Mechanics of Solids最新文献

This study investigates deformations within a homogeneous semiconductor thermoelastic medium subjected to initial stress and ramp type heating employing the theoretical photothermal model. Utilizing the normal mode method, precise expressions for key distributions, such as temperature, carrier density, stresses and displacement components, are derived. Numerical computations are facilitated through Mathematica programming, focusing on a material exhibiting properties analogous to a silicon. Integrating Photothermal model, initial stress, wave number and time, the research visually portrays the impact of these factors on the considered state variables through graphical representations. The numerical and graphical results underscore the significant influence of wave number, time, and initial stress on the various field quantities. This investigation provides valuable insights into the synergistic dynamics among an initial stress constituent, semiconductor structures, and wave propagation, enabling advancements in nuclear reactors’ construction, operation, electrical circuits, and solar cells.

This article investigates the impacts of varying thermal conductivity in the semi-infinite medium due to laser heating sources with a timed pulse. The governing formulations are based on a Lord-Shulman (LS) thermoelastic model with one thermal relaxation time under changing thermal conductivity. To study the nonlinear problems and get the governing formulations, the time-domain finite element approach is used. Laplace transforms and the eigenvalues method are used to solve the problem in the linear case implementation. The impacts of varying thermal relaxation time, time duration of a laser pulse and thermal conductivity are investigated. The numerical outcome obtained through the finite element approach are compared with analytical solutions for constant thermal conductivity to validate the precision of the numerical solution. The numerical results of temperature, stress, and displacement variation are presented graphically.

We consider the problem of the motion of a heavy bead strung on a rough heavy hoop freely rotating around a vertical diameter. Non-isolated sets of steady motions of the system are identified, and their bifurcation diagrams are constructed. The dependence of these solutions on an essential parameter of the problem—the constant of the cyclic integral—is studied. The results obtained are compared with the results obtained previously for the case when a rough hoop rotates around a vertical diameter with a constant angular velocity. Typical phase portraits are constructed for various combinations of system parameters.

Compared with traditional metal materials, the advantages of magnesium alloys are high specific strength and high specific stiffness, which are widely used in various fields of industrial production. The rolling magnesium alloy material has relatively complex mechanical properties due to its crystal structure and texture from processing. Uniaxial quasi-static tensile tests with five orientations along the rolling direction were designed based on the macroscopic elastic-plasticity theory to investigate the mechanical properties of AZ31 magnesium alloy sheets. Experimental true stress-strain and the plastic strain ratio were obtained by the DIC strain-measurement method, the initial yield strength decreases as the angle increases from 0 to 90°, while the tensile strength, in contrast, increases overall as the angle increases. The anisotropic yield criterion and plastic potential function were established in the basic form of the Hill48 yield function. The composite linear-swift hardening model was constructed according to the hardening characteristics of the material. Besides, the complete constitutive model was obtained by calibrating the parameters in the function with the experimental results. The anisotropic model was further validated based on the commercial finite element software COMOSL. The experimental results were compared to confirm the validity of the anisotropic model of AZ31 magnesium alloy sheets.

Self-oscillation systems utilizing soft active materials are gaining attention for their potential in applications like soft actuators, sensors, energy harvesters and micro/nano machines. In this study, a self-oscillator of liquid crystal elastomer (LCE) with tunable shielding area is constructed, which encompasses a light-responsive LCE fiber and a tunable shielding tube with mass. A nonlinear dynamic model for light-spurred self-oscillator motion is proposed and its dynamic behavior is investigated. Computational results reveal that the LCE oscillator exhibits two distinct motion manners: self-oscillation state and static state. The self-oscillation manner is sustained from the energy competition between absorbed light energy and damping dissipation. The triggering conditions for self-oscillation manner are obtained and the effects of various system parameters on the amplitude and frequency of self-oscillation are probed in detail. In contrast to other existing self-oscillation schemes, the constructed self-oscillator system is advantageous in some respects, e.g. simple structure, easy fabrication, and high reliability. In addition, the insights gained from this study advance our understanding in self-oscillatory phenomena and offer new design concepts in the fields of soft actuators, sensors, energy harvesters and micro/nano machines.

To research the damage variations and dynamic mechanical attributes of freeze-thawed rocks, freeze-thaw cycle and impact dynamic compression experiments were performed on samples of water-saturated red sandstone and built the dynamic constitutive model of the entire freeze-thawed rock process by using the theory of the combined model of elements and investigating the rule of damage evolution. According to the findings, the rock specimens’ dynamic peak stress and elastic modulus are enhanced with a rise in strain rate, while these properties are reduced with an increase in freeze-thaw cycles. The experimental and theoretical curves agree, with a goodness of fit of up to 0.9457. There are three stages in a rock’s dynamic damage evolution curve: linear, nonlinear, and damage destruction. The total damage value rises with the number of freeze-thaw cycles when the strain rate is certain and decreases with the strain rate rising in sequence when the freeze-thaw cycles are certain. The damage evolution law is consistent with the macroscopic deformation and destruction.

This paper presents a study on the effects of support stiffness on buckling and postbuckling of imperfect plane arch trusses. A imperfect plane truss element model considering large displacements is constructed based on the Updated Lagrangian formulation. This truss element model is used for buckling and postbuckling analysis of a plane arch truss with consideration of support stiffness, in order to investigate the effects of support stiffness on the overall stability of plane arch trusses. Some notable results presented herein include: (1) the relationship between critical load and support stiffness, (2) the load – displacement curves corresponding to different values of support stiffness, (3) the effects of imperfection on postbuckling of trusses. Two examples of plane arch truss are described and the results have been verified against the results of previous studies for a special case (i.e., rigid supports). This study shows that the effects of support stiffness on buckling and postbuckling of imperfect plane arch trusses is very significant and should be taken into account in the analysis of trusses considering large displacements.

The article analyzes the influence of nonlinear (cubic) internal damping (in the Kelvin-Voigt model) and cubic nonlinearity of elastic forces on the dynamics of a rotating flexible shaft with distributed mass. The shaft is modeled by a Bernoulli-Euler rod using the Green function; discretization and reduction of the rotating shaft dynamics problem to an integral equation are performed. It is revealed that in such a system there always exists a branch of limited periodic motions (autovibrations) at a supercritical rotation speed. In addition, with small internal damping, the periodic branch continues into the subcritical region: upon reaching the critical speed, a subcritical Poincare-Andronov-Hopf bifurcation is realized and there is an unstable branch of periodic motions below the branch of stable periodic autovibrations (the occurrence of hysteresis when the rotation speed changes). With an increase in the coefficient of internal friction, the hysteresis phenomenon disappears and at a critical rotation speed, soft excitation of autovibrations of the rotating shaft occurs via the supercritical Poincare-Andronov-Hopf bifurcation.

The problem on free spatial vibrations of an overhead transmission line conductor with an asymmetric mass distribution over the cross-section that is caused by ice deposits, which impart an asymmetric shape to the cross-section, is considered. As a result, an eccentricity between the centers of torsional stiffness and mass in the cross-section is formed; and a dynamic relation of vertical, torsional, and “pendulum” vibrations develops with the conductor leaving the sagging plane. The conductor is modeled as a flexible heavy elastic rod that resists only stretching and torsion. The case of a slightly sagging conductor, when the tension and curvature of its centerline can be considered constant within the span, is investigated. It is also considered that the elasticity of the ice casing is small compared to the elasticity of the conductor. The mathematical model considering the interaction of longitudinal, torsional, and transverse waves polarized in the vertical and horizontal planes is analyzed. The ratios of phase velocities of all types of waves are analyzed and a group of particular subsystems determining partial vibrations is identified. Partial and natural frequencies and vibration modes of the conductor are investigated. Analytical solutions for the problem on determining the spectrum of natural frequencies and spatial vibration modes are obtained. The effect of an ice casing on the spectrum of conductor vibrations is investigated. A dependence of the wave number of torsional vibrations on the frequency is found. Such a dependence is determined not only by the elastic-inertial, but also by the gravitational factor, which is strongly manifested for conductors in long spans, especially subjected to galloping. This circumstance is essential for the analysis of the phenomenon of galloping from the standpoint of linking the occurrence of galloping with the convergence of the frequencies of torsional and transverse modes during conductor icing. It is shown that the ratio of these frequencies causing the self-oscillatory process is considerably complicated.

The rapid development of technology and industry requires the search of new materials which combine high strength, light weight and corrosion resistance. Metal matrix composites reinforced with two-dimensional carbon allotropes exhibit impressive mechanical, physical and tribological properties. Diamane, a two-dimensional diamond, is a very promising material for the production of thin, ultra-high strength coatings and as the reinforcement for metal matrix composites. Simulation methods can considerably improve understanding of the interaction between the diamane and metal phase. Molecular dynamics allow to analyse different properties of new materials on the atomistic level. In the present work, the mechanical properties of new composite – nickel reinforced with diamane – are investigated by molecular dynamics simulation. The structural changes in the Ni/diamane composite during tensile loading are analyzed in detail. The Young’s modulus and ultimate tensile strength of Ni/diamanе composite are 147 and 22.1 GPa, respectively, but they can be increased by increasing the diamane layers in the composite. It was found that dislocation nucleation occurred at the interface between Ni and diamane. The tensile strength of Ni/diamane composite depends on the tensile direction. The results obtained contribute to a better understanding of the processes of formation, deformation behaviour, and mechanical properties of composites based on metal and diamane.