Mechanics of Solids最新文献

Based on the theory of porous media mixture, a computational model of two-dimensional layered unsaturated soil foundation is established and the dynamic response of layered unsaturated soil under moving load is studied. The stiffness matrix of the layered unsaturated soil foundation is obtained by the Fourier transform and Helmholtz vector decomposition principle and the numerical solutions of the layered unsaturated soil foundation in the frequency domain are solved by using the transfer matrix method and combining the boundary and interlayer continuity conditions in the derivation. The numerical solutions of displacement, stress, and pore pressure in the layered unsaturated soil are obtained by Fourier inversion. The numerical examples were used to analyze the effects of load velocity, shear modulus, and saturation on the dynamic response of two typical layered foundations: upper soft and lower hard foundations, and upper hard and lower soft foundations, respectively. The results show that when the load movement velocity is close to the shear wave velocity in unsaturated ground and causes the resonance of the soil, the vertical displacement of the surface increases rapidly to the peak; the order of the soil layers in the layered unsaturated ground has a significant effect on the surface displacement, and the vertical displacement of the upper soft and lower hard foundation is larger than that of the upper hard and lower soft foundation; the saturation degree has a significant effect on the dynamic response of the layered unsaturated ground. The saturation degree has a significant effect on the dynamic response of the layered unsaturated foundation, and the surface vertical displacement increases with the increase of the saturation degree of the surface soil in both the upper soft and lower hard foundation and the upper hard and lower soft foundation.

For the first time, an exact solution is given to the contact problem of the non-stationary action of a wedge-shaped, right-angled stamp occupying the first quadrant, which act on a deformable multilayer base. The base, which is affected by a rigid stamp in the shape of a quarter plane, can be a multilayer anisotropic composite material. It is assumed that it is possible to construct a Green’s function for it, which makes it possible to construct an integral equation of the contact problem. The geometric Cartesian coordinates of the first quadrant and the time parameter, which varies along the entire axis, are taken as parameters describing the integral equation. It is assumed that time in the boundary value problem under consideration follows from negative infinity, crosses the origin and grows to infinity, covering the entire time interval. Thus, there is no requirement in the formulation of the Cochet problem when it is necessary to set initial conditions. In this formulation, the problem is reduced to solving the three-dimensional Wiener–Hopf integral equation. The authors are not aware of any attempts to solve this problem analytically or numerically. The investigation and solution of the contact problem was carried out using block elements in a variant applicable to integral equations. It is proved that the constructed solution exactly satisfies the integral equation. The properties of the constructed solution are studied. In particular, it is shown that the solution of the non-stationary contact problem has a higher concentration of contact stresses at the edges of the stamps and at the angular point of the stamp, compared with a static case. This corresponds to the observed in practice more effective non-stationary effect of rigid bodies on deformable media, for their destruction, compared with static. The results may be useful in engineering practice, seismology, in assessing the impact of incoming waves on foundations, in the areas of using Wiener–Hopf integral equations in probability theory and statistics, and other areas.

The problem of finding the optimal orientation of the localized damage zone in a brittle material under triaxial compression with intermediate stress varying from the minimum (Karman scheme) to the maximum (Becker scheme) principal stress values is considered in the thin weak layer approximation. The undamaged material is described by the relations of the linear-elastic isotropic body, the weak zone is described by the model of nonlinear elasticity of Academician of the Russian Academy of Sciences V.P. Myasnikov with elastic moduli linearly dependent on the scalar parameter of the damage. The orientation of the weakened zone is given by two angles relative to the direction of action of the two principal stresses, and the degree of weakening is given by the value of the damage parameter. The search for the optimal orientation of the zone for fixed values of the control parameters consists in maximizing the function that determines the rate of damage growth in this zone.

As a result of the solution of the problem, the optimal orientations of the localized damage zone have been established for different ratios of principal stresses and damage level. It is shown that with intermediate stress increase the angle of inclination of the zone relative to the direction of the maximum principal stress decreases, as well as a narrowing of the interval of possible orientations of the zone relative to the direction of the intermediate principal stress. Based on the analysis of the ratio of the values of the shear components of the stress tensor in the plane of the localized damage zone, the possible shear directions along this zone are determined.

An exact analytical solution is obtained for the two-dimensional problem of a strip composed by two half-strips of equal thickness from the same linearly elastic orthotropic material with the main axes of the elasticity tensor symmetrically inclined to the interface and a central semi-infinite crack running along the interface. A self-balanced system of loads is assumed to be applied sufficiently far from the crack tip. For four independent active loading modes, expressions for stress intensity factors are found in the form of combinations of elementary functions or single integrals of combinations of elementary functions depending on three independent parameters.

In order to accurately express the train load, the quasi-static train moving load expression is derived considering the wheel flat scars and track irregularities. By performing Fourier transform on time and wavenumber transform along the track direction, the three-dimensional space problem can be simplified into a two-dimensional plane problem. Combining boundary conditions and Galerkin method, a 2.5-dimensional train track quasi saturated foundation finite element dynamic analysis model equation is obtained. The track structure is regarded as an Euler beam on an unsaturated foundation, and the modified train load is obtained in the time space domain through fast Fourier inverse transform. The influence of train speed, load conditions, and foundation saturation on track vibration is explored. Calculations show that when the wheel flat scars and track irregularities are coupled, the amplitude of track vibration is more than twice that of the ideal moving load, and much greater than the individual effect of the wheel flat scars or track irregularities. When the train speed is 120 km/h, the amplitude of track vibration caused by wheel flat scars is greater than that of track irregularities, while the opposite is true when the train speed approaches the shear wave velocity. The saturation of the foundation decreases from 100 to 95%, and the vertical displacement of the track increases significantly, while the vertical acceleration increases slightly, and the acceleration power spectrum will slightly decrease. During low and high-speed operation, the acceleration power spectrum experiences near missing phenomena at 20 and 50 Hz, respectively. The peak of acceleration power spectrum appears at 13.5 Hz during low-speed operation (for all four types of loads), and at 40 Hz and 30 Hz during high-speed operation.

The non-local theory of elasticity provides a comprehensive framework for studying the propagation of surface waves in materials with micro and nanostructures. This study, explores the propagation of shear waves in a coupled plate comprising a piezoelectric layer and an elastic layer under the non-local theory of elasticity. These composite structures leverage the complementary properties of piezoelectric and elastic materials, with applications ranging from energy harvesting to medical imaging and acoustic devices. The piezoelectric layer is assumed to be perfectly bonded to the elastic layer. Analytical derivation yields the dispersion equation for shear waves in closed form, with specific cases derived from this equation demonstrating agreement with previously published results. Numerical simulations are conducted to visualize the impacts of key parameters investigated in the study. Notably, the insights gained from this investigation are crucial for optimizing the efficiency and reliability of various types of sensors and acoustic devices.

The objective of this work is to investigate the buckling responses of nano-beams while accounting for the impacts of surface stress. To accomplish this, a continuum elasticity model based on Gurtin-Murdoch elasticity theory was used to develop non-classical beam models that included the influence of surface stress on the buckling behaviours of nano-beams for two boundary conditions (hinge-hinge and clamped-clamped) based on Haringx and Engresser theories of buckling is employing a new model beam shear deformation is presented and discuted. The formulas were developed to determine critical buckling loads, transverse and angular displacements of nano-beams, and surface stress effects relevant to each type of beam theory.

The present investigation is intended to demonstrate the effect of hydrostatic initial stress and rotation on thermoelastic medium with two temperatures. The exact expressions for the displacement components, temperature field, and stresses are obtained in the physical domain by using the normal mode technique. These are also computed numerically for a copper material and presented graphically to observe the variations of the considered physical variables. The analytical solution has been obtained, we have used the Lame’s potential, method and normal mode analysis. The results indicate that the effect of rotation and initial stress on the conductor temperature, thermodynamic temperature, displacement and stress are quite pronounced. In order to illustrate and verify the analytical development, the numerical results of temperature, displacement and stress are carried out and computer simulated results. The numerical and graphical results underscore the significant influence of initial stress, rotation, and thermal shock on the various field quantities. Comparisons of the physical quantities are shown in figures to depict the effects of initial stress, rotation, and thermal shock.

Using a three-level constitutive model, the influence of the crystal anisotropy factor, the hardening coefficient, the microscopic elastic limit and the distribution density function of the limiting elastic deformations of subelements on the shape of the deformation diagrams and the fracture conditions of a polycrystal is studied. Based on the theory of maximum normal stresses at the local level, a failure criterion was established at the macroscopic level, which includes all the parameters of the problem. The influence of the type of stress state and the geometric shape of the loading diagram on the magnitude of irreversible deformation preceding the initial process of destruction is investigated. From the established strength criterion follows the effect of a decrease in the plasticity of the material with increasing yield strength. The question of the critical value of the weight of destroyed subelements is discussed, at which a macrocrack forms, leading to the complete destruction of the body element.

For the tensor-matrix FEM system of equations describing the final state of large deformations of an incompressible elastic body, a development to solve axisymmetric problems is obtained. Also, analytical expressions for the components of the partial derivatives matrix of the system are obtained. Examples of calculating the everted state of a circular cylinder, as well as analysis of sealing rings are described.