Understanding the mechanical behaviour of isotropic points (IPs)-regions of hydrostatic stress with zero shear-is essential for interpreting photoelastic fringe patterns and analysing load transfer in solid bodies. This study investigates IP formation and evolution in circular disks subjected to four-point loading using a combination of photoelastic experiments, digital image processing, and analytical modelling. A generalised stress framework based on superposition is developed to predict isochromatic fringe fields and IP locations for arbitrary combinations of normal and tangential contact forces. Beyond case-specific solutions, the study establishes a unified physical interpretation of fringe patterns based on the concepts of zero-shear loci, symmetry constraints, and stress-topology transitions. It is shown that symmetry governs the localisation of IPs along principal axes, while symmetry breaking leads to their migration into the disk interior. Under normal loading, IPs form along boundary-induced zero-shear regions and undergo coalescence and splitting, indicating transitions in stress topology. In contrast, tangential loading produces a persistent central isotropic point corresponding to a null stress state, resulting in qualitatively different fringe evolution. A novel inverse methodology is proposed to determine contact force components from experimentally measured IP coordinates. The results demonstrate that IP locations are invariant to the load magnitude but highly sensitive to the load direction, making them reliable indicators of the load geometry. The findings highlight isotropic points as fundamental descriptors of stress redistribution and fringe topology. While the present study focuses on a circular disk under four-point loading, the framework may be extended to more complex systems such as granular assemblies and contact-driven structures, subject to further investigation.
This paper investigates the propagation of shear horizontal (SH) waves in piezoelectric nanoplates by coupling the Gurtin-Murdoch surface model with the nonlocal strain gradient theory. The Legendre polynomial expansion method with analytical integration is developed, which reformulates the complex acoustic wave partial differential equation (PDE) solution problem into a standard generalized eigenvalue problem, thereby obtaining its dispersion relation. In contrast to conventional polynomial techniques, this approach obviates the necessity of redundant integration, thereby facilitating the derivation of comprehensive solutions over the full frequency spectrum. The validity of the proposed method is verified by calculating the phase velocities of SH waves in a piezoelectric nanoplate without surface and strain gradient effects and comparing the results with literature data. The convergence and computational efficiency of the method are also demonstrated. Results indicate that the stiffness softening dominated by the surface effect and the hardening induced by the strain gradient effect form a competitive mechanical response. The surface effect increases wave velocity, while the nonlocal strain gradient effect decreases it. This interplay is frequency-dependent, with the surface effect dominating at low frequencies and the nonlocal strain gradient effect becoming dominant at higher frequencies. These findings offer valuable insights for the design of smart nano-devices.
This study examines the linear instability in a channel flow of the Navier-Stokes-Voigt viscoelastic fluid, influenced by couple stresses. It confirms the applicability of Squire's theorem and develops a generalized eigenvalue problem for two-dimensional modes using two Chebyshev collocation methods. This problem is then solved with the QZ algorithm. Despite the base flow maintaining characteristics of the Newtonian fluid, the instability of the fluid flow is significantly affected by the presence of the Kelvin-Voigt parameter and the couple stresses parameter. Numerical results showed the effect of increasing the couple stresses and the Kelvin-Voigt parameters on the stability of the system. As the value of these parameters increases, the critical values of the Reynolds number begin to increase, which initially indicates a stabilising effect.
SOLUTIONS TO THE POINT LOAD PROBLEMS for elastic solids have different applications in geomechanics, contact mechanics, tribology as well as in modeling of lattice defects in crystals. Nonlo cal elasticity assumes an integral constitutive equation for the stress tensor, takes into account interatomic long-range forces, reduces to the classical theory of elasticity in the long wave-length limit and to the atomic lattice theory in the short wave-length limit. Often, the nonlo cal kernel of a stress constitutive equation is selected as the Green function of the Cauchy problem for appropriate partial differential equation. In this paper, we obtain the solution of elasticity problems for a point force in a plane and for a point load on the boundary of a half-plane in the context of the new theory of nonlo cal elasticity in which the nonlo cal modulus is the Green function of the Cauchy problem for the fractional diffusion equation with the Caputo derivative with respect to the nonlocality parameter and the fractional Riesz derivative with respect to spatial coordinates.
A hexa-arm honeycomb unit cell derived from a traditional honeycomb structure is proposed in this study. Through the periodic arrangement of the unit cell in a two-dimensional plane, four distinct honeycomb configurations are constructed: high density hexa-arm honeycomb (HHAH), orthogonal hexa-arm honeycomb (OHAH), inclined hexa-arm honeycomb (IHAH), and staggered distributed hexa-arm honeycomb (SHAH). Their deformation patterns and compression behaviors under quasi-static in-plane compressive loading are systematically investigated. Specimens are fabricated using 3D printing and subjected to quasi-static compression tests, numerical simulation models are established to validate the experimental results. Quantitative validation shows good agreement between experiments and simulations with high repeatability. The SHAH structure exhibits superior mechanical properties: compared with a conventional hexagonal honeycomb, its specific energy absorption is up to 155% higher. All four structures show positive Poisson’s ratios. The hexa-arm honeycomb demonstrates a dual-stage deformation pattern during compression: the initial elastic stage is characterized by coordinated deformation of the entire structure, whereas further compression transitions into a second stage involving local failure or layer-by-layer collapse. The effects of different structural parameters on deformation patterns and specific energy absorption are also explored. These research findings provide valuable references for engineering applications of this type of honeycomb structure.
This study presents an analytical model to predict the ballistic performance of elastoplastic materials with strain hardening under normal impact by rigid penetrators. The model integrates the localized interaction model with the spherical cavity-expansion theory to account for dynamic material behaviour. Key parameters, including cavity-expansion pressure and strain hardening, are incorporated using the Ludwik and Voce hardening laws, enabling accurate predictions of residual velocity and ballistic limit. The model is validated using experimental data for various aluminium alloys and steel plates, demonstrating good agreement between predictions and observations. The proposed analytical approach offers a reliable and computationally efficient tool for evaluating ballistic performance, making it a valuable resource in armour design and impact mechanics research.
In this paper, the linear theory of Moore-Gibson-Thompson (MGT) thermoviscoelasticity for materials with voids is examined and the basic boundary value problems (BVPs) of steady vibrations are investigated. The governing equations of motion and steady vibrations are formulated. The fundamental solution to the system of steady vibration equations is constructed explicitly using four elementary functions, and its key properties are analyzed. Then, Green's first identity is established and the uniqueness theorems for classical solutions of the associated basic BVPs are proved. The surface and volume potentials are defined, and their essential properties are established. Singular integral operators are introduced, and their symbolic determinants and indices are calculated. Finally, existence theorems for classical solutions of the basic internal and external BVPs are established using the potential method.
THE OBJECTIVE OF THIS STUDY IS TO INVESTIGATE AEROELASTIC PHENOMENA occurring during airflow around flapping wings of a micro aerial vehicle (MAV) inspired by insect anatomy. A numerical model of the wing and the flow configuration was developed based on an experiment conducted at ESPCI Paris. Transient fluid-structure interaction (FSI) simulations were carried out in the Ansys environment, employing independent solvers for fluid flow (CFD) and structural deformation (FEM), coupled through the System Coupling module. The analysis focused on the role of wing compliance in thrust generation, with particular attention to the effects of flapping frequency and wing stiffness, determined by the thickness of the membrane forming the lifting surface. The results demonstrate a strong dependence of thrust generation on the degree of wing deformation, in good agreement with the experimental findings. These findings highlight the importance of structural flexibility in enhancing aerodynamic performance and provide practical guidelines for the design of efficient flapping-wing micro aerial vehicles.
Water hammer (WH) events are involved in pipelines when the flow is disturbed by any reason changing its velocity, which produces pressure variations and elastic waves propagating in liquid along a pipeline at the acoustic wave-speed. These phenomena stay more complex if dynamic fluid-structure interaction takes place. More dangerous scenarios may happen in the case of liquid cavitation, which appears when the instantaneous local pressure drops down to the level of the liquid vapor pressure. Bubbles of vapor are created, which can be distributed in specific areas of pipes (distributed cavitation) or may form one larger vapor space between two parts of water column (column separation = CS). In the paper analyses of CS effects are presented based upon experiments performed in the laboratory of the Institute of Fluid-Flow Machinery. Water hammer runs in a copper pipeline fixed to the foundation with elastic supports were generated while pressure oscillations and pipeline vibrations were being measured. For certain initial and boundary conditions CS effects were observed. Analyses of these events were performed for varying initial conditions and support stiffness. The general conclusion is that, more elastic pipeline fixing allows to reduce CS behaviors, more effectively. Further discussion and conclusions are also presented, specifically on WH energy dissipation effects.
THE PRESENT STUDY EXAMINES THE THERMOPHORESIS of a cylindrical particle in a direction perpendicular to its axis in the Brinkman medium. To describe the behaviour of micropolar fluid driven by a thermal gradient within such a porous medium, the modified Brinkman's equation is applied while considering low Reynolds and P & eacute;clet numbers. The governing equations for both the particle and the medium are solved using the separation of variables technique. The boundary conditions applied at the particle surface are thermal jump and heat flux continuity, with viscous slip, thermal creep, thermal stress slip and microrotation slip. The main objective of the research is to derive the expressions for thermophoretic velocity and thermophoretic force of a cylindrical particle. Graphical representations illustrate the thermophoretic velocity and force of the particle for various physical parameters, including the permeability, micropolarity parameter, thermal stress slip parameter, viscous slip parameter, Knudsen number, and thermal conductivity parameters. The results show that an increase in the micropolarity parameter decreases both the thermophoreti velocity and the force. Additionally, thermophoretic velocity increases with higher permeability, while the thermophoretic force decreases with increasing permeability and the thermal conductivity ratio. The findings of this research align with previously published studies and hold potential applications in industrial processes, including filtration, heat exchangers, air cleaning, and manufacturing thermal precipitators.
The Debye sheath that forms at the plasma-wall interface is discussed by means of the one dimensional collisionless kinetic model. We pay special attention to the simplification often adopted both in theoretical descriptions and numerical simulations, treating the wall as a perfect absorber. We show that this assumption, although it greatly simplifies the considerations, is too restrictive from the physical point of view as it leads to an overdetermined problem. This becomes somewhat understandable if we notice that this assumption does not allow for taking into account any properties of the wall.
WE DERIVE ANALYTICAL SOLUTIONS TO THE PLANE ELASTICITY PROBLEM of two interacting identical rigid non-circular inhomogeneities embedded in an infinite isotropic elastic matrix subjected to uniform remote in-plane normal and shear stresses. Explicit expressions for the pair of analytic functions due to remote normal and shear stresses are obtained with the aid of analytic continuation and a conformal mapping function for the doubly connected quadrature domain occupied by the matrix. The rigid body rotation of each rigid inhomogeneity induced by a uniform remote shear stress is determined once three corresponding regular integrals are evaluated. The remote asymptotic behaviors of the pair of analytic functions are determined once five associated regular integrals are evaluated.
THIS STUDY INTRODUCES A SIMPLIFIED APPROACH TO ASSESS THE BUCKLING AND STATIC BENDING of advanced composite beams, including those composed of functionally graded materials (FGMs) with various porosity models. The technique utilizes a straightforward integral quasi-3D approach based on the advanced shear deformation theory. This approach offers several advantages: it simplifies the analysis by reducing the number of unknowns and equations required, improves accuracy by considering the stretch effect across the entire depth of the beam, resulting in more reliable results, and accurately represents shear by satisfying the zero-traction boundary conditions on the beam's surfaces without the need for a shear correction factor. Additionally, it captures the parabolic pattern of transverse shear strain and stress throughout the depth of the beam. The governing equations are obtained by applying the concept of virtual work, and the Navier solution is employed to calculate analytical solutions for the buckling and static bending of FGM porous beams under different boundary conditions. The approach is in line with and builds upon existing research on FGMs and other sophisticated composite beams, further enhancing its validity and reliability. Finally, computational analyses demonstrate how the distribution of materials, such as power-law functionally graded materials (FGMs), geometry, and porosity, affect the deflections, stresses, and critical buckling load of the beam.
THE PAPER PRESENTS IMPROVEMENTS OVER AN EARLIER DEVELOPED three-dimensional refined plate theory. The improved theory removes the disadvantage of the earlier theory in that it does not properly satisfy transverse shear stress conditions, and deficiency in being suitable only for flexure problems. The improved theory is suitable for use in flexure, as well as, for vibrations and stability problems of plates. The theory is simple, easy to use and accurate. The number of unknown variables involved are the same as those associated with thin plates, viz. only one in the case of flexure and vibrations; and three in the case of stability. The theory is based on displacement. The theory, to keep it as simple as possible, uses the concept of targeted displacements (which contribute only towards specific stresses, moments, shear forces, axial forces). All the stresses are represented realistically. The theory uses all strain displacement relations, and satisfies, as accurately as possible, all constitutive relations. The moments and forces satisfy gross equilibrium equations. The theory has some noteworthy similarities with the earlier developed well known theories. Due to these similarities, the experience of dealing with the earlier developed theories can be harnessed. Illustrative examples bring out the eficacy of the theory.
THIS STUDY INVESTIGATES THE INFLUENCE OF ROTATION AND COUPLE STRESSES on the convective stability of the Navier-Stokes-Voigt fluid under various boundary conditions, employing both nonlinear (via the energy method) and linear (using the normal mode analysis method) approaches. The eigenvalue problem is derived for both analyses and solved using the Galerkin method to obtain the Rayleigh number. It has been observed that the critical Rayleigh number is identical for both analyses, confirming global stability and the absence of sub critical instabilities. Notably, we find that increasing the couple stress parameter significantly narrows the spectrum of wave numbers for oscillatory modes. Conversely, higher Taylor numbers and Kelvin-Voigt parameters expand the wave number spectrum for oscillatory convection. While couple stresses and rotational effects provide stabilizing influences, the Kelvin-Voigt parameter acts as a destabilizing factor for oscillatory convection. These findings offer valuable insights with potential applications in improving fluid stability and thermal management across a wide array of industries, including industrial cooling systems, aerospace engineering, biomedical devices, energy systems, and environmental engineering.
ANALYTICAL AND COMPUTATIONAL TECHNIQUES ARE DEVELOPED to carry out stress analyses for an advanced material system comprising a piezoelectric thin film bonded to a laterally graded half-plane. The piezoelectric thin film is assumed to be under electric field loading. Governing partial differential equations are derived in terms of an inhomogeneity parameter in accordance with the theory of elasticity. Applying the Fourier transformation technique and enforcing strain compatibility between the thin film and the laterally graded surface, the problem is reduced to a singular integral equation. A scheme based on the expansion-collocation approach is applied to generate the numerical results. The computational technique is developed by utilizing the finite element method and implemented by means of the general purpose software ANSYS. Comparisons of various stress components indicate a high level of accuracy and reliability in the proposed analytical and computational methods. Parametric analyses illustrate the influences of inhomogeneity, geometry, and elasticity parameters upon interfacial shear stress, thin film normal stress, and lateral normal stress at the bounding surface of the laterally graded medium. In the previous work on thin film loading of functionally graded surfaces, the shear modulus is assumed to be a function of the thickness coordinate. The main novelty in the present study is therefore the development of analytical and computational methods for surfaces possessing the shear modulus variation in the lateral direction. The methods presented could particularly be useful in design, analysis, and optimization studies involving piezoelectric thin films bonded to laterally graded surfaces.
IN THIS WORK THE THERMOPHORETIC MIGRATION OF AN AEROSOL SPHERE embedded in a hydrogel medium has been analytically investigated. The porous medium containing microstructure fluid of a micropolar type can be viewed as a hydrogel medium. The Reynolds and P & eacute;clet numbers are considered to be very small. We solve the governing equations of momentum and energy by applying a temperature jump, continuity of heat flux, and hydrodynamic boundary conditions such as viscous slip, thermal creep and thermal stress slip at the particle surface. Analytical expressions for thermophoretic velocity and thermophoretic force are obtained. The influence of the permeability, micropolarity, frictional slip, spin slip, thermal stress slip parameters, and thermal properties of particle and medium on thermophoretic velocity and force are discussed numerically. Our results show that the thermophoretic velocity and force are decreasing functions of micropolarity and microrotation thermal conductivity parameters, while the effect of thermal stress slip is to increase the thermophoretic velocity and force of the particle. The novelty of the research is the micropolarity parameter and permeability that characterizes the micropolar fluid flow through a porous medium. The results are also compared with previously published work. The study is applied to capture ash particles conducting thermophoresis in a porous filter formed by interconnected spherical pores in a hydrogel medium.
Natural convection in porous media is crucial for applications such as geothermal energy cooling systems and energy storage, where efficient heat transfer is essential. However, the combined effect of anisotropy in the porous matrix and an inclined magnetic field on nanofluid heat transfer remains poorly understood hence, this study addresses numerically the unexplored combined effects of anisotropy and inclined magnetic field on the natural convection of water-based Al2O3 nanofluid. The Darcy-Brinkman-Forchheimer model and energy transport equations describe nanofluid motion and heat transfer in a porous medium. The mathematical equations are discretized using the finite volume method in an in-house computer code. The governing parameters are the Rayleigh number the Darcy number, the Hartmann number, solid volume fraction, the permeability ratio K (a measure of porous medium anisotropy) and an inclination angle with the magnetic field. Results are reported for streamlines, temperature contours, and the average Nusselt number under different parametric conditions. It was found that increasing the Rayleigh and Darcy numbers shifts the system from conduction to convection, improving the heat transfer rate. The nanoparticle volume fraction enhances heat transfer in conduction-dominated flows but reduces it in convection-dominated regimes. A higher Hartmann number decreases the average Nusselt number, with a more pronounced effect when the magnetic field is oriented horizontally. A higher permeability ratio reduces flow resistance and enhances convective heat transfer, but beyond K > 10, further increases in permeability have minimal impact on the heat transfer rate.
THIS STUDY PRESENTS A COMPREHENSIVE FRAMEWORK for analyzing the free vibration behavior of functionally graded (FG) porous nanobeams. A high-order shear deformation theory is employed to formulate the governing equations of motion, incorporating Eringen's nonlo cal differential constitutive relations within the context of a refined three-variable beam theory. The formulation captures small-scale effects through the length scale parameter and accounts for porosity distributions through various models, including uniform, non-uniform, logarithmic non-uniform, and massdensity-based approaches. Additionally, different volume fraction profiles, such as the power-law, Viola-Tornabene four-parameter, and trigonometric models, are considered to accurately represent the material gradation within the nanobeam. A parametric investigation is conducted to elucidate the influence of critical factors, including the nonlo cal parameter, the material index, the length-to-thickness ratio, the porosity coefficient, and porosity distribution patterns, on the dynamic response of the nanobeam. The study provides valuable insights into the interplay between small-scale effects, material heterogeneity, and porosity, offering a comprehensive understanding of their collective impact on the vibration characteristics of FG porous nanobeams.
THIS PAPER PRESENTS AN ANALYSIS OF THE BENDING PROCESS in thermoplastic sheets reinforced with unidirectional continuous fibers. To capture the material's viscoelastic response during the bending process, a novel visco elastic model is described based on the concept of transient reversible networks. The model incorporates kinematic constraints of material incompressibility and fiber inextensibility during deformation of the composite sheets. An analytical solution is derived, enabling the determination of the deformed geometry and bending forces as time-dependent functions of the bending angle, the deformation rate, and material parameters. The model's performance is evaluated through comparisons with existing experimental data and a prior viscous model for bending process at various deformation rates. This comparison aids in identifying the material parameters and characteristic time associated with the transient reversible networks.
