Archive of Applied Mechanics最新文献

A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier–Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by all level sets of a scalar function, bounded by the three-dimensional bulk domain. This bulk domain is discretized with hexahedral finite elements which do not necessarily conform with the level sets but with the boundary.The resulting numerical method is a hybrid between conforming and non-conforming finite element methods. Taylor–Hood elements or equal-order element pairs for velocity and pressure, together with stabilization techniques, are applied to fulfil the inf-sup conditions resulting from the mixed-type formulation of the governing equations. Numerical studies confirm good agreement with independently obtained solutions on selected, individual surfaces. Furthermore, higher-order convergence rates are obtained for sufficiently smooth solutions.

This study focuses on the vibrational analysis of functionally graded material saturated porous annular sector plate reinforced with multi-walled carbon nanotubes (MWCNTs) on a Winkler foundation. The analysis takes into account the coupled effect of CNT waviness and agglomeration, as well as the influence of pressure in the closed cell on the vibrational properties of the composite plate. In order to assess the mechanical properties of the nanocomposite, a modified Halpin–Tsai micromechanical model incorporating orientation, waviness, and agglomeration factors of MWCNT is utilized. Also, the Biot constitutive law is used instead of the simple Hooke’s law to obtain realistic and practical conclusions. The principle of minimum potential energy and the Rayleigh–Ritz method are employed to solve the governing equations. A comprehensive investigation is conducted considering multiple parameters that can influence the natural frequency of the annular sector plate. These parameters include the CNT weight fraction, CNT distribution pattern, CNT dimension, and porosity parameters such as the porosity coefficient, Skempton coefficient, and porosity distribution. The effect of CNT waviness and agglomeration, as well as the Winkler elastic foundation coefficient, is also taken into consideration. Additionally, the dimension of the sector plate is explored through variations in the inner-to-outer radius ratio, inner-to-thickness ratio, and sector angle.

304 stainless austenitic steel (AISI 304) is renowned for its high temperature resistance and has been the subject of considerable research. To explore its rheological behavior at high temperature, isothermal hot compression experiments were conducted on the Gleeble-3800 thermal simulator at temperatures of 800–1200 °C, strain rates of 0.011–11 ({s}^{-1}), and a total strain of 60%. From the experimental data, a Johnson–Cook (JC) constitutive model was formulated and further optimized. The optimized model considers the combined effect of strain, strain rate, and temperature, resulting in a more precise constitutive equation. The enhanced JC model had excellent predictive power, with a correlation coefficient (Rco) of 0.9884 and an average absolute relative error (AARE) of 8.42%. ABAQUS simulations for verification confirmed the model to be valid. This study offers valuable theoretical information for the hot working of SS 304, enabling more precise predictions of stress behavior at high temperature and easier optimization of processing parameters and overall material behavior. Also, deformation of metastable austenitic stainless steel at temperatures below the Md point leads to the transformation of austenite into martensite. This study investigates how prior deformation, conducted at temperatures both below and above Md, affects the dynamic tensile behavior of AISI 304 stainless steel. Pre-deformation at 25 °C (below Md), as well as at elevated temperatures of 200 °C and 300 °C (above Md), enhances both the yield strength and ultimate tensile strength of the material. Notably, prior deformation at 25 °C to a small equivalent strain (< 0.03) results in significant improvements in strength (22%) and ductility (21–37%) during subsequent high strain-rate tensile loading at 200 and 300 s⁻¹. The evolution of local strain fields and strain rates is analyzed using digital image correlation. Additionally, the development of localized necking is investigated through in-situ high-speed camera imaging.

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.