Mechanics of Solids最新文献

Space exploration studies over the previous decades have shown that there are various impact craters on planetary surfaces. At present, it is generally believed that the formation of impact craters is an extremely important geological and impact dynamic process in the evolution of celestial bodies. The study and progress on impact crater formation on celestial bodies are reviewed in this paper, with an emphasis on the new insights and findings in the past decade. This paper strives to cover the frontier of research in a comprehensive manner and sorts out research threads to provide ideas for scholars. First, we briefly review the history and significance of the study of impact craters, and introduce the relevant progress of research methods, which include impact experiments and numerical simulations. Then, we summarize the emphases and limitations of recent research according to cratering stages. Finally, we discuss the current predicament and future trends of related research from numerical simulations and laboratory experiments. To advance the depth and scope of planetary cratering impacts study, some perspectives and recommendations for future investigations are provided.

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.

This paper addresses the energy absorption behavior of high-strength aluminum alloy tubes made of AA 7005 and AA 7075 for potential application in passenger vehicle bumper systems to reduce pedestrian injury. An experimental and numerical analysis was carried out to know the quasi-static lateral compression behavior of the tubes. The length to diameter ratio of both types of tubes was varied as 1, 1.5, and 2 for identical wall thickness (3.55 mm) and external diameter (34 mm). Influence of length to diameter ratio on specific energy absorption, average load, failure mechanism and load-displacement curve was explored experimentally as well as through three-dimensional numerical simulations. Experiments were performed through compressive testing machine (CTM) with crosshead velocity of 1.2 mm/min whereas Ansys LS-DYNA with linear plasticity material model was employed to carry out the numerical simulations. Moreover, the obtained results were compared with the analytical models available in the literature, which was based on rigid-perfectly plastic material model. The predicted results were found to be close enough to that of the experimental results as well as analytical results. Experimentation and Finite element analysis showed that the aluminum tube AA7005 has better credibility as energy absorber than tube of AA7075.

The implementation of a stochastic simulation was carried out using an elastic-thermodiffusion (ETD) model of the electrons-holes interaction problem, utilizing photo-thermoelastic theory. This study investigates deformations in a two-dimensional (2D) context, incorporating the influences of thermoelastic (TD) and electronic (ED) transport mechanisms. The use of a Weiner function or white noise with a boundary condition introduces a stochastic component, hence enhancing the realism of the problem. The normal mode analysis was employed to obtain deterministic and stochastic outcomes for all physical quantities. Three unique paths are developed to evaluate the dispersion of the stochastic and deterministic fields. The mean and standard deviation of the most pertinent physical variables are calculated and examined. Silicon (Si) semiconductor materials are utilized for modeling and analysis. The study included the provision of graphs and discussions about the obtained results.

This study investigates the piezomagnetic behavior of functionally graded cylinders under non-axisymmetric hygrothermal conditions using an analytical approach. The cylinders are subjected to internal pressure, magnetic potential, moisture concentration, and thermal loading, which significantly impact their mechanical response. We examine the effects of loading contributions on the elastic response of piezomagnetic functionally graded materials (FGMs), focusing on the intricate interplay between material properties and environmental conditions. The von Mises stress, maximum shear stress, and equivalent magnetic induction components are analyzed to elucidate the complex interactions between the loadings. Our findings indicate that internal pressure has a dominant influence on stress distribution, with moisture concentration and thermal effects introducing complexity to the stress relationships. Although the magnetic field’s impact may be less pronounced compared to other forces and conditions, its effect on magnetic induction components is significant and as expected. Our results provide valuable insights into the design and optimization of piezomagnetic FGMs for various engineering applications that involve exposure to non-axisymmetric hygrothermal environments.

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.