An energy-based Rayleigh-Ritz formulation is presented for the free axial vibration of tapered nanorods subjected to uniform thermal loading, represented by a prescribed effective thermal axial force, within Eringen’s nonlocal elasticity. Crucially, the weak-form approach rigorously preserves the exact gradient-dependent nonlocal mass operator, avoiding the artificial truncation of cross-sectional spatial derivatives common in the literature. A gap is addressed where prior studies have largely examined tapering, thermal, or nonlocal effects in isolation. To bridge this, the present study concurrently evaluates symmetric ( β _b=β _h=β ) and asymmetric ( β _bβ _h ) tapers under clamped-free and clamped-clamped boundary conditions. Within a consistent nondimensional setting, the combined influence of the taper parameter ( β ), temperature increment ( Δ T ), and the nonlocal parameter ( α =e_0a/L ) on the first three natural frequencies is rigorously quantified. The results indicate that uniform thermal loading and nonlocality soften the response and primarily rescale the frequency levels without changing the relative ranking among geometries. The usefulness of geometric asymmetry is governed by the boundary condition. For clamped–free support, profiles narrowing toward the free end lead to clear, temperature–insensitive increases in the nondimensional natural frequencies across Modes 1–3 (yielding gains of up to 44 β raises the nondimensional frequencies, and increasing L also raises them toward the classical local limit, since L inversely scales the nonlocal parameter ( α =e_0a/L ), making short rods more sensitive to nonlocal softening. These trends provide practical guidance for nanoscale resonators and AFM–like cantilevers operating under uniform temperature fields and moderate nonlocality by indicating which taper strategies increase resonance robustly, and they supply benchmark data for future thermo–nonlocal modeling.
We derive a closed-form solution to the three-dimensional Eshelby’s problem of a spherical Eshelby inclusion undergoing uniform deviatoric eigenstrains concentrically embedded in an isotropic elastic finite spherical domain with a traction-free boundary (the Neumann problem). We assume that a spring-type imperfect interface with vanishing thickness lies between the spherical inclusion and its supplement to the finite spherical domain. Our solution indicates that the stresses and strains within the spherical inclusion are in general non-uniform due to the influence of the finite spherical domain and the imperfect interface. The internal elastic field of stresses and strains within the spherical inclusion undergoing arbitrary uniform eigenstrains still remains uniform when the two interface parameters satisfy a condition for a given geometric parameter and given Poisson’s ratio of the finite domain.
This work develops a rigorous framework for oblique incidence of bulk shear-horizontal (SH) waves at the interface between an n-type flexoelectric-piezoelectric semiconductor halfspace and a flexomagnetic-piezomagnetic halfspace. Conventionally, upon incidence, the SH wave splits into reflected and refracted components in respective media. A key novelty of the work lies in the incorporation of carrier-induced electrostatic screening through the well-known Debye-Hückel mechanism, which governs the redistribution of carriers and attenuates the electric field exponentially over a finite spatial region. Unlike conventional models, the electrical boundary conditions are reformulated as Robin-type mixed boundary conditions, explicitly incorporating the Debye screening length to ensure a physically consistent representation of interfacial electrostatics. An analytical formulation is developed to obtain closed-form expressions for scattered wave amplitudes and energy fractions. Numerical results reveal that Debye screening acts as an effective control parameter for wave manipulation. Larger screening lengths enhance energy transmission into the flexomagnetic medium, whereas smaller screening lengths suppress electric fields and promote reflection-dominated behavior, approaching total reflection under strong doping conditions. Additionally, flexoelectric and flexomagnetic effects increase impedance mismatch, further reducing transmission. Pronounced dependence of amplitudes on incidence conditions is observed, with grazing incidence leading to near-total reflection. The model is shown to recover classical results in the limiting cases of negligible screening and vanishing flexoelectric-flexomagnetic couplings, thereby validating the formulation. These findings highlight doping-induced Debye screening as a viable mechanism for tuning wave propagation characteristics, offering potential applications in semiconductor-based sensors and bulk acoustic wave (BAW) devices requiring precise control of signal transmission and reflection.
The key objective of this research is to present a comprehensive analysis of energy transfer characteristics in unsteady mixed-convection flow of an electrically conductive hybrid nanofluid past a Darcy–Forchheimer permeable surface under slip boundary conditions. For the flow problem, the mathematical model is formulated to account for the influence of the Forchheimer term and buoyancy forces arising from mixed convection. MWCNT/SWCNT/ Blood Two hybrid nanofluid formulations are used to investigate the impact of thermophysical characteristics on transport phenomena. The governing NLPDEs are converted into coupled NLODEs via similarity transformations and solved by the Homotopy Analysis Method, which guarantees convergence of the series solution. The impacts of rotation, Forchheimer, Grashof, electric, unsteadiness, Buoyancy, Biot, porosity, and magnetic parameters on the velocity, energy, skin friction, and Nusselt number are examined graphically. The results reveal a significant reduction in fluid velocity with the inclusion of the Forchheimer parameter and porosity, owing to increased inertial resistance. In contrast, a surge in the magnetic parameter surges the fluid velocity and heat transfer rates. The study shows that hybrid nanofluids have significantly better thermal performance than traditional fluids, particularly under strong mixed-convection and porous-medium effects. The unsteadiness parameter is also observed to reduce the thickness of the thermal boundary layer and consequently increase the Nusselt number, making the present configuration a practical avenue for intermittent, energy-saving cooling cycles rather than continuous operation. The results are also valuable in the context of sustainable technical applications, such as solar-thermal collectors, permeable heat exchangers, electronic cooling, and advanced thermal management systems, where a lower pumping/energy input, combined with improved heat transfer, contributes to sustainable operation over time.
In this study, an analytical investigation of the squeezing flow of a blood-based, couple-stress ternary hybrid nanofluid between parallel horizontal channels, with the effect of thermal radiation, is presented. The ternary hybrid nanofluid is the combination of silver (Ag), alumina (Al2O3), and titania (TiO2) nanoparticles in a non-Newtonian blood base fluid (Casson). Appropriate similarity transformations are applied to the continuity, momentum, and energy equations to obtain nonlinear ordinary differential equations, which are then solved numerically using the Homotopy Analysis Method (HAM) available in the Mathematica packages BVPh 1.0 and BVPh 2.0. The effects of the squeezing parameter, the Casson parameter, the couple stress parameter, the thermal radiation parameter, and the volume fraction of the nanoparticles on the velocity and temperature profiles, the skin friction coefficient, and the local Nusselt number are investigated through a comprehensive parametric study. The results show that the fluid velocity decreases as the Casson and couple stress parameters increase, whereas the squeezing parameter increases. The temperature distribution becomes more uniform with higher thermal radiation and nanoparticle volume fraction because of increased radiative and conductive heat transport, and lower squeezing due to the squeezing force. Besides, the convergence analysis proves the stability and accuracy of HAM solutions. The results confirm that the blood-based ternary hybrid nanofluids exhibit excellent thermal characteristics that could be used in biomedical thermal management, microfluidic devices, cooling systems, and advanced heat transfer systems.
Material properties in multi-layer high temperature strain gauge structures exhibit inherent three-dimensional randomness, leading to variability in strain response even under identical conditions. This paper quantifies the influence of this uncertainty on the strain response of each layer using the stochastic finite element method. Three-dimensional random fields of elastic modulus (E), Poisson’s ratio (ν), and thermal expansion coefficient (α) are discretized via the local average method, and Monte Carlo simulation is employed to obtain response statistics. A hybrid finite element model combining solid elements for bonding layers and beam elements for the sensitive grid is established, with virtual connection elements handling the interface. Static tensile tests with digital image correlation (DIC) are conducted for validation. Results reveal a clear attenuation law: uncertainty decreases as it propagates from the specimen to the sensitive grid (cov(s1)>cov(s2)>cov(s3)>cov(s4)). The uncertainty of the specimen’s material parameters dominates the grid’s strain response, while the grid’s own parameter uncertainty is negligible. Under high temperature conditions (1000 °C), α uncertainty has an order-of-magnitude greater influence than E and ν. DIC results confirm the uncertainty propagation trend and the decrease in mean strain with increasing bonding layer thickness, providing theoretical guidance for installation process optimization and measurement reliability improvement.
The present study focuses on exploring the multiphase transport behavior of a Boger nanofluid under the coupled effects of elasticity, bioconvection, and magnetohydrodynamics in presence of thermal radiation and chemical reaction. The novelty of this study lies in incorporating surface curvature into the picture along with curious investigation of thermophoresis and Brownian diffusion on heat and mass transport phenomenon. A nonlinear mathematical framework governing the momentum, thermal energy, nanoparticle, and microorganism density is formulated and reduced to a system of ordinary differential equations using similarity transformations. The resulting equations are solved semi-analytically via Homotopy Analysis Method. The parametric influences on velocity, temperature, nanoparticle concentration, microorganism distribution, Nusselt number, and Sherwood number are analyzed through detailed 2D and 3D graphical representations. The results reveal that surface curvature significantly alters the velocity field, while enhanced magnetic and radiative effects suppress fluid motion and modify thermal and concentration boundary layers. Thermophoresis and Brownian motion are found to strongly regulate nanoparticle distribution and bio-convective behavior. These findings provide useful insights for the design of advanced heat transfer systems, nanofluid-based energy technologies, industrial coating processes, and microscale bioreactors requiring precise thermal and solutal control.
Based on the conjugate meshing theory, this study achieves line contact transmission for intersected beveloid gears. A mathematical model for the spatial gearing of both involute and non-involute beveloid gears is established and the tooth surface equations for the non-involute beveloid gears is derived. Based on tooth surface modification, the tooth flank differences between involute and non-involute beveloid gears are compared. Precise solid models of both gear pairs are developed, and loaded tooth contact analysis (LTCA) is performed under various loading conditions, misalignments, and modification approaches. The results demonstrate that applying non-involute modifications to beveloid gear pairs increases the tooth contact pattern from approximately 50
Extended surfaces are widely employed in thermal engineering applications to augment heat transfer and improve the efficiency of compact thermal systems. However, their performance is limited due to single-particle nano fluids and basic thermal assumptions. The use of hybrid nano fluids ensuring to overcome these limitations due to enhanced thermo-physical properties. Despite this, most existing fin studies overlook the combined influence of realistic non-linear effects when hybrid nano fluids are used. In this particular study, a unified non-linear mathematical model is developed to investigate heat transfer in four different fin geometries along with hybrid nano fluids. Furthermore, this model incorporates size-dependent thermal conductivity, non-linear internal heat generation, and wavelength-dependent surface emissivity within a single framework that addresses gaps in existing studies. The non-linear governing equations are tackled using the Legendre Wavelet Collocation Method (LWCM). The outcomes are validated with the exact solution showing good agreement. In contrast, temperature is decreasing as a rise in size-dependent thermal conductivity and the surface emissivity. Moreover, the rate of heat dissipation increased when non-linear internal heat generation increases in magnitude. The influence of N_cc and K_n on fin efficiency η _f obtained using θ _s provide useful insight for improving fin performance.
Efficient thermal management is a fundamental requirement in contemporary engineering applications, encompassing electronic cooling systems, semiconductor fabrication, thermal insulation frameworks, and nuclear reactors. The integration of magnetohydrodynamic (MHD) nanofluids within porous media has surfaced as an innovative strategy for augmenting heat transfer efficacy under intricate thermal scenarios. This investigation examines the synergistic impacts of magnetic field intensity, Ohmic heating, internal heat generation, thermal radiation, and variable permeability on the mixed convection flow of Cu–H2O nanofluids over a buoyancy-driven vertically heated plate situated in a porous medium. The governing nonlinear boundary-layer equations are reformulated into a system of ordinary differential equations through similarity transformations and solved numerically utilizing the MATLAB BVP4C solver. The findings indicate that an increase in nanoparticle volume fraction, heat absorption, and magnetic parameter considerably diminishes the velocity field, whereas heat generation amplifies the temperature profile for both uniform permeability (UP) and variable permeability (VP) scenarios. An escalation in the buoyancy parameter (Gr/Re2) promotes fluid flow and decreases the thermal boundary layer thickness, thereby enhancing convective heat transfer. Elevated radiation and permeability parameters improve heat transport attributes, while stronger magnetic fields diminish velocity owing to the influence of the Lorentz force. The Nusselt number exhibits an upward trend with increasing Grashof number across all radiation parameters, signifying enhanced buoyancy-driven heat transfer. Under conditions of variable permeability, the velocity distribution ranks as Ag–water < Cu–water < CuO–water. These results underscore the critical influence of MHD phenomena, Ohmic heating, and the characteristics of porous media in regulating heat transfer efficiency and offer valuable perspectives for the development of sophisticated thermal management and energy systems.
Auxetic materials, known for their negative Poisson’s ratio, are increasingly explored in biomedical engineering for their exceptional mechanical properties, offering superior adaptability, durability, and potential for patient-specific designs. This study introduces a round auxetic structure based on a modified re-entrant unit cell, in which the addition of a small-diameter feature enhances the mechanical performance of the conventional re-entrant design. A combined approach of finite element simulations, response surface methodology (RSM), and experimental validation was employed to provide both predictive modeling and practical confirmation of the structure’s behavior. The strong agreement between simulation and experimental results validates the predictive accuracy of the developed models and confirms the superior auxetic behavior of the optimized designs. Increasing the small-diameter value significantly enhanced stiffness and buckling force but reduced buckling strain, indicating a trade-off between strength and deformability. In contrast, unit-cell thickness was found to be the most influential factor for stiffness and energy absorption, while also exerting a positive effect on the auxetic response. Width played a complementary role, strengthening the impact of thickness on stiffness and energy absorption. Importantly, the interaction between width and thickness emerged as the dominant factor controlling both buckling force and Poisson’s ratio.
A sensitivity-based optimization for heat transfer (HT) in hydromagnetic flow of carbon nanotubes (CNTs) based hybrid nanofluids (HNFs) is conducted. The effects of nonlinear radiation, slip, and catalysis are also considered. The leading PDEs are transmuted into their non-dimensional forms and then tackled numerically. The impacts of the radiation, magnetic field, slip, viscous dissipation, and nanoparticle volume fraction on the flow and thermal dynamics are assessed. To show the reliability of the chosen numerical method, a comparison in a limiting case with available data in the literature is made, and an error estimation of less than 10−4 is achieved. The sensitivity analysis shows that the magnetic parameter lowers the Nusselt number by over 65
Integrating the lightweight and high-strength characteristics of honeycomb and trabecular structures, the load-path rerouting mechanism of the Bouligand helicoidal configurations, and the stress-concentration-reducing benefits of rounded corners, this study proposes a biomechanically inspired helicoidal sandwich structure with progressive failure characteristics. Using 3D printing technology to fabricate the experimental specimens, quasi-static compression tests and finite element simulations were conducted to systematically investigate the influence of core geometrical parameters, with particular emphasis on the helicoidal angle ranging from 0° to 360°, on the compressive behavior and failure modes. The results indicate that increasing the helicoidal angle reduces structural strength and stiffness but promotes stress redistribution, delays local buckling, and significantly enhances energy absorption capacity. Compared with the conventional honeycomb configuration, the trabecula-reinforced structure achieves increases of up to 42
In this paper, we propose an innovative design framework for synergistic optimization of multiple mechanical properties in response to the urgent need for lightweight, high-stiffness, and near-zero Poisson’s ratio metamaterials in aerospace. The arc-star shape honeycomb-rodless (ASH-R) and the bidirectional re-entrant honeycomb-rodless (BRH-R) are constructed, providing ideal solutions for eliminating the imbalance of strength-mass ratio caused by insufficient relative density of traditional honeycomb structures. Through systematic finite element analysis (FEA), the mechanical behaviors of the two honeycombs are comprehensively evaluated. Based on the analysis data, the response surface modeling (RSM) is accurately constructed, which provides a reliable basis for the subsequent optimization. Combining the non-dominated sorting genetic algorithm-II (NSGA-II) and RSM, multi-objective optimization design is carried out for ASH-R and BRH-R to achieve multi-objective synergistic optimization, such as equivalent tensile modulus, bending modulus, mass and Poisson’s ratio. The equivalent tensile modulus and equivalent bending modulus of the ASH-R are increased by 710
For the theoretical model of multi-stage amplification mechanisms, two main deficiencies exist. On the one hand, when analyzing flexure hinges, the Euler–Bernoulli beam theory is typically adopted, which ignores the influence of shear deformation on hinge flexibility. On the other hand, the coupling effect between the bending and axial flexibility of flexure beams is neglected. These two factors together result in a significant discrepancy between the theoretically calculated magnification and experimental results. To address this issue, this paper proposes a precise mechanical modeling method based on the flexibility matrix. First, the flexibility matrix of flexure hinges considering the shear effect is derived using the Timoshenko beam theory. Then, for the flexure beams connecting the 1st and 2nd stages as well as the 2nd and 3rd stages of the mechanism, a comprehensive beam element model is established that accounts for axial, bending, and shear deformations simultaneously. Finally, finite element simulation and experimental results are presented to verify the rationality and accuracy of the proposed theoretical model.
This paper presents a natural vibration analysis of functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) rotor blades, idealized as pre-twisted shallow conical shells. A finite element framework based on the first-order shear deformation theory (FSDT) is developed using an eight-noded isoparametric quadratic element. Various layerwise gradation schemes of graphene origami (GOri) content and folding degree across the thickness are considered to tailor the auxetic and stiffness characteristics of the composite blade. A genetic programming (GP)-assisted micromechanical model is employed to estimate the position- and temperature-dependent effective material properties. The dynamic equilibrium equations of the rotating blade operating at moderate rotational speeds under through-thickness thermal gradients are derived using Lagrange’s equations of motion. Two types of temperature gradients, namely linear and sinusoidal distributions, are considered. A comprehensive parametric study is carried out to investigate the effects of GOri content, GOri folding degree, length-to-reference width ratio, pre-twist angle, temperature gradient, and rotational speed on the natural frequencies. The numerical results demonstrate that the vibration characteristics can be effectively tuned through appropriate tailoring of the GOri reinforcement and its spatial distribution. The findings provide valuable design guidelines for the development of next-generation rotor blades with controllable dynamic behavior, thereby enhancing operational reliability and service life in turbomachinery, helicopter rotors, wind turbines, and other rotating systems operating under thermal gradients.
The dynamic response of laser-irradiated polymer nano-spherical shells subjected to thermal shock is examined through a unified nonlocal Moore–Gibson–Thompson (MGT) thermoelastic framework. The principal novelty of this work lies in the unprecedented integration of Eringen’s nonlocal elasticity, memory-driven viscoelasticity, and MGT non-Fourier heat conduction within a spherical coupled-field configuration, an integration that captures the simultaneous effects of size-dependent stiffness, finite-speed thermal waves, and intrinsic material damping. The governing equations, which incorporate temperature-dependent thermal conductivity and transverse magnetic field effects, are solved analytically using Laplace and Kirchhoff transformations, yielding closed-form solutions in terms of modified spherical Bessel functions. Beyond resolving the paradox of infinite thermal propagation speed inherent in classical thermoelasticity, the present analysis reveals a novel coupled damping mechanism arising from the synergistic interaction between MGT thermal relaxation and spatial nonlocality. Quantitative parametric analyses demonstrate that this coupling profoundly attenuates the thermomechanical fields: increasing the nonlocal parameter from 0.00 to 0.16 induces a 41.7
Magneto-micropolar fluids have emerged in various advanced technological and biomedical applications, including electronic cooling devices, drug delivery processes, and thermal control in magneto-thermal environments. In the proposed investigation, the synergetic incorporation of nanoparticles such as Al_2O_3 and TiO_2 into water-based fluid provides superior thermal performance because of enhanced conductivity. The heat and fluid flow characteristic of a magneto-micropolar hybrid nanofluid, combined with the effect of dissipation properties with improved the physical system. The governing mathematical models are transformed into standard form utilizing similarity rules, and further, the Differential transform method (DTM) is implemented, which ensures the analytical convergence and computational efficiency. The analysis of the induced electric field coupled with magnetic intensity modifies the rotational and translational behaviour. The dissipative heat impact is found to enrich the transport phenomenon. The irreversibility conducted by various properties gives rise to the impact of entropy generation. This feature arises owing to heat transfer irreversibility, irreversibility caused by dissipation, etc. The results of various factors implemented in the flow patterns are deployed graphically, followed by validation of the results in particular cases. Further, the variations are reported, and physical descriptions are provided briefly.
Discrete Ritz method (DRM) is combined with virtual spring technique, first-order shear deformation theory (FSDT), and Newton–Raphson method, for the first time, to analyze the nonlinear bending problem of arbitrarily shaped plates under different geometric boundary conditions. DRM constructs a rectangular domain enclosing the geometric domain of the plate, and then, by using Gauss points in the rectangular domain for discretization associate with variable stiffness properties, the plate geometry is numerically simulated by cutouts within the rectangle. The global displacement field of the plate is approximated by Legendre polynomials based first-order shear deformation theory. The geometric nonlinearity is considered in terms of the von Kármán nonlinear theory. Virtual spring technique is used to simulate spring stiffness coefficient of distinct boundary conditions on complex geometric domain and embedded into the global stiffness matrix. DRM is combined with Newton-Raphson method to solve the nonlinear bending equations of plate with complex geometries. Numerical examples and comparisons with the results in the literature and FEM demonstrate that DRM based on constraint springs can be used to analyze the geometric nonlinearity of arbitrarily shaped plates under different boundary conditions with good feasibility and accuracy.
This research examines the nonlinear forced vibrations of magneto-electro-elastic laminated nanoplates, incorporating the flexomagnetoelectric influence. The system’s displacement field is formulated using higher-order shear deformation theory, with geometric nonlinearities captured via the von Karman theorem. Size-dependent phenomena are integrated through the nonlocal strain gradient theory. The nonlinear formulas of kinematics are founded by applying Hamilton’s principle and variational methods, where the Airy stress function is brought to address nonlinear-nonlocal interactions. These governing formulas are subsequently disposed of employing the Galerkin procedure and the method of multiple scales, yielding the system’s amplitude-frequency response equations and corresponding curves. Utilizing this model, a granular scrutiny is orchestrated on the flexomagnetoelectric impact, scale parameters, temperature, moisture, electric potential, magnetic potential, and elastic foundations that affect the nonlinear primary resonance performances of the magneto-electro-elastic laminated nanoplates. The results show that the flexomagnetoelectric effect can reduce the amplitude of the nonlinear primary resonance in the magneto-electro-elastic system. The outcomes of this work offer a notional foundation for employing magneto-electro-elastic materials in intelligent sensors.
