite elastic-viscoplastic strains are presented. The problem with specifying reversible and irreversible deformations by differential equations of their transfer is reduced to solving a system of differential equations with no-slip conditions on the pipe walls. An approximate solution of such a problem by the finite-difference method remains within the framework of the classical approach, without encountering additional difficulties. The elastic properties of an incompressible material are specified by a three-constant dependence of the elastic material on the invariants of the Almansi tensor, viscoplastic properties by flow theory with a generalized condition of maximum von Mises octahedral stresses for the case of taking into account the viscous resistance to plastic flow. The time and place of origin of viscoplastic flow, the patterns of movement of elastic-plastic boundaries, the elastic core, the evolution of stagnation zones in the corners of the pipe are calculated.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):75–98
75–98
ROLE OF SHIELD AROUND CRYSTAL IN CZOCHRALSKI PROCESS
Аннотация
The influence of shield around crystal on gas-and hydrodynamics, heat transfer and defects formation in Czochralski silicon crystal growth process is studied by means of mathematical modeling. The domestic silicon crystal growth furnace Redmet-90M is considered, which allows the silicon single crystal growing with 200 mm in diameter and 1.5 m in length. The growth process occurs under argon flow pumping in the rarefied atmosphere of growth camera. High-temperature heating ensures silicon melting in crucible and silicon ingot crystallization by Czochralski pulling from a melt. The mathematical model considers the conjugation of heat exchange and silicon monoxide transfer processes. The effect of shield around crystal on axial temperature distribution in grown single crystal is considered. For dislocation-free single crystals this characterizes the type of forming intrinsic point defects. The international verification results of the shield around crystal influence on axial temperature distribution in the growing crystal for Czochralski crystal growth furnace EKZ-1300 are discussed. Also, the verification results in application to Czochralski crystal growing on EKZ-1600ELMA are presented, which illustrate the application of defect formation theory of V.V. Voronkov in dislocation-free single silicon crystals.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):99–113
99–113
ON THE APPLIED THEORY OF RECTANGLE STRETCHING
Аннотация
The paper considers deformation of isotropic rectangular samples within the generalized plane stress state. Approximate models of different orders for elongated samples are constructed by representing the displacement field as an expansion in first- and second-order polynomials with unknown coefficient functions. The Kantorovich method within the Lagrange variational principle allows one to reduce the problem to a system of ordinary differential equations with constant coefficients and to form the corresponding boundary conditions. The models are verified by the finite element method (FEM) implemented in FlexPDE, the suitability of the obtained models is investigated depending on the relative thickness parameter of the rectangle. The inverse problem of reconstructing the Poisson ratio and Young’s modulus from information on the displacement field on the lateral face is solved.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):114–127
114–127
IDENTIFICATION OF A THERMOVISCOELASTIC CROSSLINKED POLYMER MODEL TAKING INTO ACCOUNT LARGE DEFORMATIONS AND ITS APPLICATION
Аннотация
The purpose of the work is to develop a model of viscoelastic thermomechanical behavior of cross-linked polyethylene (CLPE) products with a shape memory effect. The main area of application of this class of materials is heat-shrinkable tubes and their modifications. They are characterized by initial expansion values of 100 percent or more. Simo and Holzapfel proposed modified defining relations representing a synthesis of the viscoelastic Proni model and the hyperelastic model based on the elastic energy potential. The published work proposes a methodology for identification of both damping and nonlinear elastic material constants in case of large deformations. An experimental program is developed and implemented to determine the material constants of cross-linked polyethylene. It includes the procedure of reducing the dimension of the nonlinear optimization problem when finding exponential approximation coefficients of the relaxation function. A description is given of the developed algorithm for searching for the material constants of a hyperelastic model based on the results of an experiment on cyclic loading of a sample with large deformations in the range of highly elastic behavior. An adaptation of the hyperelastic model in ANSYS is made taking into account the presence of relaxation properties. As an illustration of the application of the updated physical model, an example of a finite element calculation of the pressure of heat-shrinkable tubes when deposited on a rigid cylindrical surface is given. An engineering technique is also proposed that allows similar calculations to be made in the Excel spreadsheet.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):128–151
128–151
BASIC RELATIONS FOR COMPLEX POTENTIALS OF ELECTROMAGNETOVISCOELASTICITY AND THEIR USE IN SOLVING PROBLEMS OF THE ACTION OF CONCENTRATED FORCES
Аннотация
The main relations for complex potentials of a plane problem of electromagnetic viscoelasticity, their general representations for singly and multiply connected domains, and boundary conditions for their determination are presented. Using these functions, solutions are obtained for problems of concentrated effects (mechanical forces, electric charges, and magnetic dipoles), exact for a singly connected plate, and approximate, with high accuracy of satisfying the boundary conditions, for a multiply connected plate. The results of numerous studies are described for a plate with one or two circular holes or rectilinear cuts-cracks, with a hole and a cut, with two cuts, and the cases are considered when the contours of the holes intersect or the cuts go to the contour of the hole. The patterns of influence of the geometric characteristics of the holes and cuts, the physical-mechanical and electromagnetic properties of the plate materials, and also the time after applying external forces on the values and nature of the distribution of stresses and inductions are established.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):152–175
152–175
ELECTROMAGNETIC COUPLING OF PIEZOELECTRIC/FERRITE COMPOSITE WITH QUASI-PERIODIC STRUCTURE, INITIAL STRESS STATE AND MAXWELL-WAGNER RELAXATION
Аннотация
Analytical solutions have been obtained for tensors of effective electromagneticmotive properties of a composite with a quasi-periodic structure, taking into account the anisotropy of the disordered inclusions relative to the corresponding ideal periodic structure in a generalized singular approximation of the method of periodic components of statistical mechanics. The magnitude and anisotropy of the disordered inclusions (fibers) are taken into account in the solution through the coefficients of periodicity and anisotropy of the disordered inclusions relative to the corresponding ideal periodic structure, the effective properties of which are considered known. For the case of isotropic disordered inclusions, analytical solutions for tensors of effective electromagneticmotive elastic and pyroelectric properties of a composite with a quasi-periodic structure are obtained as simple linear decompositions of the desired solutions through known tensors of corresponding effective properties for a periodic structure and for a statistical mixture using the periodicity coefficient. The results of numerical modeling of the frequency dependences of the electromagnetic coupling coefficients are presented, taking into account a given initial stress state and the Maxwell-Wagner relaxation of the electric fields of the structural elements of a quasi-periodic composite.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):176–201
176–201
THERMOMECHANICAL AND THERMOPHYSICAL PROPERTIES OF LITHIUM NIOBATE
Аннотация
A new thermodynamic model of lithium niobate is proposed, based on the use of the sixth-degree Landau potential. Its feature is the nonlinear dependence of the coefficient at the square of polarization along the polar direction on temperature. In contrast to the previously used fourth-degree potential, this ensures good agreement between the behavior of spontaneous polarization and deformation calculated on its basis and the results of experimental studies. Using the proposed thermodynamic potential, a complete set of material constants determining the thermomechanical properties of lithium niobate, as well as constants of the electro-optical and acousto-optical effects in a wide range of temperature changes, is constructed. Independence of the elastic moduli of lithium niobate from temperature is confirmed, in contrast to piezoelectric, acousto-optical and electro-optical constants, some of which undergo significant changes. The results are of interest when choosing the orientation of the crystal cut in the process of developing micro- and nanoscale acousto- and optoelectronic devices.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):202–216
202–216
ON THE ELASTIC-PLASTIC DEFORMATION OF A CIRCULAR PLATE UNDER CENTRALLY SYMMETRIC NORMAL LOADING
Аннотация
In the approximation of the Föppl—von Kármán model, which takes into account the presence of plastic deformations, the solution of the problem of elastoplastic bending of a thin plate was obtained, under the boundary conditions of the type of rigid, or generalized elastic embedment type. The model of ideal plasticity with the Tresca—Saint-Venant yield surface was used. The use of the standard Kirchhoff—Love hypotheses allowed to reduce the problem to a system of ordinary differential equations. The numerical solution of this system for the boundary conditions of the generalized elastic embedment was obtained. The solution for the boundary conditions of rigid clamping is obtained as a particular case.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):217–243
217–243
DETERMINATION OF INCUBATION CHARACTERISTICS OF THE HIGH RATE PLASTIC DEFORMATION PROCESS OF MATERIALS DURING IMPACT TESTS OF A CYLINDRICAL SAMPLE ON A RIGID ANVIL
Аннотация
A fundamentally new method is proposed for assessing the plastic response of a material to dynamic loading during tests of cylindrical specimens impacted against a rigid barrier. Unlike the traditional Taylor test, this study considers a temporal yield criterion based on the concept of incubation time. This approach allows for a transition from averaged rate-based estimates to a more accurate and physically grounded description of material behavior over time. Impact tests of cylindrical specimens against a rigid anvil were conducted to determine the yield strength exhibited by the material at various impact velocities. The material behavior under high rate elastoplastic deformation was investigated. The impact-on-anvil test incorporates new dynamic characteristics of the material, which define the rate sensitivity of the yield strength based on the incubation time criterion. The test results are interpreted as a time-dependent yield strength, i.e., the threshold amplitude of the impact load as a function of its duration. It is shown how the parameters that enable prediction of the rate and temporal dependence of the yield strength under arbitrary impact-wave loading can be estimated from a single test.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):244–260
244–260
ALTERATION OF NATURAL VIBRATION FREQUENCIES BY PIEZOELECTRIC ELEMENTS EMBEDDED IN ELASTIC BODIES
Аннотация
This paper addresses the problem of altering the natural vibration frequencies of an elastic body with embedded piezoelectric elements by applying an electric potential to them. Presented mathematical formulation of the problem based on the principle of virtual displacements for a piecewise-homogeneous electroelastic body. Finite deformations are represented as the sum of linear and nonlinear parts, which are linearized with respect to a state featuring a small deviation from the initial equilibrium position caused by the reverse piezoelectric effect. Provided experimental and numerical results validate the reliability of the numerical algorithm based on the finite element method. Using a plate with an embedded piezoelectric element as an example, presented numerical results demonstrate the influence of various parameters on the change in natural vibration frequencies: the stiffness characteristics of the elastic body; the dimensions, location, and number of piezoelectric actuators; the area ratio of the piezoelectric element to the elastic body; and the magnitude and sign of the electric potential.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(6):261–276
261–276