Mechanics of Solids最新文献

The reasons for the occurrence of failures are considered, the consequence of which can be considered the progressive collapse of structures and the consideration of structural safety in more expanded concepts than when assessing the first and second groups of limit states for low-rise buildings built from local materials.

The strong engraving and large deformation processes of multi-layer metallic materials with an initial impact are studied in this work based on a new propulsion pattern under a new two-stage combustion technology from two types of propellants that can improve the launch stability and safety of the vehicle composed of multi-layer metallic materials. The research focuses on analyzing the stress-strain characteristics, which involve complex interactions between multi-layer materials and the steel launcher. This is achieved through the development of a comprehensive dynamical model in conjunction with two-stage ignition combustion ballistic equations. Simulation results are meticulously compared with experimental data to validate the accuracy of this intricate coupled model. Further, the influences of the launcher structure on the deformation and engraving characteristics of the vehicle are also investigated, demonstrating that the launcher structure can obviously affect the stress-strain distribution and the groove patterns with obvious variations of engraving resistance generated in the deformation motion process of the vehicle. Based on this, this work also obtains the impact engraving resistance equations under different conditions. By integrating theoretical modeling with experimental verification, the study provides valuable reference into optimizing the design and operation of vehicles composed of multi-layer metallic materials, thus contributing to advancements in launch stability and safety technology.

Because of mechanical loads, thermal fields, or the limitation of the manufacturing technology, initial stresses in functionally graded (FGM) structures are inevitable in various engineering applications. In the context of “Mechanics of Incremental Deformations”, the effect of the initial stresses in the axial direction on dispersion relations of guided waves in FGM fan-shaped cylindrical structures is investigated by exploiting the double orthogonal polynomial series method. The influence of the variation in the graded function and cross-section size on the effect of initial stresses is analyzed. Results indicate that the effect of the initial stretch and compressive stresses on dispersion curves is usually (but not always) opposite. The variation in graded function and cross-section size significantly influences the effect of initial stresses on the dispersion curves, and its influence on different modes is also distinct. The obtained results provide theoretical guidance on guided wave non-destructive testing for FGM fan-shaped cylindrical structures.

Problem of sliding of a periodic system of asperities along the boundary of a viscoelastic half-space with a coating is under consideration. The coating is modeled by a layer with flexural rigidity. The solution is based on reducing the problem to the contact of a limited system of asperities with the action of others being replaced by distributed pressure; the accuracy of such approach is evaluated. The numerical-analytical solution is based on double integral Fourier transforms, the boundary element method and the iterative procedure. The influence of the shape of asperities, sliding velocity, and coating thickness on the deformation component of the friction force and on the effect of mutual influence of asperities has been analyzed. To identify the effect of mutual influence, a comparison of the results (distribution of contact pressure and friction force) obtained for multiple contacts and for the isolated asperity has been made. For comparison, the results of solving a similar problem for viscoelastic half-space without a coating have been obtained and analyzed.

Love wave propagation in the conductive polymer structure is investigated in this study. The silicone rubber polymer of finite thickness is used in the guiding layer with conductive and viscous effects. The functionally graded lithium tantalate with piezoelectric effect is taken in the substrate. The propagation behavior of the Love wave is examined under the influence of the external force, sinusoidal diversity (SSD), conductivity, and viscoelasticity of the polymers. The impulsive force due to point source is considered at the interface of the layer and substrate. The equations of motion in the presence of impulsive force are solved by Fourier transform and Green’s function technique. The dispersion curve of the Love wave propagation is derived by using boundary conditions. The influence of the conductivity, viscosity, SSD parameters, and piezoelectricity on the propagation velocity of the wave is examined for the first three modes of the Love wave. The dispersion equation reduced to the conventional form of the Love wave dispersion in particular cases. The derived results are appropriate for the manufacturing and design of the surface acoustic wave (SAW) device, transducer, and sensors. Moreover, the results may be useful to enhance the performance of the surface acoustic wave devices and sensors.

There are a number of cases of operation of structures in which external influences are of a random oscillatory nature. These are, first of all, transportation cases – rail and road transportation.

Therefore, when forming loading modes to assess the service life strength of structures in these cases, a probabilistic-statistical approach is used. The basic principles of this approach are presented in the formation of cyclic loading spectra for testing and analyzing the service life of products. The levels of cyclic loading were assessed and proposals were made for using the developed approach in assessing the service life strength of structures.

A new closed solution of the non-axisymmetric coupled unsteady problem of thermoelectroelasticity for a long piezoceramic cylinder is constructed while satisfying the boundary conditions of thermal conductivity of the 1st and 3rd kind. The cylindrical surfaces of the element are electroded and connected to a measuring device with a high input resistance. Limiting the rate of change of the temperature field on the inner surface of the cylinder allows us to include the equations of equilibrium, electrostatics and thermal conductivity in the mathematical formulation of the problem. To study the resulting non-self-adjoint system of equations and construct a closed solution, a generalized biorthogonal finite integral transformation is used. The obtained dependencies make it possible to determine the temperature, electric and elastic fields in the piezoceramic cylinder, as well as the potential difference between its electrode surfaces under the action of a non-stationary non-axisymmetric temperature “exposure”.

A schematic diagram and mathematical model of the functioning of a new piezoelectric membrane (MDS) actuator with double spirals (DS) electrodes on the upper and/or lower surfaces of a thin piezoelectric layer with axisymmetric and periodic (small period) reciprocal electric polarization along the radial coordinate are presented. The polarization of the layer is carried out as a result of connecting the polarizing value of the electrical voltage to the outputs of the double spirals of the electrodes. The electrodes of each (upper and lower) double helix of the MDS actuator are made in the form of electroded tape coatings on the surfaces of the piezoelectric layer in close proximity to each other (due to the small pitch of the helix) to create high electric field strengths along the field lines in local areas of the piezoelectric layer between them when connecting an alternating or direct control electrical voltage to the electrodes, in particular, with positive and negative values of electrical potentials. It is important that the electric field lines and, as a consequence, the polarization of the piezoelectric layer of the MDS actuator are oriented mainly along (i.e., towards or against) the radial coordinate of the membrane, in contrast to many traditional actuator schemes. The results of numerical simulation for a round elastic membrane with piezoelectric actuators installed on its upper and lower surfaces confirmed the effectiveness of the proposed piezoelectric MDS actuator when operating according to the “bimorph” scheme, including using the proposed new structural element (section) - piezoelectric MDS- “compression rings” for various geometric and control parameters. The effect of a significant increase in the deflection of the membrane with installed piezoelectric MDS actuators was revealed compared to the use of traditional homogeneous plate piezoelectric actuators of the bimorph type for various conditions of fastening the membrane, in particular, stationary (rigid) fastening of its center. For a hybrid piezoelectric MDS actuator, including independent concentric circular and annular (i.e., “pressure ring”) sections, a non-monotonic character was revealed and a numerical analysis was carried out of the nonlinear dependence of the largest deflection in the center of a membrane hinged and fixed at the edge on the radius ratio its circular and annular MDS sections. Cases have been identified in which the “pressure ring” effect manifests itself, i.e. when the maximum deflection of a membrane with a “pressure ring” exceeds the best possible deflection of this membrane without using it according to the traditional “bimorph” scheme. The new piezoelectric MDS actuator can be used in micromechanics, controlled optics, sensor technology, acoustics, in particular, in the manufacture of piezoelectric acoustic or membrane-type sensor elements, electromechanical transducers for collecting vibration energy.

The article is an analytical review and is devoted to the theory of thin, isotropic elastic plates. The basic relations of the theory based on the kinematic hypothesis are presented, according to which tangential displacements are distributed linearly over the thickness of the plate, and its deflection does not depend on the normal coordinate. As a result, a system of sixth-order equations was obtained for two potential functions: the penetrating potential, which determines the deflection of the plate, and the edge potential, which makes it possible to set three boundary conditions on the edge of the plate and eliminate the well-known contradiction in the theory of Kirchhoff plates. Problems that do not have a correct solution within the framework of Kirchhoff’s theory are considered - cylindrical bending of a plate with a free edge, bending of a rectangular plate with a non-classical hinge, torsion of a square plate by moments distributed along the contour, bending of a plate with a rigid stamp. In conclusion, a brief historical review of works devoted to the theory of plate bending is presented.

An exact solution to the contact problem of indentation of an absolutely rigid stamp with a straight base, taking into account friction, into one of the edges of a finite crack located in a homogeneous elastic plane is constructed. It is assumed that tangential contact stresses are directly proportional to normal contact pressure. In this case, it is believed that the friction coefficient is directly proportional to the coordinates of the contacting points of the contacting surfaces. The defining system of equations for the problem is derived in the form of an inhomogeneous Riemann problem for two functions with variable coefficients and its closed solution in quadratures is constructed. Simple formulas for contact stresses and the normal dislocation component of displacements of crack edge points are obtained. The patterns of changes in contact stresses and crack opening depending on the maximum value of the friction coefficient have been studied.