Mechanics of Solids最新文献

The current research investigates the propagation behavior of Rayleigh-type waves in a prestressed functionally graded orthotropic substrate. Two types of material gradation, exponential and logarithmic, are considered. The influence of these gradation profiles is analyzed under two boundary conditions: stress-free and rigid. The derived dispersion relations account for the effects of gradient parameters, initial stress, and density variations. A comprehensive numerical analysis is performed to evaluate the phase velocity and attenuation coefficient. The results reveal that both gradient types significantly affect the wave dispersion and attenuation behavior. Specifically, the exponential gradient induces stronger changes at lower and moderate wave numbers, while the logarithmic gradient affects attenuation more at lower wave numbers and phase velocity at higher wave numbers. The initial stress parameter is found to decrease phase velocity across wave numbers, while density variation shows contrasting behavior depending on the boundary type. The findings provide critical insights into material design, seismic analysis, and non-destructive testing techniques.

This study presents a unified fractional three-phase-lag heat conduction model within the framework of Green–Naghdi thermoelasticity, formulated to describe the coupled magneto-electro-thermoelastic response of a perfectly conducting, infinitely long hollow cylinder subjected to a uniform axial magnetic field. The model introduces fractional-order derivatives to generalize classical and generalized thermoelastic theories (e.g., Biot, Lord–Shulman, GN types I–III) as limiting cases. A single fractional formulation governed by three phase-lag parameters enables a seamless transition across different heat transport behaviors while capturing nonlocal and memory effects. Field equations are derived using Laplace transforms and solved semi-analytically. Numerical inversions provide time-domain distributions of temperature, stress, displacement, and induced electromagnetic fields. Results show that the fractional order significantly influences thermal and mechanical wave propagation, suppressing displacement while amplifying induced magnetic fields. The model offers new insight into the thermal response of materials with memory, and the unified structure supports broader applicability in material characterization and advanced engineering systems.

The regularities of residual stress formation and distortion of the product shape occurring during wire-arc surfacing are studied. Therefore, the results of full-scale experiments carried out by Cranfield University are reproduced numerically. In the experiments, surfacing of wire material is carried out in 9, 10, and 18 layers on a fixed substrate along a reciprocating path at a speed of 10 mm/s, including interlayer roller burnishing with variable pressure. The numerical modelling includes several stages, during which the following uncoupled problems are sequentially solved: a) thermal – surfacing of 9 to 18 layers of wire material, b) thermal elastic-plastic – formation of eigenstrains and residual stresses due to air cooling of the deposited wall with non-uniform temperature distribution, c) thermal elastic-plastic – forging of a stressed workpiece with a pneumatic tool at elevated temperature (the stage may be omitted), and d) elastic-plastic – changes in the field of residual stresses and distortion of the structure after its release. The problem of thermal conductivity (a), as well as the problems of deformation (b), and (d) during surfacing of wire material are implemented in the Comsol Multiphisics software package, and the problem (c) is solved in the LS-DYNA software package. In addition, an “engineering” beam-rod structural model of the built-up wall is developed, which makes it possible to predict the wall distortions and the distribution of eigenstrains and residual stresses along its height, and verify the numerical calculation. This model represents the magnitude of longitudinal bending of the specimen during surfacing, but excessively takes into account the effect of roller burnishing. Even a single roller burnishing causes the bending of the structure in the opposite direction, while in the experiment it only straightens.

Functionally Graded Materials (FGMs) are a revolutionary class of materials whose properties are varied along specific dimensions, allowing properties that are as diverse as mechanical strength and thermal resistance to be integrated in one member. This unique property makes FGMs very suitable for advanced engineering applications in aerospace, biomedical, and energy industries. This review focuses on static and dynamic behaviors, material gradation, and nonlinearities of FGMs. Advanced computational techniques have been used, considering Finite Element Method (FEM) and many other methods, in order to highlight the strong influence of material gradation on important issues such as the investigation of stress distribution, deformation, vibration, and wave propagation. Despite these promising advances, poor experimental validation, the relatively unexplored multidirectional FGMs, and a lack of understanding concerning environmental effects are still major challenges. Specific gaps to be addressed relate to scalable manufacturing techniques, sustainability-driven production methods, and rigorous experimental validation with the aim of achieving long-term reliability in real service conditions. This review uniquely integrates insights on computational modeling and sustainable manufacturing while charting a roadmap for future research. FGMs will no doubt bridge the existing gaps and bring about a revolution in engineering, innovate, and meet the ever-evolving demands of state-of-the-art technologies.

This study examines the propagation of shear waves on a highly inhomogeneous multi-layered elastic cylinder embedded in Winkler elastic foundations. The interface of the structure has been considered to bear generalized interfacial conditions, upon which the widely used perfect interfacial conditions turn out to be a special case. The harmonic wave solution has been deplored for the examination. Certainly, the discussion highlighted the roles of the Winkler foundation and layer thickness and the influence of material homogeneity versus non-homogeneity on the scaled phase velocity, dimensionless wave number, and scaled frequency, respectively, concerning layer thickness. In addition, it is observed that dimensionless vibrational displacements varied in response to changes in both the contact parameter ({{varepsilon }_{a}}) and the angle (theta ). Moreover, this study is set to supplement the known literature concerning the emerging field of multi-layered construction and provide insights into constructing reliable materials in the field of material science.

Analytic solutions for stresses and displacements for perfectly joined homogeneous orthotropic and transversely elastic half-spaces due to a line source situated in the upper half-space are derived in this study. As a particular case, expressions for displacements and stresses for a vertical strike–slip fault are derived. For numerical and graphical interpretation, we considered Olivine, Baryte and Topaz as orthotropic materials and Magnesium, cobalt, ice etc. as transversely isotropic materials to study the behavior of displacement and stresses near interface and near the source and it is observed that in orthotropic half-space, displacements and stresses are agreeing maximum value for Topaz irrespective of the choice of material in transversely isotropic half-space. Also numerically, the displacements and stresses are studied and the effect of anisotropy has been shown graphically by drawing line graphs and 3-D mesh-grid maps using MATLAB.

Porous functional gradient material (FGM) sandwich structures are widely used in various fields. However, the study of their dynamic response under multiple blast excitations is lacking. This paper develops a nonlinear dynamic model of a porous FGM sandwich hyperbolic panel based on Winkler-Pasternak elastic foundation and von Kármán strain-displacement relations. The model comprehensively incorporates the effect of material inhomogeneity, geometric nonlinearity, and time-varying blast loading for the first time. Subsequently, a numerical solution strategy is constructed by coupling the finite difference method in the spatial domain with the Newmark method in the time domain. In addition, the effects of porosity distribution, geometric parameters, foundation stiffness, and blast load parameters on the structural response frequency, deflection amplitude, and damping performance are investigated. Results reveal that sandwich panels with uniformly distributed porosity in the FGM exhibit superior dynamic stability and blast resistance under repeated explosive loads. The findings can provide theoretical support and engineering guidance for the blast-resistant design and intelligent optimization of novel porous FGM sandwich composite structures.

In order to explore the difference of site seismic response between quasi-saturated soil layer and saturated soil layer under elastic wave incidence, based on the theory of quasi-saturated porous media, the dynamic response of quasi-saturated soil foundation overlying bedrock layer is studied. By establishing the mathematical model of quasi-saturated porous medium and single-phase elastic medium, the seismic response of quasi-saturated soil foundation site is analyzed. The governing equations of the quasi-saturated soil layer are derived by using the Biot theory, and the potential function expression of the wave field is obtained by combining the Helmholtz vector decomposition principle. The correctness of the model is verified by numerical examples, and the effects of saturation, porosity, permeability coefficient, viscosity coefficient, stiffness ratio and incident angle on the surface movement of the saturated soil foundation are discussed in detail. The results show that the existence of gas phase in the quasi-saturated soil layer has a significant effect on the ground motion. The vertical displacement of the surface decreases with the increase of saturation, while the horizontal displacement shows the opposite trend. The surface displacement amplitude is greatly affected by the change of porosity, and the permeability coefficient and viscosity coefficient have little effect on the surface displacement amplitude. It is worth noting that when the saturation Sr = 1, that is, when the quasi-saturated soil foundation degenerates into a saturated soil foundation, the maximum difference between the vertical displacement amplitude corresponding to the saturation Sr = 0.97 reaches 94%, and the horizontal displacement amplitude.

There are a large number of primary and regenerated defects in the rock mass of deep underground engineering, such as primary joints, regenerated cracks and geological holes. When the cracks are subjected to external loads, especially dynamic loads, the dynamic fracture phenomenon will occur. The uncontrolled propagation of cracks will further aggravate the fragmentation of roadway surrounding rock and reduce its stability. To this end, this article simplifies geological fractures into a prefabricated crack and anchor bolt drilling into a single circular hole, thus constructing three types of single crack single hole board experimental configurations (SCSH) with horizontal, vertical, and single hole size variations. The Split Hopkinson Pressure Bar test system (SHPB) is used to explore the influence of single hole on the dynamic fracture behavior of cracks under dynamic load. The effect of physical experiment is verified by the explicit dynamic software AUTODYN, and its influence mechanism is further explored. The results show: (1) as the distance between the circular hole and the tip of the pre-crack increases along the crack direction and propagates to the vicinity of the circular hole, the propagation path tends to the hole; (2) as the increase of vertical distance between hole and pre-crack, the guiding stress field at the tip of the propagating crack and the guiding effect of the hole on the crack are both gradually decrease; (3) with the diameter increase of the hole, which presents a significant guiding phenomenon for the crack dynamic propagation, however, when the hole diameter is less than a certain value, it will have no guiding effect on crack propagation. The research results of this paper can provide strong theoretical support for the corresponding prevention and control measures to ensure the stability of roadway surrounding rock in underground impact pressure mines.

The present study focuses on wave analysis in modified couple stress thermoelastic diffusion with multiple mode. After converting the governing equation into two-dimensional case, equations are mode dimensionless and potential functional are used for further simplification. Normal mode approach is applied to solve the problem. This approach is a powerful technique that provide apt with no presumable restriction on displacement, temperature and chemical potential and stress distribution. For stress free isothermal and isochemical potential, frequency equation is determined for wave propagation mode. Analytical solutions for displacements, temperature, and stresses have been obtained as functions of all external parameters inserted on the wave propagation phenomenon. Specific loss and penetration depth are computed numerically are presented in form of graphs to illustrate the impacts of three phase lag and one relaxation time. A comparison has been made between the thermal phase lags considered. The results obtained indicated to the strong impact of the modified couple stress and multi-phase-lag on waves analysis in the context of thermoelasticity and has applicable applications in diverse fields as geophysics, astronomy, engineering and acoustics.