Mechanics of Solids最新文献

Preserving the integrity of wells and preventing sand production processes are among the key problems in the operation of underground gas storage facilities. Previously, the authors have stated that a key role in the processes of destruction and sand production is played by changes in formation pressure in the reservoir as a whole, since it has a decisive influence on the magnitude of the stresses acting in the vicinity of the wells. This thesis differs from the point of view of many researchers who associate these negative processes with a change in the stress state in the bottomhole zone of the formation caused by drawdown/overbalance in wells. The main goal of the article is to study the influence of unequal components of the initial stress state, as well as elastic and strength anisotropy of reservoir rocks on the stability of wells. It is shown that the presence of unequal components of the initial stress state and elastic anisotropy can lead to stress concentrations on the well contour that differ significantly from the isotropic case. It is also shown that in the presence of strength anisotropy, a change in the location of the points of the beginning of well destruction can be observed. The calculations performed have been confirmed by experimental studies carried out on rocks of the Uvyazovsky underground gas storage facility under conditions of true triaxial independent loading.

The study focuses on the application of Haar wavelet discretization method (HWDM) and the differential quadrature method (DQM) to analyse the free vibration of a piezoelectric functionally graded porous (FGP) curved nanobeam embedded in a Kelvin-Voigt viscoelastic foundation and subjected to a hygrothermal magnetic environment. The nanobeam is composed of aluminium (Al) as the metal constituent and alumina (Al₂O₃) as the ceramic constituent, with material properties changing continuously along the thickness via a power-law distribution and described by an uneven porosity distribution. Base on Hamilton’s principle, grounded in quasi-3D higher-order shear deformation beam theory and nonlocal elasticity theory is employed to derive the governing equation for the FGP curved nanobeam. Pointwise convergence studies for HWDM and DQM have been conducted to exhibit the effectiveness of the methods. The study incorporates a Winkler-Pasternak-Visco elastic foundation model, assuming a Kelvin-Voigt-type viscoelastic foundation. Precision of the current model is effectively demonstrated through a comparative analysis of results obtained using both HWDM and DQM, showcasing outstanding accuracy. A comprehensive exploration of the power-law exponent, porosity volume fraction index, and thickness to material length scale parameter is undertaken to assess their impact on the natural frequencies. The investigation encompasses various boundary conditions, namely simply supported (S-S), clamped-clamped (C-C), clamped-free (C-F), and simply supported-free (S-F), elucidated with in-depth physical explanations. Additionally, mode shapes are graphically presented to qualitatively evaluate the dynamics of the structural component.

Negative creep of single crystals of two nickel-based superalloys has been studied. This phenomenon was observed for both alloys at temperatures of 980–1000°C and low or zero loading stresses. It is assumed that the main reason for negative creep is the formation of short-range order of atoms in the highly alloyed lattice of the matrix γ-phase. Additional factors influencing the magnitude and anisotropy of negative creep deformation can be the relaxation of residual stresses: at the microscopic level - misfit stresses between the γ-matrix and the strengthening γ′-precipitates, and at the mesoscopic level - dendritic stresses between the dendritic axes and interdendritic regions.

This research investigates the thermoelastic behavior of a three-dimensional homogeneous half-space with temperature-dependent material properties. The study aims to address the limitations of previous analysis that primarily focused on materials with temperature-independent properties, which may not accurately represent real-world scenarios, particularly in high-temperature environments. By incorporating the Lord–Shulman model and employing analytical techniques such as normal mode analysis and eigenvalue approach, analytical solutions are derived for temperature, stress, strain, displacement, and thermal stresses. The effects of temperature-dependent modulus of elasticity and Poisson’s ratio on these physical quantities are explored. Numerical examples illustrate the variations of physical quantities under different material properties, highlighting the significant influences of temperature dependency and Poisson’s ratio on stress, strain, displacement, and thermal stresses. Additionally, three-dimensional distributions of physical quantities with respect to distance and time provide comprehensive insights into their spatiotemporal behavior. This research contributes to a deeper understanding of thermoelastic phenomena in materials with temperature-dependent properties.

In this work, an analytical method based on machine learning (AM-BML) is proposed to predict the stress distribution around a cased borehole in the formation with anisotropic in-situ stresses. Firstly, the stress field equations with undetermined coefficients are derived using the elasticity theory to formulate the stress field near the cased borehole. Secondly, the regression functions of a machine learning algorithm, least squares support vector machine (LS-SVM), are constructed according to the derived stress field equations. Thirdly, the undetermined coefficient equations are developed to determine the undetermined coefficients in the derived stress field equations according to the constructed LS-SVM regression functions and the derived stress field equations. The derived stress field equations and the developed undetermined coefficient equations together constitute the proposed AM-BML, which can well predict the stress distribution around a cased borehole in the formation with anisotropic in-situ stresses. Compared with the traditional analytical methods, the proposed AM-BML is more convenient for practical applications because it is difficult and complex to determine the undetermined coefficient in the stress field equations according to the traditional analytical methods. Finally, the proposed AM-BML is validated through the comparisons with numerical simulation experiments; and it is also used to investigate the influencing factors on the stress field of a cased borehole system, which gives some useful results. This work is helpful for the study of borehole stability and the other study related to the petroleum engineering.

The problem of translational-rotational motion of a variable body is considered under the assumption that the inertial properties of the body, as well as the external forces and torques acting on it, explicitly depend on explicitly. The conditions are indicated under which the equations of motion are reduced to classical equations that describe the motion of a rigid body in a force field that does not depend on time. There are cases when the equations of motion are reduced to completely integrable ones. Elements of the discussion of the 1920–1930s about the description of the motion of a material point of variable mass in a time-dependent gravitational field are reproduced.

In this work, based on the general formulation of the problem of steady-state vibrations of an inhomogeneous elastic isotropic body, a direct problem of planar vibrations of a rectangular plate within the framework of a plane stress state is formulated. The left side of the plate is rigidly fixed, vibrations are forced by tensile load applied at the right side. The properties of the functionally graded material are described by two-dimensional laws of change in Young’s modulus, Poisson’s ratio and density. For generality of consideration, a dimensionless formulation of the problem is given. The solution to the direct problem of determining the displacement field was obtained using the finite element method. The effect of material characteristics on the displacement field and the value of the first resonant frequency are shown. An analysis of the obtained results was carried out. The inverse problem of determining the law of density from data on the values of the displacement field components at a fixed frequency is considered. To reduce the error in calculating derivatives of table functions of two variables, an approach based on spline approximation and a locally weighted regression algorithm is proposed. Reconstruction examples of different laws are presented to demonstrate the possibility of using this approach.

The paper deals with a method of the Nye figures construction for micropolar elastic solids. The method of tensors of the 4th and 3rd ranks representations by means of blocks of two-dimensional matrices and relationships between their elements is widely known in crystallography. Such approach makes it possible to simply determine the number of independent constitutive constants for micropolar elastic solids and guarantee the absence of relationships between them. In frameworks of the present study, the two-dimensional Nye figures for an ultraisotropic micropolar elastic solid were figured out based on the corresponding figures for hemitropic and isotropic micropolar elastic solids. It is shown that the constitutive tensors of ultraisotropic material characterized by only 4 independent constitutive constants: shear modulus of elasticity, Poisson’s ratio, characteristic nano/microlength and another dimensionless constant.

The problem on natural vibrations of a flat strip of anisotropic two-dimensional Cosserat medium under the assumption of small deformations and in the absence of external forces and moments is investigated. It is shown that two natural frequencies correspond to each wave number. The natural forms of oscillations and the relation between them are found. It is concluded that at oscillations with the lower of the two frequencies the inclusion rotations accompany the longitudinal displacement of the strip, and at oscillations with a higher frequency they prevent it. The obtained results are illustrated on the example of a medium model with specific parameter values. The plots show the dependences of natural frequencies, phase and group velocities on the wave number, and their asymptotic behavior is studied.

The reconfigurable parallel robots are highly adaptable to different tasks and environments, making them suitable for a wide range of industrial and medical applications. Optimizing the geometrical and structural parameters is a crucial aspect of designing a parallel robot. However, due to different degrees of freedom and workspaces, the optimization of reconfigurable parallel robots is a challenge. This paper presents the design, unified dynamic modeling and multi-objective optimization methodology of an innovative 3UPS-PU/S robot. This parallel robot can be reconfigured from a Tricept mechanism into a fully spherical mechanism through the reconfiguration of the PU/S central passive limb. For this purpose, the unified dynamic model of the robot is derived. With respect to workspace, manipulability and dynamic dexterity, three performance indices are considered as the objective functions. The robot is optimized with respect to the design and geometrical constraints using the non-dominated sorting genetic algorithm II (NSGA-II), which is used to find the Pareto fronts. The obtained solutions are a set of optimal geometric parameters to adjust the kinematic and dynamic performances. The results depict that the process effectively identified a 3UPS-PU/S robot with an efficient dexterous workspace. Also, based on the optimization results a prototype of the robot was fabricated. Overall, this paper provides a novel framework for the multi-objective optimization of reconfigurable parallel robots.