Mechanics of Solids最新文献

Using the example of four-dimensional equilibrium equations for kinetic stresses in Eulerian rectangular coordinates, it is shown that the operator of the four-dimensional Cauchy strain tensor is conjugate (transposed) to the operator of the equilibrium equations. The same connection between the operators of the equilibrium equations and the Cauchy strain tensor also holds in the three-dimensional case. Three variants of the derivation of the conditions for the compatibility of Cauchy deformations are given. In the four-dimensional case, there are 21 compatibility conditions, and in the three-dimensional case, there are six Saint-Venant compatibility conditions. It is shown that the Cauchy strain tensor, both in Eulerian and Lagrangian variables, completely determines the deformed state of a continuous medium. At the same time, no restrictions on the amount of displacements, deformations or rotations are required. The Lagrange-Green and Euler-Almancy tensors, the so-called large or finite deformations, and the displacements are expressed using Cesaro formulas in terms of the Cauchy strain tensor. The defining equations of an elastic continuous medium relate the Cauchy true stress tensor and the Cauchy strain tensor one to another. Using proper bases in the spaces of symmetric stress and strain tensors, the de ning relations can be written as six separate independent equations containing functions of only one argument. For continuous media with crystallographic symmetries, we can use the bases obtained on the basis of the generalized Hooke’s law.

The long-term destruction of a long thin-walled cylindrical shell during creep under conditions of a non-stationary complex stress state that takes into account the influence of the active medium is studied. The influence of the active medium on the creep and long-term strength of the shell is determined by the diffusion penetration of medium elements into the shell material. Using the kinetic theory by Yu. Rabotnov, we have determined the destruction time of such a shell under unsteady loading. A singular linear fractional model of creep and long-term strength, in which the ultimate strength of the material at the appropriate temperature plays the role of the ultimate stress, is used. To take into account the accumulation of damage during creep and determine the criterion before failure, scalar and vector damage parameters are used, while the components of the vector damage parameter are related to the space of principal stresses. To estimate the rate of the diffusion process, an approximate method for solving the diffusion equation is used, based on the introduction of a diffusion front. Taking into account the influence of the medium on the time to failure is carried out by introducing a function of the integral average concentration into the constitutive and kinetic linear fractional relations. A comparison of time to fracture using scalar and vector damage parameters has been carried out. The features of using a linear fractional model to describe processes of long-term destruction are determined.

The problem of determining the replacement of independent variables in the partial differential equations of three-dimensional problem of the perfect plasticity theory (for the stress states corresponding to an edge of the Tresca prism) is considered in order to reduce these equations to the analytically simplest Cauchy normal form. The original system of equations is presented in the isostatic coordinate net and is essentially nonlinear. A criterion of maximum simplicity is formulated for the Cauchy normal form. The coordinate net is found to reduce the original system to the analytically simplest Cauchy normal form. The obtained condition when the system of equations takes the simplest normal form, is stronger than the t-hyperbolicity condition of Petrovskii if we take t as the canonical isostatic coordinate which level surfaces form the spatial layers that are normal to the field of the principal directions corresponding to the greatest (or lowest) principal stress.

Traditional three-axis coordinate measuring machines often face limitations in measurement efficiency, hindering their application in high-speed manufacturing environments. This study proposes a novel comparator design based on a parallel mechanism, aiming to enhance measurement speed and precision in geometric inspection tasks. A comprehensive kinematic analysis and spatial simulation of the proposed parallel mechanism comparator were conducted to validate its performance advantages. Initially, a detailed model of the parallel mechanism comparator was established, accompanied by the construction of a spatial coordinate system. Utilizing screw theory, the mechanism’s degrees of freedom were rigorously analyzed to ensure optimal mobility and constraint conditions. Subsequently, inverse kinematic equations were derived, enabling the computational filtering of coordinate points that satisfy system constraints. The workspace of the mechanism was then mapped, with particular emphasis on investigating the influence of motor stroke length on the reachable spatial volume. Finally, kinematic simulations of the actuator-driven parallel mechanism were performed to assess output stability and dynamic behavior. The results demonstrate that the designed parallel mechanism comparator achieves an extensive workspace and exhibits stable actuator performance, confirming its potential to significantly improve measurement efficiency. This work not only provides a theoretical foundation for high-speed, high-precision geometric inspection but also suggests promising applications of parallel mechanisms in the medical diagnostics field as a key enabling technology.

The study in this paper deals with the investigation of the Moore-Gibson-Thompson model of generalized thermoelastic solid subjected to internal heat generation along the z-axis having axisymmetric heat supply. Governing equations of the problem have been derived for different models of thermoelasticity such as the Green-Naghdi III, Moore-Gibson-Thompson, and Lord-Shulman models. Time harmonics and Hankel transformation techniques are used to obtain solutions from governing equations to ordinary differential equations. The inverse Hankel transform is estimated by using numerical methods with the help of Romberg integration (Simpson’s one-third rule), followed by extrapolation to the limit as the step size tends to zero. Unknown field functions have been calculated from a system of equations obtained through boundary conditions using the Gauss Elimination numerical technique. Analytical results of temperature variations, displacements and stresses are derived from significant expressions authenticated with existing literature. Numerical results are represented graphically with respect to the radial distance for different models of thermoelasticity.

This paper established three simulation models of the typical 5.8 mm small caliber firearm and evaluated the validity of the model. The three models adopted different geometric models and loading methods. Experimental verification is conducted for the numerical models. The muzzle velocity of the bullet, vibration of barrel, posture of the bullet of the experiment and simulation were compared and analyzed. And the accuracy of the models is evaluated. The calculation results of the three models were evaluated which included velocity of bullet, relative swing angle of bullet, simulation calculation time and pressure of barrel inner wall. The results indicated that these three models could be used in different scenarios as required. When only the motion of the bullet in the chamber is studied, the analysis can be carried out using Model no. 1 with simple barrel and load method, which has a shorter computational time. Model no. 2 takes into account the actual effect of propellant gas pressure in the barrel and is suitable for the study of the inner wall of the barrel. Model no. 3 is the closest to the actual gun situation and is suitable for considering the study of gun system. Combined with the calculation time and simulation results, the three models can have different application scenarios.

The study of the mechanical behavior of micro-nano materials and structures is one of the main topics and frontier areas in current nanoscience. Under this demand challenge, this paper focuses on a two-dimensional nano-thin plate with axial velocity, establishing a model based on the nonlocal strain gradient theory. The analysis is primarily based on non-classical continuum theory, and the dynamic mechanical behavior and stability of the axially moving nano-plate are studied using numerical methods such as the complex modal method and multiscale method. Considering different boundary conditions, the intrinsic frequency and critical speed of the linear derived system are analyzed. The influence of thin plate deformation is further considered, introducing nonlinear terms. Numerical simulation results show that the vibration frequency of the system changes due to nonlinear effects. Moreover, this frequency variation is closely related to the scale parameters. This research can provide theoretical support for the design and application of nano-components.

The article focuses on a comprehensive theoretical model for wave reflection in a rotating, isotropic semiconductor half-space exposed to laser pulse heating. The formulation incorporates the combined effects of variable thermal conductivity, hydrostatic initial stress, Eringen’s nonlocal elasticity, and the three-phase lag (3PL) heat conduction model an integrated approach not previously applied in wave propagation studies. The governing equations account for Coriolis and centrifugal forces due to rotation, as well as laser-induced carrier dynamics. A key contribution of this work is the use of Global Sensitivity Analysis (GSA) with Sobol indices to systematically evaluate the influence of physical parameters on reflection amplitudes. The results reveal that nonlocal effects soften the stress field, reducing reflection by dispersing energy across microstructural scales, while temperature-dependent conductivity alters thermal gradients and stress localization. These findings provide new physical insights into thermo-mechanical wave behavior in microscale semiconductor media and inform the design of advanced opto-thermoelastic systems.

Disturbance factors such as clearance, wear, and elastic deformation of components severely constrain accuracy and stability of mechanism, and further lead to chaotic phenomena, seriously affecting dynamic of mechanism. The main purpose of this paper is to establish a multi-body system dynamics model of a multi-link mechanism that considers coupling effects of clearance, wear, and elastic deformation of rods, accurately predicting the wear characteristics, dynamic response, and nonlinear characteristics. Firstly, a wear model for clearance of the rotating pair was established based on the Archard model. Secondly, establish a model of flexible rods based on Absolute Node Coordinate Formula. Then, Lagrange multiplier method was used to establish exact dynamic equation considering coupling effects of clearance, wear, and elastic deformation of component. Finally, influence of different parameters on dynamic and wear characteristics were analyzed, and nonlinear characteristics were studied through phase diagrams, Poincaré maps, and maximum Lyapunov exponents. The results indicate that wear intensifies irregularity of clearance surface contour, leading to an increase in the instability of dynamic response and a decrease in motion accuracy. Excessive clearance value, and fast driving speed can both lead to increased wear of motion pair, resulting in decreased stability of mechanism and enhanced chaos.

In this paper, we deal with boundary value problem in two-dimensional medium based on non-local couple stress orthotropic micropolar thermoelastic solid with voids. A traction-free insulated and isothermal boundary of a non-local thermoelastic solid are considered. The governing equations for two-dimensional problem of the medium are obtained as a vector matrix differential equation which are then solved by using eigenvalue approach. The effect of non-local, couple stress and void parameter on the displacements and temperature are computed numerically and presented graphically. Particular cases are also established and compared with the known results.