Archive of Applied Mechanics最新文献

This study presents a computational framework for optimizing material orientations in geometrically nonlinear inflatable shell structures. The proposed method employs a tensor-field representation of material orientation, which avoids the nonlinear constraints and numerical instabilities often encountered in conventional angular or vector-based formulations. In particular, a relaxed orientation tensor, whose trace may take values less than unity, is introduced to allow smooth optimization and to represent a moderate reduction in material stiffness when required by the deformation state. The shell structures are modeled using the three-node Mixed Interpolation of Tensorial Components (MITC3) element with displacement-dependent follower forces to represent the internal pressure. The material is assumed to be transversely isotropic with a single preferred direction. The optimization problem is solved within a gradient-based framework incorporating Helmholtz filtering and a smoothed Heaviside projection to achieve smooth and physically meaningful orientation fields. Sensitivities of the objective function with respect to the design variables are efficiently computed using an adjoint method combined with the complex-step derivative approximation. Several numerical examples are provided to demonstrate the accuracy, robustness, and effectiveness of the proposed optimization framework.

The problem of reflection and transmission of inhomogeneous plane waves caused by incident longitudinal (P) and shear vertical (SV) waves at the interface between an isotropic thermoelastic solid under magnetic field and an isotropic thermoelastic solid is examined mathematically using the theory of fractional-order thermoelasticity. The boundary conditions are taken at the plane interface which result in three reflected waves in one of the half-spaces and three transmitted waves in the other half-space. The effect of magnetic field and fractional parameter on the phase speed, the amplitude ratios, the bulk energy ratios and the interacting energy ratios are analyzed numerically and the results are illustrated graphically.

This study introduces an enhanced modified Anand model with a single set of parameters for the investigated thermo-mechanical conditions for 95.5Sn–4.0Ag–0.5Cu (SAC405) solder. The goal was to develop a unified parameter set that accurately captures the viscoplastic response of SAC405 solder starting from yielding through the hardening and saturation stages, across diverse thermal and mechanical conditions. Experimental stress–strain data from a wide range of strain rates (ɛ̇ = 0.001 s⁻¹, 0.0001 s⁻¹, 0.00001 s⁻¹) and temperatures (T = 298 K to 398 K) were used to determine and validate both the original and modified Anand parameters. For the modified Anand model, three critical parameters; initial stress (s₀), saturation stress (ŝ) and hardening coefficient (h₀), were expressed as quadratic functions of temperature and strain rate. The modified model and parameters demonstrated improved predictive performance, especially in the low-strain and low-temperature regime, achieving average R² values exceeding 98% across all loading conditions. Furthermore, analysis of yield and saturation stress evolution confirms dominant thermal softening, strain-rate strengthening and progressive suppression of hardening capacity at elevated temperatures, demonstrating the mechanistic consistency of the modified formulation. This unified, modified Anand model enables more reliable simulation of SAC405 solder joints within the investigated temperature and strain-rate range.

This paper presents a strain-based finite element formulation for the static, free vibration, and buckling analyses of laminated cross-ply plates within the framework of the High-Order Shear Deformation Theory (HSDT). The existing strain-based formulations are predominantly limited to First-Order Shear Deformation Theory (FSDT) or restricted analyses (mainly static or vibration), without a unified framework for complete mechanical behavior assessment of laminated plates. The novelty of the proposed approach lies in the integration of HSDT into a strain-based formulation, together with a new hyperbolic shear deformation function specifically developed in this work, which accurately captures transverse shear effects, enforces zero shear stresses at the plate surfaces, and reduces the number of kinematic unknowns from six to five. Unlike existing polynomial or trigonometric shear functions commonly used in HSDT formulations, the proposed hyperbolic function provides a more physically consistent representation of shear deformation distribution, leading to improved accuracy in transverse shear response prediction. The formulation is implemented through a High-order Strain-Based Laminated Quadrilateral Plate element (HSBLQP), obtained by coupling a strain-based in-plane element with a strain-based plate bending element. The present work introduces a hyperbolic shear deformation function within a strain-based HSDT finite element formulation for a complete structural analysis including static, free vibration, and mechanical buckling of laminated composite plates. The accuracy and reliability of the proposed element are first validated through static analysis of elliptical plates and free vibration analysis of L-shape plates by comparison with benchmark solutions available in the literature. Notably, this work also introduces, for the first time in this context, validation cases involving L-shaped and elliptical plates within a strain-based HSDT framework, demonstrating the robustness of the proposed formulation for complex geometries. Subsequently, a comprehensive parametric study is carried out to investigate the influence of geometrical and material parameters on the static, free vibration, and buckling responses of laminated cross-ply plates. The numerical results demonstrate excellent agreement with reference solutions, confirming the accuracy, robustness, and computational efficiency of the proposed strain-based HSDT formulation for laminated composite plate analysis.

Laser ultrafast heating technology is extensively applied to the micro-machining of metallic materials, of which the transient thermoelasto-diffusive responses analysis is crucial important for avoiding the unwanted vibrations and isolating the harmful stresses. Nevertheless, in such extreme non-isothermal environment, the inherent spatio-temporal nonlocal effects of the heat transport and electron–phonon coupling mechanism remain unconsidered on thermoelasto-diffusive constitutive models and heat-impact responses predictions. This work establishes nonlocal electron–phonon two-temperature thermoelastic diffusion theory with the aid of extended irreversible thermodynamics principles. By using Laplace transform method, the newly developed model is adopted to analyze the thermoelastic-diffusive responses of 1D metallic sandwich composites with perfect interfaces subjected to non-Gaussian laser irradiation. The dimensionless numerical results indicate that the increase of the spatio-temporal nonlocal parameters of electron temperature remarkably accelerate or decelerate propagation velocity of thermal wave. And the absolute peak values of stress and chemical potential are accordingly enlarged. The increasing laser energy density parameter lifts the maximum values of stress and chemical potential, which are lowered with the increase of pulse duration time parameter. Additionally, the different ratios of material physical parameters improve/reduce the impact responses of thermal, mechanical, or diffusive fields. This study is expected to extend the thermoelastic diffusion theory based on nonlocal electron–phonon two-temperature thermal transport mechanism in metallic materials, providing a theoretical basis for the optimized design of metal sandwich structures under laser heating condition.

In this article, Newton’s classical law of cooling is revisited using a generalized Caputo-type derivative. One of the fundamental assumptions of the classical model is that the system’s behavior depends solely on the instantaneous temperature difference. However, in many physical processes, memory effects and past-dependent influences play a significant role. Therefore, in this work, the concept of fractional derivatives is applied in its generalized form to capture these dynamic behaviors that the classical model fails to explain. The solution of the model is obtained analytically using the Laplace integral transform method, and the results are compared with both the classical solution and the Caputo fractional derivative solution commonly found in the literature. Analyses conducted through numerical examples indicate that the generalized model provides a wider range of dynamic responses compared to the classical model and may better represent temperature variations, capturing the system’s memory effects more effectively. The findings demonstrate that the generalized Caputo-type derivative can more effectively model the system’s memory effects, thus yielding more accurate results than the classical approach. In conclusion, the proposed method not only offers a novel perspective on Newton’s law of cooling but also provides a robust alternative for modeling similar physical systems.

Porous materials are increasingly utilized in sandwich structures due to their exceptional energy absorption. This paper develops a hierarchical beam element to predict the nonlinear vibration characteristics of sandwich beams with functionally graded material (FGM) face-sheets and a porous core. Several homogenization models, namely the Voigt, Reuss, Mori-Tanaka, and Hashin-Shtrikman, are employed to determine the effective properties of the FGM. The element formulation is based on Timoshenko beam theory, employing hierarchical interpolation functions to approximate the displacement field and eliminate shear-locking. The resulting nonlinear governing equations are solved for frequencies using a direct iterative method. Numerical results demonstrate that the proposed element is efficient, and it can provide accurate nonlinear frequencies with a small number of elements. Results show that increasing the porosity coefficient reduces the nonlinear frequency ratio, and this trend is amplified by higher vibration amplitudes but mitigated by higher material grading indices. While homogenization models significantly impact results at high amplitudes, their influence diminishes as porosity increases. It is also shown that the beam with more constraints exhibits lower sensitivity to both porosity and the choice of homogenization model.

To overcome the issue of compressive buckling instability and the inconvenience of strain extensometer installation in conventional strain-controlled low-cycle fatigue tests using small specimens, a plate-shaped small specimen enabling stable strain control via side-span strain was designed based on elasto-plastic finite element deformation analysis, and its optimal dimensions were determined. Based on the equivalent energy density principle, a semi-analytical true stress–strain relationship of plate-shaped small specimens was proposed, which enabled an effective conversion between the side-span-controlled nominal strain and the true strain at the specimen center. Based on this, a new low-cycle fatigue testing method for plate-shaped small specimens was established. Low-cycle fatigue tests on 6061 aluminum alloy at room temperature were conducted using both the small specimens and standard cylindrical specimens. The results show that, at the same strain level, the stress–amplitude response and the stress–strain hysteresis loops obtained from the small specimens are in excellent agreement with those from the standard cylindrical specimens. The fatigue curve of 6061Al derived from the small specimens also closely matches that obtained from the standard specimens. Despite a certain degree of scatter in the fatigue life data, the fatigue lives obtained from both types of specimens fall within a factor of 1.5 error band. The results indicate that, under the specific specimen configuration and material conditions investigated in this study, the proposed method can accurately characterize the low-cycle fatigue behavior of the material and yield fatigue life results consistent with those of the standard specimens.

Hyperelastic heterogeneous materials featuring microstructures display distinctive multiscale mechanical behaviors, rendering them crucial for advanced engineering applications. However, the geometric structural uncertainty inherent in such heterogeneous materials may give rise to unexpected structural damage or failure, which poses a critical challenge to their reliable application in engineering and medical fields. To address this issue, a novel computational framework for quantifying geometric stochastic effects in such materials is proposed. To tackle the computational challenges posed by material heterogeneities, a mesh- and material-independent method is developed to avoid the remeshing process of the geometric model. Subsequently, a backpropagation artificial neural network is trained to approximate finite element results, substantially reducing the costs of stochastic simulations. The proposed method is validated through three benchmark examples, and further verification is carried out with an atherosclerotic artery model. The results highlight the capability of this framework to handle heterogeneous structures, providing a powerful tool for reliability analysis of bio-inspired materials and medical devices.

This study presents a higher-order zigzag theory (HOZT) for the static bending analysis of laminated composite and sandwich plates under sinusoidally distributed transverse loading. The formulation superimposes higher-order through-thickness displacement polynomials onto the Murakami Zigzag Function (MZF), extending the simplified kinematics of Ali et al. [29], originally restricted to symmetric cross-ply laminates, to a unified framework for general lamination schemes. Transverse shear stresses are recovered through equilibrium-based integration, and analytical solutions are obtained via Navier’s method for simply supported plates. The present formulation offers three principal advances. First, the higher-order zigzag kinematics are systematically applied, within a single formulation, to symmetric and anti-symmetric cross-ply, symmetric and anti-symmetric angle-ply, arbitrary unsymmetric, and sandwich configurations. Second, compared with Murakami’s zigzag theory (MZT) and the Enhanced Refined Zigzag Theory (Enhanced-RZT), which employ linear zigzag enrichment only, the present higher-order terms provide substantially improved accuracy for thick laminates. For a four-layer anti-symmetric cross-ply plate at (a/h=4), errors in the in-plane displacement (u_2) are reduced from approximately (61%) to below (4.5%), while errors in (sigma _{yy}) decrease from over (22%) to below (1%). Third, the model captures through-thickness displacement asymmetry induced by unsymmetric stacking sequences and surface loading, effects that conventional HSDT and FSDT formulations cannot reproduce. A key limitation is also identified and quantified: Because the MZF depends solely on geometric layer distribution, accuracy deteriorates for highly heterogeneous sandwich plates, with transverse displacement errors reaching approximately (48%). This observation provides motivation for the development of constitutively consistent higher-order zigzag theories. Comprehensive numerical studies across diverse thickness ratios, anisotropy levels, and layer counts confirm the superior predictive capability of the proposed model.