Archive of Applied Mechanics最新文献

The study uses FEM to analyze the creep behavior of a rotating FGM disc made of Al-SiC_p. The disc thickness and SiC_p reinforcement in the disc are assumed to vary according to the exponential functions of the disc radius. The yielding and creep behavior of the disc material are described by Tresca’s criterion and threshold stress-based law, respectively. The disc is assumed to rotate at constant angular velocity under free-free boundary conditions. The disc domain is discretized radially using 3-noded one-dimensional elements with quadratic shape functions. Galerkin’s approach has been used to derive the expressions for stresses and strain rates in the disc. For numerical computation of the creep results, a MATLAB code has been developed corresponding to the FE formulation. The creep results estimated using the FE approach are noticed to be in excellent agreement with those obtained using the analytical technique (continuum mechanics approach), experiment results, and commercial FE software. The study reveals that with the increase in SiC_p gradient in the disc, the elastic as well as creep components of the tangential stress (near the inner radius) and the radial stress increase significantly, though the tangential stress exhibits a sizable decrease toward the outer radius. The increase in SiC_p gradient results in a significant reduction in the steady-state radial and tangential strain rates in the disc, besides resulting in a relatively more uniform distribution of the strain rates, which is desirable for reducing distortion in the disc. The study indicates that the rupture time of the FGM disc could be enhanced significantly by employing a steeper SiC_p gradient in the rotating disc.

Wire arc additive manufacturing enables the production of components with high deposition rates and the incorporation of multiple materials. However, the manufactured components possess a wavy surface, which is a major difficulty when it comes to simulating the mechanical behavior of wire arc additively manufactured components and evaluation of experimental full-field measurements. In this work, the wavy surface of a thick-walled tube is measured with a portable 3D scanning technique first. Then, the surface contour is considered numerically using the finite cell method. There, hierarchic shape functions based on integrated Legendre polynomials are combined with a fictitious domain approach to simplify the discretization process. This enables a hierarchic p-refinement process to study the convergence of the reaction quantities and the surface strains under tension–torsion load. Throughout all considerations, uncertainties arising from multiple sources are assessed. This includes the material parameter identification, the geometry measurement, and the experimental analysis. When comparing experiment and numerical simulation, the in-plane surface strains are computed based on displacement data using radial basis functions as ansatz for global surface interpolation. It turns out that the finite cell method is a suitable numerical technique to consider the wavy surface encountered for additively manufactured components. The numerical results of the mechanical response of thick-walled tubes subjected to tension–torsion load demonstrate good agreement with real experimental data, particularly when employing higher-order polynomials. This agreement persists even under the consideration of the inherent uncertainties stemming from multiple sources, which are determined by Gaussian error propagation.

This paper studies the dynamics of an atomic force microscopy (AFM) cantilever that is considered to be operating under continuous viscoelastic surface contact with material profiles based on the modified nonlocal theory of elasticity. The contact between the cantilever’s tip and the sample surface is modeled using a linear stiffness–damper pair and a lumped mass at the beam’s free end. The higher-order partial differential equation (PDE) governing the AFM nanocantilever transverse motion and its associated higher-order boundary conditions (BCs) are derived employing extended Hamilton’s principle based on the nonlinear nonlocal higher-order constitutive relation in Euler–Bernoulli beam model. The Galerkin’s decomposition method is applied to discretize the higher-order PDE and BCs of motion into a set of ordinary differential equations (ODEs) via the mode summation technique using eigenfunctions (mode shapes) of a classic cantilever thin beam. Then, using state-space form of ODEs of motion the frequency analysis is performed based on the eigenvalues of vibration motion. The obtained results are validated with the literature works. The impact of various parameters including nonlocal nanoscale elasticity parameter, added point mass, contact stiffness and viscous damping factors and the specific position where the concentrated mass and the contact stiffness–damper pair are attached to the beam on the resonant frequencies of AFM cantilever is comprehensively investigated. Numerical simulations showed that the resonance frequencies of the AFM cantilever increase by increasing the value of nonlocal nanoscale parameter. Also, it was concluded that an increase in the nonlocal parameter and surface contact stiffness leads the AFM cantilever to be more stiffened. Moreover, it was seen that by increasing the position distance of lumped mass on the beam and contact spring–damper pair from the beam’s fixed end, the resonant frequency reduction in the larger values of the surface contact stiffness is more noticeable.

The present work presents the investigation of the dynamics and influence of chaotic behavior on energy capture for a U-shaped structure (portal frame) that contains shape memory alloy (SMA), piezoelectric material (PZT), a nonlinear energy sink (NES) and a non-ideal excitation source represented by an unbalanced electric motor coupled to the U-structure. The mathematical model presents nonlinearities arising from the nonlinear stiffness of the U-structure, the NES system, the SMA, and the PZT material. Chaotic behavior is assessed through time history, bifurcation diagrams, phase diagrams, and the 0–1 test. Energy capture is carried out through a piezoelectric material (PZT), represented by a non-linear electromechanical coupling model, and electromagnetic induction generated by the non-linear electromagnetic energy sink coupled to the structure (NES). Dynamic analysis is performed through parametric analysis of parameters related to piezoelectric coupling and NES parameters. Numerical simulations demonstrate that the system has chaotic behavior for specific parameters and that its energy capture is influenced by parametric variation. It is shown numerically that the parameters of the SMA material, the PZT material, and the NES significantly influence the chaotic behavior and energy capture of the investigated electromechanical system.

This work studies crack propagation in particulate nanocomposites using the phase-field method. The crack propagation has been simulated in a wide range of loadings and the critical load for the crack growth has been obtained. Surface tension, as an inelastic stress, is introduced in the model in a thermodynamically consistent way. The effect of surface tension on the crack tip velocity and the crack evolution has been discussed. The finite element method via COMSOL multiphysics software has been utilized to solve the coupled phase-field and elasticity equations. Modeling and prediction of crack propagation for nanocomposites including different nanoparticles and under different loadings are the main purposes of this work. It is found that the kinetics and morphology of the crack propagation depend on the elastic moduli and the surface energy of nanoparticles as well as their longitudinal and angular distances to each other.

Scissor-like isolation platform (SIP) with magnetorheological damper (MRD) has been commonly studied and applied successfully in vehicle vibration isolation. This paper concerns passive nonlinear magnetorheological (MR) characteristics of the SIP via geometric nonlinearity induced by MRD’s layout ways. A dynamic parametric model of the SIP with six assembly types is derived based on Lagrange equation. Then, the parameter analysis is performed to estimate MR damping function in SIP. The analytical steady-state response of the isolator is derived using harmonic balance method, and its effectiveness is validated with numerical results. Metrics are defined to access the performance of the isolator, followed by comparison on displacement transmissibility for six types. The effect of MR damping coefficient and input amplitude on the performance of the isolator is investigated. Finally, comparative study with existing isolators is conducted. Results indicate that, passive MR damping is dependent on vibration displacement, which is beneficial to suppressing peak transmissibility with a little effect at non-resonant frequencies. The results also reveal that the isolator by type 1 or 3 has broader isolation band over other types. And the SIP in type 1 has wider isolation band and lower peak transmissibility compared with existing isolators in allowable workspace.

Solving problems in fluid mechanics plays an essential role in science and engineering, especially when it comes to optimal design, reconstruction of biomedical and geophysical flows, parameter estimation, and more. In some of these problems, only part of the data (or parameters) are known, and they fall within the broad categories of inverse and mixed problems. Thus, solving them using traditional methods is challenging or sometimes even impossible. Moreover, generating simulated data for such problems can become very costly since simulations need to be performed several times to either discover missing physics or calibrate the free parameters in the model. One possible alternative for overcoming these drawbacks is through the use of Physics-Informed Neural Networks—PINNs, in which we approximate the problem’s solution using neural networks (NNs) while incorporating the known data and physical laws when training it and also easily enabling us to take advantage of computational resources like GPUs. Here, we show a Level-Set PINN-based framework for reconstructing the velocity field for bubble flows. Given only the bubble position, we apply the framework to reconstruct gas bubbles rising in viscous liquid problems. We use synthetic data generated by adaptive mesh refinement and coarsening simulations with a different method, a phase-field approach. The only data provided is a set of snapshots containing the bubble position, i.e., the phase field, from which we try to infer the velocities. Our approach does not require any reinitialization scheme, as is usual when using a level-set approach and traditional numerical methods. Such a scheme can reconstruct the flow quantities with reasonable accuracy, and it is straightforward to parallelize when using a data-parallel approach.

A robust method for uncertainty quantification is undeniably leading to a greater certainty in simulation results and more sustainable designs. The inherent uncertainties of the world around us render everything stochastic, from material parameters, over geometries, up to forces. Consequently, the results of engineering simulations should reflect this randomness. Many methods have been developed for uncertainty quantification for linear elastic material behavior. However, real-life structure often exhibit inelastic material behavior such as visco-plasticity. Inelastic material behavior is described by additional internal variables with accompanying differential equations. This increases the complexity for the computation of stochastic quantities, e.g., expectation and standard deviation, drastically. The time-separated stochastic mechanics is a novel method for the uncertainty quantification of inelastic materials. It is based on a separation of all fields into a sum of products of time-dependent but deterministic and stochastic but time-independent terms. Only a low number of deterministic finite element simulations are then required to track the effect of (in)homogeneous material fluctuations on stress and internal variables. Despite the low computational effort the results are often indistinguishable from reference Monte Carlo simulations for a variety of boundary conditions and loading scenarios.

Thanks to compact structural integration and high locomotion performance, introducing vibration and asymmetric interaction with the ground is known as an important driving strategy in medium-sized (roughly cm ~ dm scale) mobile robots. For vibrations of different relative intensities, the vibro-bot may be in a continuous sliding state during movement (sliding locomotion), or may be in intermittent jumping and sliding states (hopping locomotion). Herein we conduct a mechanical analysis to reveal the locomotion mechanism of the vibro-bot. Specifically, the nonlinear governing equation of the vibro-bot is derived first. By approximately solving the governing equation, the trigger conditions of the sliding and locomotion modes are predicted, the detailed motion process is outlined, and the optimal design strategies to improve sports performance are clarified. This work not only promotes the design of mobile motion robots, but also has enlightening implications for understanding the locomotion behavior of animals with similar motion characteristics.

In this study, a numerical model for electro-mechanical coupling analysis of geometrically nonlinear functionally graded piezoelectric shell is developed based on the weak form quadrature element method. Both piezoelectric and flexoelectric effects are introduced to establish the geometrically exact shell model with its constituent BaTiO₃ and PZT-5H graded through the thickness. The electric potentials are assumed quadratic along the shell thickness to introduce the electric field for numerical implementation, while four different closed- or open-circuit conditions are considered. Four typical examples are presented to demonstrate the effectiveness of the present model and illustrate the influences of electro-mechanical couplings and functional graded materials on the responses of shells undergoing large displacements and rotations. This model is a feasible scheme for studying complex nonlinear behaviors of piezoelectric shells that might be helpful in devising piezoelectric shell-based nanoelectronics.