Archive of Applied Mechanics最新文献

Recent advances in the study of thin beams within the framework of nonlocal elasticity demonstrate a close relationship between micro-structured beam systems and Eringen’s differential-type nonlocal beams. In this paper, we establish relationships between a micro-structured beam system and a two-phase nonlocal beam through the equivalence of natural frequencies under two typical boundary conditions: clamped-free and doubly clamped. The analytical characteristic equations of two-phase nonlocal beams are derived and compared to approximately analytical equations to prevent numerical overflow in cases with small volume fractions of material and nonlocal parameters. This work proposes calibrated procedures that may facilitate the equivalence of material mechanics commonly used in engineering applications.

The Taylor analogy model has proven effective in predicting droplet dispersion in spray systems and deformation in planar extensional flow. The aim of this study is to leverage the insights from the Taylor analogy model in flat flow to construct a model for predicting droplet deformation in shear flow, specifically under low Reynolds number conditions ((Rell 1)) with Newtonian fluids. Additionally, a simplified theoretical model is designed to predict droplet orientation angles, providing deeper understanding of the complex dynamics of droplets under shear flow conditions. Utilizing three-dimensional numerical analysis, the influence of viscosity ratios within the range below 1 is explored, offering a comprehensive insight into the intricate interactions between fluid properties and droplet behavior. Model validation is conducted through comparison with experimental data from existing literature, ensuring its robustness and reliability. The results demonstrate the model’s capability to accurately predict droplet deformation and orientation angles in shear flow, thereby contributing to ongoing efforts to improve droplet dynamics predictions. This advancement paves the way for more precise control and optimization in diverse fluidic applications.

Hexagon-based architected polymer composites are designed for simultaneous stiffness–damping properties. In particular, this study focuses on the stiffness–damping performance of filled hierarchical hexagon, irregular hexagon, layered hexagon. In addition, we propose spiderweb-inspired and interlocking hexagon-based designs to tailor the performance. In the process, we also consider the combination of the structure and filler materials to optimize the performance from the material perspective. These architectures are analyzed with the constituent materials being stiff polymethylmethacyrylate (PMMA) for stiffness and soft polyurethane (PU) for damping. Simulations are performed with RUCs of the architectures along with periodic boundary conditions to capture the properties. Quasi-static stiffness and complex modulus are determined from quasi-static tensile and cyclic loads at different frequencies. The figure of merit for performance is represented by (|E^*| times tan delta ). The performance is compared with that of the constituent PMMA and PU materials. The study shows that simultaneous performance can be tailored using hexagon-based simple yet elegant architectures. Among the architectures investigated, interlocking hexagon demonstrates superior figure of merit, achieving (|E^*| times tan delta =0.1) GPa. While the predictions are for idealized geometries ignoring the manufacturing defects, the results highlight the potential of these architected composites and tailorability for applications demanding high-performance mechanical and damping properties.

This work presents a new type of non-conventional finite elements (FE) that utilize trigonometric-based shape functions. The selection of the shape functions is inspired by the analytical expression of structural modeshapes. The proposed element consists of two “regular” nodes and a middle “hidden” node that basically enriches the local approximation and leads to the partition-of-unity property. Two different element types are constructed: a rod element with axial degrees of freedom and a Timoshenko beam element with two degrees of freedom: vertical displacement and rotation. Both the proposed elements are tested against conventional 3-node FE in free vibration and transient dynamic simulations of isotropic rod and beam structures. Numerical results show that the proposed trigonometric FE yield more accurate estimations of natural frequencies than the traditional 3-node FE. Also, the maximum natural frequency of each case is not only more accurate but also has smaller numerical value. This leads to the selection of larger time steps when employing explicit time integration, resulting in lower computing times. Finally, the presented elements evince higher convergence rates than the conventional 3-node FE in wave propagation simulations of rods and beams, further increasing the proposed method’s efficiency. This is explicitly quantified, since the proposed FE appears to be twice as fast as the conventional 3-node FE, in obtaining a transient wave response with the same level of accuracy.

This study presents a meshfree Jacobi-radial point interpolation (Jacobi-RPI) method for the dynamic analysis of functionally graded elliptical shell with varying thickness (FGESVT) in supersonic flow and thermal environment. The material properties of FGESVT are assumed to vary along the direction perpendicular to the bottom surface. The thermal stress due to the variation of environmental temperature is considered by introducing the nonlinear part of the Green–Lagrange strain. A meshfree shape function is constructed by combining the radial basis with Jacobi polynomials with fast convergence, numerical stability and high accuracy, and the displacement components of the FGESVT are expanded by using the meshfree Jacobi-RPI shape function. The equations of motion of the closed FGESVT are obtained by coupling the equations of several open shells. The accuracy and reliability of the proposed method are validated through a sufficient number of numerical studies for the free vibration and dynamic response analysis of open and closed FGESVT. Finally, the effect of thermal load, thickness variation and boundary condition on the free vibration and dynamic response of the FGESVT are discussed.

This study presents a comprehensive free and forced vibration analysis of functionally graded porous beams resting on variable elastic foundations. The governing equations are formulated and solved to investigate the dynamic behavior of the beams under different boundary conditions utilizing higher-order beam theory and the meshless collocation method. Various porosity distributions and foundation types, including Winkler and Pasternak models with linear, parabolic, sinusoidal, cosine, and exponential stiffness variations, are considered. The effect of porosity patterns and foundation stiffness on the natural frequencies and forced response is analyzed in detail. The results indicate that porosity distribution significantly influences the vibrational characteristics, with specific configurations enhancing stiffness and stability. The effectiveness of the proposed meshless method is validated through comparisons with available benchmark results, demonstrating its accuracy and computational efficiency. The findings contribute to the optimal design and analysis of functionally graded porous beams in engineering applications where dynamic performance is critical.

Assessing the validity of tensile strength determination in the Brazilian test is a classical problem in fracture mechanics. According to reports, the Brazilian splitting strength is generally lower than the direct tensile strength in most cases, while in a minority of cases it is higher. Based on the analytical solution of the stress field in an uncracked disc under parabolic loading and Griffith's fracture criterion, this paper proposes a novel modified formula for calculating tensile strength σ_t that accounts for the influence of the load contact angle. Additionally, according to the principles of error analysis, an error transfer function is derived to evaluate the effect of measurement error on contact angle. Finally, the modified formula presented in this paper is applied to calculate the tensile strength of sandstone under both flat-platen and curved-jaw loading conditions. The results are then compared with those obtained using a classical formula. The theoretical analysis shows that the classical formula underestimates the tensile strength of materials at small contact angles, whereas it overestimates the tensile strength at large contact angles. Additionally, measurement errors in the contact angle have a certain influence on the determination of σ_t. For the case of contact semi-angle γ ≥ 10° with measurement error Δγ ≤ 1°, the tensile strength determination error remains below 5%. The experimental results show that the classical formula yields lower tensile strength values for sandstone under flat-platen loading compared to curved-jaw loading, whereas the proposed modified formula demonstrates excellent consistency between both loading configurations. The modified formula accounts for the dual-aspect influence of contact angle on tensile strength determination: (i) qualitative—governing the fracture initiation position of the disc, and (ii) quantitative—modulating the magnitude distribution of internal stress components.

Ti6Al4V alloy is widely used in aerospace, marine, and chemical industries due to its excellent specific strength and good biocompatibility. Understanding the damage and fracture mechanism of Ti6Al4V is crucial for the practical applications. In this work, the deformation and failure behaviors of Ti6Al4V were studied by digital image correlation method. Post-fracture surface analysis was performed to investigate the influence of stress triaxiality on failure behavior. A machine learning-based identification strategy was proposed to determine the strain hardening and Johnson–Cook damage model parameters. The datasets were obtained by finite element simulations for training the artificial neural network (ANN) models, which were utilized to establish the relation between the mechanical response and model parameters. The effect of ANN structure hyperparameters on prediction performance was discussed and whale optimization algorithm (WOA) could improve the prediction accuracy of neural network model. The results indicated that the WOA algorithm optimized three-layer BP neural network with 16 hidden neurons and activation functions of tansig + tansig can be used to effectively identify the plastic and damage model parameters of Ti6Al4V alloy.

This study models and analyzes the thermomechanical vibration behavior of biocompatible sandwich plates under compressive forces, thermal fields, and magnetic fields, employing high-order plate theory. The sandwich plate is composed of a solid and foam structured ZK60 magnesium alloy reinforced with graphene in the core layer, with surface layers consisting of functionally graded ZK60 ceramic material in the inner sections and zirconia ceramic material in the outer sections. The results indicate that the metal foam structure in the core layer and the distribution of metal ceramic materials in the surface layers significantly influence the thermomechanical vibration behavior of the sandwich plate. The application of an external magnetic field was found to enhance the thermal buckling resistance of the sandwich plate. The study results indicate that the wave propagation characteristics of the sandwich plate can be significantly influenced by different foam structures in the core and top layers, as well as by variations in material distribution qualities. The study’s findings are expected to substantially enhance the existing body of research and are applicable to emerging applications in fields such as sonar radars, aircraft, and marine vehicle stealth technologies.

The dual-phase-lag (DPL) model and Lord–Shulman (LS) theories, incorporating a single relaxation time, are utilized to analyze the impact of hydrostatic initial stress on a medium. A novel model will be introduced, utilizing two-temperature factors, to improve the photothermal theory. This study analyzes the effects of changing thermal and electrical conductivity. We examined the phenomenon of thermal loading on the exposed surface of an indefinitely extending semiconducting material in one dimension. This medium was also affected by plasma waves and the mechanical force generated during a photothermal process. The exact values of the variables in question are obtained using the Laplace transform (LT) approach. Furthermore, the two values of temperature coefficients were obtained by analytical methods. The field quantities are exhibited as numerical results in the physical domain and visually represented to illustrate the influence of distinct characteristics, such as electrical conductivity. The findings are compared with and without two-temperature components, as well as for two distinct values of the hydrostatic starting stress. A comparison is made between the computed variables obtained from generalized thermoelasticity using the DPL model and the LS theory. This comparison is performed in the absence and presence of the electrical conductivity parameter.