Mechanics of Solids最新文献

The effect of the energy dissipation mechanisms, including the viscoelasticity and the charge leakage, on the electromechanical coupling behavior of circular dielectric elastomer membranes is the focus of this study. Based on the principle of non-equilibrium thermodynamics and the theory of nonlinear dissipative dielectrics, this study develops a physical model to describe the influence of the viscoelasticity and the charge leakage on the electromechanical coupling behavior, allowing for the examination of both their independent and combined effects. Through numerical simulations, we first analyze the effect of the viscoelasticity on membrane stress and deformation while isolating the charge leakage. Next, we investigate the radial distribution characteristics of the leakage current in a fixed membrane state. Finally, we examine the combined effects of the viscoelasticity and the charge leakage under varying voltage slopes. The results indicate that both the viscoelasticity and the charge leakage significantly affect the electromechanical response rate of the membrane, while the voltage slope primarily influences the growth rates of various physical quantities within the membrane. This effect is particularly evident in the responses of the radial stretch and the leakage current. This study elucidates the complex effects of the viscoelasticity and the charge leakage on the electromechanical performance of dielectric elastomer membranes, offering valuable reference data for optimizing and designing their applications.

The present paper aims to study the reflection phenomena of plane waves in a rotating, non-local, functionally graded orthotropic thermoelastic half-space with a three-phase lag. Normal mode analysis is used to obtain the solution and the boundary is assumed to be stress-free having the influence of the impedance parameter. The analytical solution to the problem reveals the existence of a quasi longitudinal wave (QL), quasi transversal wave (QT), and a quasi thermal wave (T). Amplitude ratios are derived corresponding to the incidence of each wave. With the help of these amplitude ratios, energy ratios are obtained and presented graphically demonstrating the impact of the functionally graded parameter (FG) and various heat conduction models. The energy ratios depend on the angle of incidence as well as the properties of the medium. The nature of dependence is distinct for distinct reflected waves. The obtained results justify that the summation of energy ratios is unity at each angle of incidence, which thus proves the law of conservation of energy. Moreover, comparative analysis has also been performed with dual phase lag model (DPL) and Lord Shulman model (LS). The results obtained through the investigation are useful to study the rock structure and thermoelastic properties of the inner structure of the earth.

For engineering the development of tunnels or the laying of underground pipelines are essential engineering projects in modern society, and in canyon tunnels and canyon pipeline projects, surface motion and cavity edge motion have been topics of concern in ground vibration problems. In this paper, the wave scattering problem in an elastic half-space medium containing semicircular depressions and subsurface cylindrical cavity is investigated by using the theoretical method, the wave function expansion method, the complex function method and the mirror image method to solve the control equations in the form of Helmholtz equations satisfying the zero stress boundary conditions and to solve the corresponding displacement functions. Then the unknown coefficients in the set of equations to be solved by the free boundary conditions, combined with the Fourier expansion method. The displacement field is a superposition of the appropriate wave fields. Finally, the effects of the relevant parameters on the surface motion |w₁|(w), the dynamic stress concentration factor (DSCF) of the cylindrical cavity and the displacement amplitude of the cylindrical cavity edge |w₂| are investigated by frequency and time domain analysis. This study not only provides a theoretical basis for practical unlined tunnels or pipeline projects, but also can provide a basis for seismic design of underground structures.

Within framework of complex continuous media, the structure is modeled and the stress-strain state of a spherical object approximated to the Earth model under dynamic internal and constant external influences is determined. The spherical body consists of four layers. The outer layer, modeling the mantle, is represented by a hardening elastic-viscoplastic dilating medium. The core has three layers, the outer one is represented by the model of an incompressible ideally plastic von Mises body, the second and third by the model of an incompressible elastic-viscoplastic body. The dynamic load is uniformly distributed along the inner surface of the third layer of the core, and the load of constant intensity is uniformly distributed along the outer surface of the spherical body. Within the framework of the axisymmetric stress-strain state, an analytical solution to the problem is obtained. Relationships for displacement and stress fields in plastic and elastic regions of layers are determined. A system of equations for determining the integration constants and radii of elastic-plastic boundaries is obtained. This system of equations requires a numerical solution. The paper also presents the conditions for exhaustion of the bearing capacity of a spherical object.

To investigate the impact response of interfacial bonding strength on ultra-high molecular weight polyethylene (UHMWPE) fiber soft target plate, this study prepared 6UD structural sheets with varying interfacial bonding strengths by adjusting the adhesive formulation. These sheets were fabricated into UHMWPE fiber soft target plates with identical areal densities. Ballistic penetration tests employing 1.1 g wedge-shaped fragments were conducted, followed by comprehensive damage morphology and anti-penetration performance analysis. Combined with the LS-DYNA simulation software, the 6UD structural sheets were subdivided into three 2UD units, and the TIEBREAK contact method was introduced to simulate the difference in interfacial bond strength between the 2UD units. The velocity attenuation patterns of the fragments, the evolution of delamination zones, and the damage morphology of the rear-side projectile holes were analyzed across different models. The results revealed that the target plate with lower bonding strength was likelier to have extensive projectile holes and fiber debonding. At similar impact velocities, the total damage area of projectile holes in targets with different interfacial bonding strengths was comparable. The simulation results demonstrated that increasing interfacial bonding strength significantly enhances the targets' energy absorption capacity and ballistic limit velocity. In the early stages of penetration, interfacial bonding strength had minimal influence on shear failure. In contrast, in later stages, increased bonding strength played a notable role in energy dissipation and damage retardation. Furthermore, as bonding strength increased, the internal delamination zones expanded, while the projectile hole area on the rear-side layers of the same ply count decreased comparatively.

We consider plane contact problems with a limited contact area for elastic bodies with a regular microrelief (RMR) applied to their surfaces. It is assumed that Flamant’s solution to the problem of the action of a concentrated normal force on the boundary of an elastic half-plane can be used to determine the stress-strain state of bodies. When modeling the contact interaction, a calculation scheme was used in which one of the bodies is considered as a rigid punch, and the second is considered as an elastic half-plane with a composite modulus of elasticity. The single-parameter families of punches with RMR are considered, the parameter of which is the number of microprotrusions. The regularities of contact interaction of punches with RMR and elastic half-plane were investigated by the method of computational experiment. Based on the established patterns, a method for approximate calculation of load distribution between RMR elements, as well as assessment of contact pressure, sizes of actual contact areas and average final gaps on microprotrusions is proposed.

Two-dimensional nanomaterials (graphene, carbon nanotube) are high-strength and ultra-light materials that have several promising areas of application. From theoretical and applied perspectives, it is relevant to study various problems of their statics, stability, vibrations, and calculations of the required mechanical characteristics based on the corresponding continuum theory of the deformation behavior of two-dimensional nanomaterials.

In this work, based on the moment-membrane theory of elastic plates, which is interpreted as the continuum theory of the deformation behavior of graphene, stability problems of a freely supported graphene sheet (rectangular plate) are studied. The sheet is uniformly compressed in one direction, compressed in two directions, and subjected to shear stresses in its plane. The stability problem of uniformly compressed graphene sheets, freely supported on two opposite sides and having different boundary conditions on the other two sides, is also considered.

When solving stability problems of the graphene sheet (rectangular plate), the Euler method is applied, considering a form of equilibrium that is slightly deviated from the initial (moment-free) position (buckled plate). Differential equilibrium equations and boundary conditions are formulated for this shape. The critical load value is determined from the solution of these boundary problems, i.e., the load value at which the initial flat form of the plate becomes unstable. All solutions are accompanied by numerical results: tables or diagrams providing the critical load values for each particular case.

For a three-axis satellite with a ball damper, resonant rotations in the central gravitational field are studied. The equations of the rotational motion of a satellite in an elliptical orbit are obtained. For the case of a circular orbit, spatial resonance rotations of 1 : 1 and 2 : 1 were investigated using the averaging method.

A planar equilibrium problem of a heavy homogeneous thin wire triangle suspended on a thin horizontal nail is considered. The existence of equilibrium positions and their dependence on the coefficient of friction and the lengths of the sides of the triangle are studied under the assumption of the presence of a dry friction force acting between the triangle and the nail. The problem is solved in barycentric coordinates associated with the vertex system of the triangle in question. The equilibrium condition is written in a form that allows a cyclic shift of the indices of the quantities included in it to obtain an equilibrium condition for any of the sides of the triangle with which it contacts the nail.

The article considers the nonlinear dynamics of a cylindrical resonator of a wave solid-state gyroscope with electromagnetic control sensors. A mathematical model that describes nonlinear resonator oscillations and electrical processes of the oscillation control circuit in an interconnected form is deduced. The resulting mathematical model represents a nonlinear system of differential equations, which contains singularly perturbed equations, and the equations of electrical processes are singularly perturbed. The nonlinearity caused by the finite ratio of the small deflection to the small gap of the control sensor is taken into account. The methods of constructing approximate solutions are proposed. The fundamental difference between the nonlinear terms of the equations of resonator dynamics using eight and sixteen control sensors is shown. It is shown that by using electromagnetic control sensors it is necessary to take into account a small parameter singularly included in the differential equations of electrical processes. According to the estimation of the angular drift velocity, it is concluded that the gyroscope circuit with eight electromagnetic control sensors is inapplicable due to the obtained value of the uncompensated angular drift velocity. In the case of a gyroscope with sixteen control sensors, a formula for the angular drift velocity which can be compensated is derived and a method for calculating the displacement of the resonant peak of the amplitude-frequency response is proposed.