Search Results (26)

Aiming at the engineering problems of the severe wear and limited service life of mandrels during the hole extrusion strengthening of critical aerospace components, this study proposes a surface modification strategy for mandrels based on the anti-friction mechanism of micro-textures. Based on the Lame stress equation and the Mises yield criterion, a plastic strengthening stress distribution model of the hole wall was developed. Integrating Bowden’s adhesive friction theory, a parameterized numerical model was constructed to investigate the influence of micro-texture morphology on interfacial friction and wear behavior. An elastic–plastic contact model for micro-textured mandrels during hole extrusion strengthening was established using ANSYS. The effects of key parameters such as the micro-texture depth and area ratio on the contact pressure field, friction stress distribution, and strengthening performance were quantitatively analyzed. The results show that a circular micro-texture with a depth of 50 μm and an area ratio of 20% can reduce the fluctuation and peak value of the contact pressure by 41.0% and 29.7%, respectively, and decrease the average friction stress by 8.1%. The interfacial wear resistance and the uniformity of the residual compressive stress distribution on the hole wall are significantly enhanced, providing tribological insight and surface optimization guidance for improving the anti-wear performance and extending the service life of mandrels. Full article

We investigate an inverse problem involving source and damping term with variable-exponent nonlinearities. We establish adequate conditions on the initial data for the decay of solutions as the integral overdetermination approaches zero over time within an acceptable range of variable exponents. This class of inverse problems, where internal terms such as source and damping are to be determined from indirect measurements, has significant relevance in real-world applications—ranging from geophysical prospecting to biomedical engineering and materials science. The accurate identification of these internal mechanisms plays a crucial role in optimizing system performance, improving diagnostic accuracy, and constructing predictive models. Therefore, the results obtained in this study not only contribute to the theoretical understanding of nonlinear dynamic systems but also provide practical insights for reconstructive analysis and control in applied settings. The asymptotic behavior and decay conditions we derive are expected to be of particular interest to researchers dealing with stability, uniqueness, and identifiability in inverse problems governed by nonstandard growth conditions. Full article

This study investigates the mechanisms driving current generation, power output, and charge storage in carbon nanotube springs under mechanical strain, addressing the gap between experimental observations and theoretical modeling, particularly in asymmetric electrical responses. Leveraging the Dirac equation in curved spacetime, we analyze how curvature-induced scalar and pseudo-gauge potentials shape two-dimensional electron gases confined to carbon nanotube springs. We incorporate applied mechanical strain by introducing time-dependent variations in the Lamé coefficient and curvature parameters, enabling the analysis of mechanical deformation’s influence on electrical properties. Our model clarifies asymmetric electrical responses during stretching and compression cycles and explains how strain-dependent power outputs arise from the interplay between mechanical deformation and curvature effects. Additionally, we demonstrate mechanisms by which strain influences charge redistribution within the helically coiled structure. We develop a new equivalent circuit model linking mechanical deformation directly to electronic behavior, bridging theoretical physics with practical electromechanical applications. The analysis reveals asymmetric time-dependent currents, enhanced power output during stretching, and strain-dependent charge redistribution. Fourier analysis uncovers dominant frequency components (primary at $\Omega$, harmonic at $2\Omega$) explaining these asymmetries. Theoretical investigations explain the mechanisms behind the curvature-driven time-dependent current source, the frequency-dependent peak power, the characteristics of open-circuit voltage with strain, and the asymmetric electrical property response under applied strain as the generated current and the charge distribution within the carbon nanotube springs. These findings highlight carbon nanotube springs applied to energy harvesting, wearable electronics, and sensing technologies. Full article

A spatial problem of elasticity theory is solved for a layer located on two bearings embedded in it. The bearings are represented as thick-walled pipes embedded in the layer parallel to its boundaries. The pipes are rigidly connected to the layer, and contact-type conditions (normal displacements and tangential stresses) are specified on the insides of the pipes. Stresses are set on the flat surfaces of the layer. The objective of this study is to obtain the stress–strain state of the body of the layer under different geometric characteristics of the model. The solution to the problem is presented in the form of the Lamé equation, whose terms are written in different coordinate systems. The generalized Fourier method is used to transfer the basic solutions between coordinate systems. By satisfying the boundary and conjugation conditions, the problem is reduced to a system of infinite linear algebraic equations of the second kind, to which the reduction method is applied. After finding the unknowns, using the generalized Fourier method, it is possible to find the stress–strain state at any point of the body. The numerical study of the stress state showed high convergence of the approximate solutions to the exact one. The stress–strain state of the composite body was analyzed for different geometric parameters and different pipe materials. The results obtained can be used for the preliminary determination of the geometric parameters of the model and the materials of the joints. The proposed solution method can be used not only to calculate the stress state of bearing joints, but also of bushings (under specified conditions of rigid contact without friction on the internal surfaces). Full article

The four-dimensional ellipsoid of an anisotropic hyper-structure corresponds to the four-dimensional sphere of an isotropic hyper-structure. In three dimensions, both theories for spherical and ellipsoidal harmonics have been developed by Laplace and Lamé, respectively. Nevertheless, in four dimensions, only the theory of hyper-spherical harmonics is hitherto known. This void in the literature is expected to be filled up by the present work. In fact, it is well known that the spectral decomposition of the Laplace equation in three-dimensional ellipsoidal geometry leads to the Lamé equation. This Lamé equation governs each one of the spectral functions corresponding to the three ellipsoidal coordinates, which, however, live in non-overlapping intervals. The analysis of the Lamé equation leads to four classes of Lamé functions, giving a total of 2n + 1 functions of degree n. In four dimensions, a much more elaborate procedure leads to similar results for the hyper-ellipsoidal structure. Actually, we demonstrate here that there are eight classes of the spectral hyper-Lamé equation and we provide a complete analysis for each one of them. The number of hyper-Lamé functions of degree n is (n + 1)²; that is, n² more functions than the three-dimensional case. However, the main difficulty in the four-dimensional analysis concerns the evaluation of the three separation constants appearing during the separation process. One of them can be extracted from the corresponding theory of the hyper-sphero-conal system, but the other two constants are obtained via a much more complicated procedure than the three-dimensional case. In fact, the solution process exhibits specific nonlinearities of polynomial type, itemized for every class and every degree. An example of this procedure is demonstrated in detail in order to make the process clear. Finally, the hyper-ellipsoidal harmonics are given as the product of four identical hyper-Lamé functions, each one defined in its own domain, which are explicitly calculated and tabulated for every degree less than five. Full article

In this paper, we present certain complete solutions in the dilatation theory of elasticity. This model can be derived as a special case of Eringen’s linear theory of microstretched elastic solids when microrotations are absent. It is also a version of the theory of materials with voids. The dilatation theory can be considered the simplest theoretical model of microstructured materials and is suitable for investigating various phenomena that occur in engineering, geomechanics, and biomechanics. We establish three complete solutions to the displacement equations of equilibrium that are the counterpart of the Green–Lamé (GL), Boussinesq–Papkovich–Neuber (BPN), and Cauchy–Kowalevski–Somigliana (CKS) solutions of classical elasticity. The links between these BPN and CKS solutions are established. Then, we present a representation of the BPN solution in the case of axisymmetry. The results presented here are useful for solving axisymmetric problems in semi-infinite and infinite domains. Full article

The residual stress field induced by interference-fit riveting in aircraft panel structures significantly affects the fatigue performance around the rivet holes. Common residual stress analytical models often overlook the non-uniformity of interference between the rivet and the hole, which impacts the applicability of these models. Addressing this issue, an analytical model of residual stress around the rivet hole is proposed for a typical single-riveted structure based on the thick-walled cylinder theory and Lame’s equations, considering the non-uniform interference along the axis of the rivet hole. This novel model is then extended to multi-riveted structures in fuselage panels. Using vector synthesis, analytical models for single-row double-rivets and double-row quadruple-rivets configurations were derived. The established analytical models provide a three-dimensional characterization of the residual stress field in typical riveted structures. Finally, the accuracy of the model is verified through X-ray diffraction experiments and FEM simulation results. Full article

In this work, by the use of a semigroup theory approach, we provide a global solution for an initial boundary value problem of the wave equation with logarithmic nonlinear source terms and fractional boundary dissipation. In addition to this, we establish a blow-up result for the solution under the condition of non-positive initial energy. Full article

Mechanical couplings in engineering usually use interference fits to connect the shaft and hub. A railway wheel axle is a press fit that is connected by interference and can be subjected to bending stress. In loaded press fits, a high concentration of contact stresses can be generated in the area of the axle-fillet beam, which in most cases leads to the failure of the axle due to fatigue and fretting fatigues. Therefore, it is crucial to determine the ability of the press-fitted joints to provide sufficient frictional resistance that can withstand the loads and torques by evaluating the safety factor, especially when the mechanical or structural system is loaded. In this paper, the contact pressure and stress distribution along the radius of the wheel axle are studied using the analytical calculation of Lame’s equation, and the numerical method used is by ANSYS software. It was found that interference fits have a great influence on the connection strength of interference fits, which are directly related to the contact pressure. Increasing the interference increases the contact pressure, which allows higher torque and load capacity to be transmitted. The finite element analysis showed good agreement for the highest interference value of 230 µm with a relative error of 1.4%, while this error increased to the maximum relative error of 14.33% for a minimum interference of 100 µm. Full article

The average sizes ${\overline{L}}_i$, and their dispersion $W_i$ along the i-th axis, of crystallites in powders are used to determine X-ray diffraction sizes, $D_{i XRD}$, averaged over crystallite columns within the BWA method. Numerical calculations have been carried out for an orthorhombic lattice of crystallites, such as LiFePO₄, NMC, having a Lamé’s g-type superellipsoid shape. For lognormal distributions, the analytical expression for the normalized coefficient $K_n$ has been found: $K_n=D_{i XRD}{/\overline{L}}_i=\left(K_{g,0}+K_g{W}^2\right)$, where $K_{g,0}$ is a constant at W→0, $K_g$ is a constant depending on the g -type shape. The dependences of $D_{i XRD}$ are also calculated for normal distribution. A fairly simple equation can be obtained as a result of analytical transformations in the framework of experimentally validated approximations. However, a simpler way is to carry out numerical computer calculations with subsequent approximation of the calculated curves. Using the obtained analytical expressions to control technologies from nuclear fuel to cathode materials will improve the efficiency of flexible energy network, especially storage in autonomous and standby power plants. Full article

The main goal of deformable solid mechanics is to determine the stress–strain state of parts, structural elements, and their connections. The most accurate results of calculations of this state allow us to optimize design objects. However, not all models can be solved using exact methods. One such model is the problem of a layer with cylindrical embedded supports that are parallel to each other and the layer boundaries. In this work, the supports are represented by cylindrical cavities with zero displacements set on them. The layer is considered in Cartesian coordinates, and the cavities are in cylindrical coordinates. To solve the problem, the Lamé equation is used, where the basic solutions between different coordinate systems are linked using the generalized Fourier method. By satisfying the boundary conditions and linking different coordinate systems, a system of infinite linear algebraic equations is created. For numerical realization, the method of reduction is used to find the unknowns. The numerical analysis has shown that the boundary conditions are fulfilled with high accuracy, and the physical pattern of the stress distribution and the comparison with results of similar studies indicate the accuracy of the obtained results. The proposed method for calculating the stress–strain state can be applied to the calculation of structures whose model is a layer with cylindrical embedded supports. The numerical results of the work make it possible to predetermine the geometric parameters of the model to be designed. Full article

An acoustic emission (AE) is caused by the sudden release of energy by a material as a result of material degradation related to deformations, cracks, or faults within a solid. The same situation also occurs in leaks caused by turbulence in the fluid around the leak. In this study, analytical modeling for an AE due to leakage through a circular pinhole in a gas storage cylinder was performed. The displacement fields responsible for AEs, excited by the concentrated force (CF) associated with the turbulent flow though the pinhole, were derived by solving the Navier–Lamé equation. The CF as an excitation source was formulated in terms of a fluctuating Reynolds stress (FRS) and spatial Green’s function. In particular, a series of experiments were conducted under different operating conditions to explore the characteristics of the AE signals due to leak in a gas cylinder. Finally, the simulation and experimental results were compared to verify the accuracy of the simulation results. Full article

This study investigates the strain and stress states in an aluminum single lap joint bonded with a functionally graded Al${}_2$O${}_3$ micro particle reinforced adhesive layer subjected to a uniform temperature field. Navier equations of elasticity theory were designated by considering the spatial derivatives of Lamé constants and the coefficient of thermal expansion for local material composition. The set of partial differential equations and mechanical boundary conditions for a two-dimensional model was reduced to a set of linear equations by means of the central finite difference approximation at each grid point of a discretized joint. The through-thickness Al${}_2$O${}_3$-adhesive composition was tailored by the functional grading concept, and the mechanical and thermal properties of local adhesive composition were predicted by Mori–Tanaka’s homogenization approach. The adherend–adhesive interfaces exhibited sharp discontinuous thermal stresses, whereas the discontinuous nature of thermal strains along bi-material interfaces can be moderated by the gradient power index, which controls the through-thickness variation of particle amount in the local adhesive composition. The free edges of the adhesive layer were also critical due to the occurrence of high normal and shear strains and stresses. The gradient power index can influence the distribution and levels of strain and stress components only for a sufficiently high volume fraction of particles. The grading direction of particles in the adhesive layer was not influential because the temperature field is uniform; namely, it can only upturn the low and high strain and stress regions so that the neat adhesive–adherend interface and the particle-rich adhesive–adherend interface can be relocated. Full article

In this work, using the noncommutative integration method of linear differential equations, we obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. It is shown that the noncommutative reduction of the Schrodinger equation leads to the Lame equation. The resulting set of solutions is determined by the Lame polynomials in a complex parameter, which is related to the geometry of the orbits of the coadjoint representation of the rotation group. The spectrum of an asymmetric top is obtained from the condition that the solutions are invariant with respect to a special irreducible $\lambda$-representation of the rotation group. Full article

In one of our previous publications, we developed the first mathematical model for acoustic emission from an internal point source in a transversely isotropic cylinder. The point source, as an internal defect, is the most fundamental source generating AE in homogeneous media; it is represented by a spatiotemporal concentrated force and generates three scalar potentials for compressional, and horizontally and vertically polarized shear waves. The mathematical formulas for the displacements were derived by introducing the concentrated force-incorporated potentials into the Navier–Lamé equation. Since the publication of that paper, we detected some errors. In this paper, we correct the errors and extend the analytical modeling to a cylindrical shell structure. For acoustic emission in general circular cylindrical structures, we derived solutions by applying the boundary conditions at inner and outer surfaces of the structures. Under these conditions, we solve the radial, tangential, and axial displacement fields. Analytical simulations of the acoustic emission were carried out at several point source locations for circular cylindrical geometries. We show that the maximum amplitude of the axial displacement is dependent on the point source position and 2π-aperiodicity of the cylindrical geometry. Our mathematical formulas are very useful for characterizing AE features generated from an internal defect source in cylindrical geometries. Full article