Archive of Applied Mechanics最新文献

This work presents a unified bioheat transfer model that integrates dual-phase-lag (DPL) heat conduction, memory-dependent derivatives (MDD), and nonlocal elasticity to capture the complex thermal and mechanical behavior of skin tissue under localized heating. The model incorporates nonlinear kernel functions to represent temporal memory effects and spatial heterogeneity, enabling a more realistic simulation of thermal wave propagation and stress development. Analytical solutions are obtained through Laplace and Fourier transforms, with Zakian’s method applied for numerical inversion. The results demonstrate that the combined influence of DPL, MDD, and nonlocality significantly enhances thermal precision, modulates stress distribution, and governs displacement dynamics during thermal shock. The interaction between blood perfusion temperature and stress response demonstrates physiologically consistent thermoregulatory patterns. These findings highlight the potential of the proposed framework to inform personalized thermotherapy protocols, particularly in managing conditions such as diabetic ulcers and superficial burn injuries.

This study proposes a two-dimensional higher-order deformation gradient element based on the floating frame of reference formulation to meet the dynamics control requirements of systems with large deformations/rotations. The proposed model can be regarded as an equivalent element of absolute nodal coordinate formulation, since its derivation process only involves the transformation relationships between coordinate systems without the small deformation assumption. Furthermore, a dynamics model of flexible hub-beam system is derived using the Green-Lagrange strain tensor and the Lagrange’s equation of the second kind, which can precisely describe dynamic behavior undergoing large deformation. Ultimately, several traditional numerical examples, such as a cantilever beam subjected to a vertical tip force, are shown to verify the performance of the proposed model. The results are then compared with existing model methods and ANSYS simulation results. As the results indicate, the computational accuracy of the proposed element is higher than the traditional model. Moreover, the proposed model accurately captures the higher-order deformation characteristics of beam cross sections and effectively address the effects caused by shear locking, including the overestimated bending stiffness and excessively high natural frequency of the system.

This study presents a mathematical framework to examine the thermoelastic response of an unbounded isotropic medium with a cylindrical cavity exposed to a continuous line heat source. The analysis employs the dual-phase-lag (DPL) heat conduction model under traction-free and ramp-type thermal conditions within generalized thermoelasticity. Building upon earlier eigenvalue-based formulations in Cartesian coordinates, this work extends the analytical methodology to cylindrical geometry, enabling a more realistic representation of thermal and elastic interactions induced by line heat sources. The governing equations are transformed into the Laplace domain and reduced to a vector–matrix system of coupled differential equations. Analytical expressions for field variables are obtained in the transformed domain and numerically inverted into the time domain using Stehfest’s algorithm implemented in MATLAB. The results graphically demonstrate how ramp-type heat, phase-lag, and time parameters influence the propagation of field variables, emphasizing the analytical significance of the adopted methodology. The novelty of this study lies in the combined analytical and numerical formulation of a DPL-based thermoelastic model for cylindrical geometry under ramp-type heating, offering a realistic representation of finite-speed thermal and elastic wave propagation pertinent to advanced engineering and biomedical systems.

This work presents the application of variational principles to an inhomogeneous beam having orthotropic material properties. A planar beam with arbitrary transverse loading has been considered. Variational asymptotic method (VAM), a synergy between variational principles and asymptotic expansion, has been used. Application of VAM has simplified the analysis by assisting in providing the solution equations in an ordinary differential equation (ODE) format. Moreover, these equations are in functional form. ODEs are easier to solve and facilitate a closed-form analytical solution, whereas the functional form widens the scope of these equations by permitting solutions for a wider class of inhomogeneity models. For illustrations, four different inhomogeneity models are adopted from the literature, and a closed-form solution for each has been presented. The verification of the obtained results has been done by comparing them with some of the prominent literature results, as well as with finite element analysis (FEA) results obtained using Abaqus. Furthermore, it has been observed that the analytical solutions of this study also perform very well in situations involving isotropic material properties. There has been a considerable savings in computational cost between an FEA analysis and the analytical analysis. Based on this, the following are some of the key contributions from this work: (a) The given formulation successfully handles orthotropic as well as isotropic materials. Isotropy is handled by doing suitable reductions in the stiffness coefficients of the orthotropic material matrix. (b) In line with the mechanics, the ordered warping solutions result in Euler–Bernoulli-type deformation in the zeroth order, whereas the higher-order solutions result in transverse shear contribution.

This study addresses the unclear mechanisms of shear deformation effects and the contradictory design thresholds in the buckling analysis of pultruded GFRP (glass fiber-reinforced polymer) compression members. By integrating test data from 322 specimens across 17 studies, a large-sample experimental database was established. The Engesser and Haringx shear correction theories were systematically validated, with results indicating that the Engesser model provides the optimal prediction accuracy (R² = 0.89). Shear deformation can reduce the buckling load by up to 48%. Theoretical derivation revealed the decomposition law of the core parameter: (P_{{text{E}}} /left( {{text{KGA}}} right) = left( {pi^{2} /K} right) cdot left( {E/G} right) cdot lambda^{ - 2} ,) which for the first time clearly identifies the slenderness ratio ((lambda)) as the dominant geometric factor controlling the shear effect, while the elastic modulus ratio ((E/G)) is a secondary material factor. Based on this mechanism, a practical design criterion with a threshold of (lambda =86.6) is proposed: The Engesser formula must be used for shear correction when (lambda le 86.6,) whereas the shear effect becomes negligible (< 5%) when (lambda >86.6). This threshold is significantly higher than that for steel ((lambda approx 31.4),) revealing the unique buckling characteristics of GFRP materials due to their anisotropy. The research outcomes provide a theoretical basis and practical tools for the refined design of GFRP compression members.

The present study provides an effective step in the advancement of relevant studies on the mechanical behavior of materials. Although bi-films have a great effect on the mechanical behavior as well as fracture of materials, most of our knowledge about this phenomenon is related to experimental predictions to the extent of knowing their structure and how they are formed. Regarding the formation and structure of bi-films as well as their laboratory limitations and scales, it is necessary to look for the general mathematical modeling of their mechanical behavior and development it to the most known behavior of them as viscoelasticity behavior. The size effects are considered using Eringen’s nonlocal elastic theory. In this paper, for the first time, mechanical analysis of bi-films is studied. Oxide films as double-layer cavities in the material structure create a combined system with connections between components that have a specific structure. In order to study their mechanical modeling efforts lead to sufficiently valuable results, it is necessary to investigate them with a special attitude. In this paper, considering all required thermal and mechanical variables with their changed classes, the second law of thermodynamics is considered using a novel version of the Borchers’ (Rep Math Phys 22:29–48, 1985) perspective. According to the mathematical structure and physical foundations of Borchers’ approach, it provides the possibility of generalization to composed systems and can be considered a special solution for the purpose of mechanical modeling of bi-films. In this paper, unified general energy-based model for all loading classes is established, and in the following, the extracted equations are developed considering nonlocal viscoelasticity theory. Due to the fact that strain has the main essential role in the investigation of the mechanical behavior of bi-films, established model is developed to the complete kinematic form as a reasonable form for the desired problem. Finally, the mathematical structure of the established model as well as its physical bases are studied and discussed generally using one of the well-known unified continuum mechanics approaches. An applied example is studied, and the matching of the results with the expected results is shown generally. It is concluded that due to that the established model simultaneously has the first and second laws of thermodynamics as its basis, and therefore, can be presented as a unified model to study mechanical behavior of bi-films.

Locally resonant metamaterial plate exhibiting mechanically sub-wavelength tunable bandgaps is utilized to simultaneously mitigate the structural vibration as well as attenuate the noise radiation inside an acoustic cavity in a coupled fluid–structure system. A typical configuration of a three-dimensional metamaterial plate consisting of a flexible plate with an array of local mass–spring–damper resonators is coupled with an acoustic cubical cavity. For the sake of comparison, the vibration responses of the structural plate in the presence and absence of the resonators are considered to investigate the vibroacoustic characteristics of the coupled fluid–structure system. The differences between the vibroacoustic responses of the acoustic cavity coupled with the conventional plain plate and the damped metamaterial plate are also outlined. The effects of resonators’ mass and damping values and their numbers on each of the unit cells in the overall array of the metadamping plate configuration on the width of the bandgaps and vibration reductions are investigated. A conducted sensitivity analysis on the uncertainty values of the absorber resonators’ mass and spring demonstrates that a coefficient of variation of 5% could affect the tunable bandgap width and the vibration reduction. The coupled system was numerically solved using finite element method. The obtained results and the sensitivity analyses can be used as cornerstone for design guideline of metamaterial plate for achieving prescribed vibroacoustic characteristics.

In this work, a hybrid LSTM-PINN fatigue life prediction model is proposed, integrating long short-term memory (LSTM) and physics-informed neural networks (PINN). Without processing the load path data, the raw strain data obtained from experiments, combined with the material’s mechanical properties, are utilized as inputs, while fatigue life is designated as the output. Three physical constraints are introduced: (1) a positive correlation exists between fatigue life and yield strength, (2) a positive correlation exists between fatigue life and tensile strength, and (3) fatigue life is capped at 1 × 10⁷ cycles. The model’s performance is validated using a comprehensive dataset and compared to other machine learning models. The results demonstrate that the proposed model achieves superior predictive performance, with an R² value of 0.930 and an RMSE of 0.210. Nearly, 85% of the predictions on the test set fall within the twice scatter band. In addition, the research shows that LSTM effectively captures relevant information from the loading path. Integrating physical constraints enhances predictive accuracy, accelerates model convergence, and reduces overfitting during training while aligning with the underlying data patterns.

This work delves into the mathematical modeling and analysis of scattering of Love-type wave (LTW) owing to the existence of surface irregularity on a dissimilar inhomogeneous slightly compressible elastic layer (IHSCEL) concatenated to another inhomogeneous slightly compressible elastic half-space (IHSCEHS) with spring and sliding interfaces. By means of applicable mathematical techniques, the expressions for displacement components (DCs) and dispersion relations (DRs) of LTW for incident as well as scattered wave fields are established in a closed form. Considering surface irregularities in the forms of rectangular-shaped irregularity (RSI), parabolic-shaped irregularity (PSI) and triangular-shaped irregularity (TSI), closed-form expressions of reflected displacement fields (RDFs) of LTW are also determined for both the cases of spring and sliding interfaces. As special cases of the present study, the determined results of DRs and RDFs of LTW are found to be in line with the existing results of the literature. The impacts of considered irregularity forms and associated parameters, viz. irregularity width, irregularity depth, inhomogeneity parameters and interfacial spring parameter, on RDF of LTW are delineated graphically by means of numerical computation. In addition to this, the influences of wave number, inhomogeneity parameters and interfacial spring parameter on the phase velocity of LTW are also manifested. Further, a comparative analysis between inhomogeneous slightly compressible elastic layered structure and its homogeneous counterpart for spring and sliding interfaces is explored based on RDF and phase velocity of LTW for the associated affecting parameters. The outgrowth of the present study evidently emphasizes the role and impact of inhomogeneity, irregularity, wave number, spring and sliding interfaces on the concealed characteristics of LTW.

This study investigates sandwich FGM diaphragms for high-temperature capacitive pressure sensors. A three-dimensional high-order shear deformation theory with novel polynomial–trigonometric shape function is developed, with solutions obtained using Galerkin’s method. Results reveal boundary conditions significantly impact performance, with clamped boundary conditions reducing deflection by 50.75% versus simply supported boundary conditions. Material composition in sandwich FGM diaphragms substantially affects sensitivity, as metal-rich configurations (1-3-1) demonstrate 6.01% higher capacitive response than ceramic-rich configurations (2-1-2). Geometric parameters create competing effects: Increased width enhances sensitivity up to 37.36%, while thicker plates show reduced responsiveness despite higher initial capacitance. The inclusion of elastic foundation modeling reveals how foundation stiffness modulates both sensitivity and linearity, providing an additional design parameter for application-specific optimization. Temperature gradients and microscale effects further enable fine-tuning of sensor performance. The analytical model shows excellent agreement with finite element simulations (discrepancies < 5%), offering valuable design guidelines for high-temperature pressure-sensing applications.