Mechanics of Solids最新文献

The question of the necessary class of smoothness of solutions to quasi-static problems in the mechanics of a deformable solid in terms of displacements is discussed. It is shown that in order for the equations of compatibility of deformations to become identities when substituting displacements into them, the existence of some third mixed derivatives of displacements is required. For a linearly elastic compressible isotropic elastic medium, a counterexample is given in which the displacement field, being a doubly differentiable solution to the boundary value problem for the system of Lamé equations in the entire domain, is not a solution to the problem in displacements at all points of this domain.

In this paper, we have examined the reflection of plane waves at the stress-free boundary of nonlocal micropolar transversely isotropic half-space with nonlocal theory. Using convenient boundary conditions, the mathematical expression of reflection coefficients and phase velocity for the reflected waves are derived in closed form. The expressions of energy ratios are also obtained in explicit form. Numerical computations have been performed to exhibits the analytical findings for graphical means with the aid of numerical data. The effects of the nonlocal parameter on the reflection coefficients, phase velocity and energy ratios are discussed numerically and illustrated graphically. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each incident angle.

This study investigates the behaviour of Love wave propagation within a transversely isotropic fluid saturated porous layer (TIFSPL) with rigid boundary, situated over a nonhomogeneous elastic half space. An irregularity in the shape of parabola is considered at the interface of porous layer and half space. The displacement vector and dispersion equation for propagation of Loves waves has been derived by applying Biot’s theory of elasticity, perturbation method, and Fourier Transformation method. The numerical results have been carried out to illustrate the variation of dimensionless phase velocity against dimensionless wavenumber with the help of MATLAB graphical routines for different values of inhomogeneity parameters and the ratio of depth of irregularity to the layer’s height. It has been observed that the derived dispersion equation for Love waves is affected by rigidity, wavenumber, depth of irregularity, height of layer, size and shape of irregularity, and inhomogeneity parameter. The findings from this study holds a significant importance in the field of seismology, geophysics and earthquake engineering.

The presence of defects, including Stone–Wales (SW) defects, can lead to a deterioration of the mechanical properties of carbon nanotubes (CNTs). In this study, a continuum-discrete multiscale coupling (CDMC) method is used to investigate the improvement of the pressure resistance of defective CNTs containing SW defects. By employing the moving least squares (MLS) approximation as a bridging mechanism, a seamless integration can be achieved between the deformation fields of discrete atomic configurations and their corresponding continuum models. Based on the CDMC method, a meshless computational framework, devoid of numerical integration, is formulated to accurately predict the buckling behaviors of defective CNTs. The results show that the position of SW defects almost has no effect on the anti-buckling ability of defective CNTs; and the pressure resistance of defective CNTs can be improved by coating/inserting CNT when the deference of the radius between the two nested CNTs is greater than 0.2nm.

The recent earthquake in the Kahramanmaraş region on 06.02.2023 in Turkey and Syria had a magnitude of Mw 7.8, its intensity in some areas of Turkey reached XI points on the modified Mercalli scale. The earthquake caused catastrophic consequences, leading to the death of more than 52,800 people, as well as numerous destructions of infrastructure. The article analyzes the consequences of the appearance in the seismogram of an earthquake of an unusually strong delta pulse, associated with the arrival of a horizontally polarized S-wave. The issues of creating seismic protection systems against high-intensity delta-shaped pulses are discussed.

The subject of the study is the problem of precession of a gyrostat with a fixed point in three homogeneous force fields. The class of precessional movements under consideration is characterized by the properties of constancy of the nutation angle and commensurability of the precession rates and the gyrostat’s own rotation. The equations of motion of the gyrostat are reduced to three second-order differential equations with respect to the precession rates and the proper rotation of the gyrostat. Integration of these equations was carried out in the case of precessional-isoconic movements (the speeds of precession and proper rotation are equal) and in one case the resonant values of the speeds of precession and proper rotation (the precession speed is twice the speed of proper rotation – resonance 2 : 1). It is proven that the solutions obtained in the article are characterized by elementary functions of time.

The fractional heat conduction equation in thermoelasticity by the definitions of Riemann-Liouville and Caputo has some shortcomings. In this paper, we introduce a conformable fractional order theory of thermoelasticity that remedies this shortcoming. Firstly, we derive the heat conduction equation based on the conformable fractional derivative. Then, the theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases. Finally, we apply these new governing equations to the problem of the general thermo material. The analytical expressions for physical quantities are obtained using normal mode analysis in the physical domain. These expressions are numerically calculated and graphically illustrated for a given material. The findings were predicted and tested in the presence and absence of fractional parameter.

Waterflood-induced fractures, also known as self-induced fractures, are spontaneously created at injection wells during waterflooding. They propagate for sufficiently large distances in rock and transfer injected fluids far away from a well, both along the flooding layer and outside it. Essentially, the mechanics of waterflood-induced fracture propagation is similar to that for hydraulic fractures intentionally created for reservoir stimulation. However, there are several peculiarities that differ self-induced fractures from hydraulic fractures. Initiation of a waterflood-induced fracture is not an instant process and can take a lot of time. Depending on parameters of a formation, well orientation and injection rate, a fracture can either initiate quickly or not initiate at all. The part of the fluid that flows into the initialized fracture is also a question. As initial aperture of the waterflood-induced fracture is very small, it cannot take all the injected fluid, so part of it still filtrates into the formation through wellbore. In this work, we consider the process of initiation and fluid flow in waterflood-induced fractures. We develop an analytical model that can predict time of fracture initiation, taking clogging effects in account. Also, we present a semi-analytical model for injection fluid sharing between a fracture and a reservoir. The fracture is described by PKN analytical model. Finally, we collect initiation, flux partitioning and geometry data of self-induced fractures and compare them with hydraulic fractures. The present work investigates the differences between hydraulic and waterflood-induced fractures and is important for accurate modeling of the latter.

Honeycomb structures are used widely nowadays and honeycombs with negative Poisson’s ratio has attracted widespread attentions. The compression tests of 3D printed concave hexagonal honeycomb model is compared with the results of the finite element model, which confirms the effectiveness of the finite element models. It is known that the curved wall honeycomb can effectively alleviate the stress concentration compared with straight-walled honeycombs. The curved walls in sinusoidal shape replace the straight walls which are mainly carried in the concave hexagonal honeycomb cells in this paper. Python is used to generate a large number of finite element models and then establish a dataset corresponding to the parameters and mechanical properties of the curved wall honeycombs. The neural network is proposed to predict energy absorption properties of the honeycombs. The sensitivity analysis of the parameters is carried out to provide guidance for the design of curved wall honeycomb structures. The specific absorption energy is optimized, and the energy absorption capacity is evaluated by using the neural network. The results show that the total energy absorption of the concave straight wall honeycomb is higher, but the energy absorption efficiency of the concave curved wall honeycomb is higher.

Two approaches to obtaining dynamic equations for the propagation of small displacement disturbances, based on the use of models of hyperelastic and hypoelastic materials, are considered. It is shown that these equations are interrelated. For the case of a plane monochromatic wave, expressions for the acoustic tensors are obtained. A comparative analysis of the influence of preliminary deformations on the speed of propagation of acoustic waves in isotropic and anisotropic materials was carried out. Effects have been identified that can only be described within the framework of a hypoelastic medium model.