Three-dimensional fluid-structure interaction simulation of the Wheatley aortic valve

Valvular heart diseases (such as stenosis and regurgitation) are recognized as a rapidly growing cause of global deaths and major contributors to disability. The most effective treatment for these pathologies is the replacement of the natural valve with a prosthetic one. Our work considers an innovative design for prosthetic aortic valves that combines the reliability and durability of artificial valves with the flexibility of tissue valves. It consists of a rigid support and three polymer leaflets which can be cut from an extruded flat sheet, and is referred to hereafter as the Wheatley aortic valve (WAV). As a first step towards the understanding of the mechanical behavior of the WAV, we report here on the implementation of a numerical model built with the ICFD multi-physics solver of the LS-DYNA software. The model is calibrated and validated using data from a basic pulsatile-flow experiment in a water-filled straight tube. Sensitivity to model parameters (contact parameters, mesh size, etc.) and to design parameters (height, material constants) is studied. The numerical data allow us to describe the leaflet motion and the liquid flow in great detail, and to investigate the possible failure modes in cases of unfavorable operational conditions (in particular, if the leaflet height is inadequate). In future work the numerical model developed here will be used to assess the thrombogenic properties of the valve under physiological conditions.

Dynamic Design of a Quad-Stable Piezoelectric Energy Harvester via Bifurcation Theory

The parameter tuning of a multi-stable energy harvester is crucial to enhancing harvesting efficiency. In this paper, the bifurcation theory is applied to quantitatively reveal the effects of structural parameters on the statics and dynamics of a quad-stable energy harvester (QEH). Firstly, a novel QEH system utilizing the geometric nonlinearity of springs is proposed. Static bifurcation analysis is carried out to design quad-stable working conditions. To investigate the cross-well and high-energy vibration, the complex dynamic frequency (CDF) method, suitable for both weakly and strongly nonlinear dynamic problems, is then applied to deduce the primary response solution. By using the unfolding analysis in singularity theory, four steady-state properties and dozens of primary resonance modes are demonstrated. Based on the transition set, the effective bandwidth for energy harvesting can be customized to adapt well to various vibration environments by parametric adjustment. Finally, the experimental tests verify that the output power can reach up to 1 mW. The proposed QEH and its mechanics optimization can guide energy supply for next-generation wireless systems and low-power sensors under magnetic forbidding environments.

A New Mathematical Model of Functionally Graded Porous Euler-Bernoulli Nanoscaled Beams Taking into Account Some Types of Nonlinearities

A new mathematical model of flexible physically (FN), geometrically (GN), and simultaneously physically and geometrically (PGN) nonlinear porous functionally graded (PFG) Euler-Bernoulli beams was developed using a modified couple stress theory. The ceramic phase of the functionally material was considered as an elastic material. The metal phase was considered as a physically non-linear material dependent on coordinates, time, and stress-strain state, which gave the opportunity to apply the deformation theory of plasticity. The governing equations of the beam as well as boundary and initial conditions were derived using Hamilton's principle and the finite difference method (FDM) with a second-order approximation. The Cauchy problem was solved by several methods such as Runge-Kutta from 4-th to 8-th order accuracy and the Newmark method. Static problems, with the help of the establishment method, were solved. At each time step, nested iterative procedures of Birger method of variable elasticity parameters and Newton's method were built. The Mises criterion was adopted as a criterion for plasticity. Three types of porosity-dependent material properties are incorporated into the mathematical modeling. For metal beams, taking into account the geometric and physical nonlinearity, the phenomenon of changing the boundary conditions, i.e., constructive nonlinearity (CN) was found.

Indirect reduced-order modelling: using nonlinear manifolds to conserve kinetic energy

Nonlinear dynamic analysis of complex engineering structures modelled using commercial finite element (FE) software is computationally expensive. Indirect reduced-order modelling strategies alleviate this cost by constructing low-dimensional models using a static solution dataset from the FE model. The applicability of such methods is typically limited to structures in which (a) the main source of nonlinearity is the quasi-static coupling between transverse and in-plane modes (i.e. membrane stretching); and (b) the amount of in-plane displacement is limited. We show that the second requirement arises from the fact that, in existing methods, in-plane kinetic energy is assumed to be negligible. For structures such as thin plates and slender beams with fixed/pinned boundary conditions, this is often reasonable, but in structures with free boundary conditions (e.g. cantilever beams), this assumption is violated. Here, we exploit the concept of nonlinear manifolds to show how the in-plane kinetic energy can be accounted for in the reduced dynamics, without requiring any additional information from the FE model. This new insight enables indirect reduction methods to be applied to a far wider range of structures while maintaining accuracy to higher deflection amplitudes. The accuracy of the proposed method is validated using an FE model of a cantilever beam.

Numerical Analysis of Bowing Phenomenon Due to Thermal Stresses in Marble Slabs

Bowing is a pathology known by the deformation experienced in some external covering systems in ornamental stones, especially in marble, and thermal action is one of the key factors that lead to this degradation. Previous studies presented remarkable contributions about the mechanical behavior of bowing but they were based on classical beam’s theory and improper assumptions might mislead the evaluation of internal stresses. This study proposes to evaluate internal stresses in bowing due to thermal loading considering the true deformed shape in continuum media. Finite displacement concepts are proposed to calculate stress-strain relationship and comparison with linear elastic theory is also addressed. Internal stresses not predictable in the Euler-Bernoulli beam were found in parametric analyses. Moreover, the numerical analysis accomplished in this paper indicates that transient heat flux should induce higher stresses than just considering higher gradients of temperature in steady flux which could explain the larger decohesion through width in bowing tests.

Geometric Nonlinear Model for Prediction of Frequency-Temperature Behavior of SAW Devices for Nanosensor Applications

Surface acoustic wave (SAW)-based sensors have become highly valued for their use as nanosensors in industrial applications. Accurate prediction of the thermal stability is a key problem for sensor design. In this work, a numerical tool based on the finite element method combined with piezoelectric Lagrangian equations has been developed to accurately predict the thermal sensitivity characteristics of surface acoustic wave devices. Theoretical analysis for the geometric nonlinearity contributing to the frequency-temperature characteristic and material constants' dependency on temperature were taken into consideration. The thermomechanical equilibrium equation built on the three-dimensional finite element method (3D-FEM) mesh node took mesh movement into account because thermal expansion was employed. The frequency-temperature characteristics of different SAW modes, including Rayleigh waves and leaky waves excited on a piezoelectric substrate of quartz or lithium tantalate, respectively, were calculated. The theoretical accuracy of the proposed numerical tool was verified by experiments.

Using Video Processing for the Full-Field Identification of Backbone Curves in Case of Large Vibrations

Nonlinear modal analysis is a demanding yet imperative task to rigorously address real-life situations where the dynamics involved clearly exceed the limits of linear approximation. The specific case of geometric nonlinearities, where the effects induced by the second and higher-order terms in the strain–displacement relationship cannot be neglected, is of great significance for structural engineering in most of its fields of application—aerospace, civil construction, mechanical systems, and so on. However, this nonlinear behaviour is strongly affected by even small changes in stiffness or mass, e.g., by applying physically-attached sensors to the structure of interest. Indeed, the sensors placement introduces a certain amount of geometric hardening and mass variation, which becomes relevant for very flexible structures. The effects of mass loading, while highly recognised to be much larger in the nonlinear domain than in its linear counterpart, have seldom been explored experimentally. In this context, the aim of this paper is to perform a noncontact, full-field nonlinear investigation of the very light and very flexible XB-1 air wing prototype aluminum spar, applying the well-known resonance decay method. Video processing in general, and a high-speed, optical target tracking technique in particular, are proposed for this purpose; the methodology can be easily extended to any slender beam-like or plate-like element. Obtained results have been used to describe the first nonlinear normal mode of the spar in both unloaded and sensors-loaded conditions by means of their respective backbone curves. Noticeable changes were encountered between the two conditions when the structure undergoes large-amplitude flexural vibrations.

Analytical Solutions for Stochastic Vibration of Orthotropic Membrane under Random Impact Load

Orthotropic membrane materials have been applied in the numerous fields, such as civil engineering, space and aeronautics, and mechanical engineering, among others. During their serving lifespan, these membranes are always facing strong stochastic vibrations induced by the random impact load such as hail, heavy rain, and noise, among others. In this paper, the stochastic vibration problem of orthotropic membrane subjected to random impact load is investigated. The statistical characteristics of random impact load are initially obtained based on the stochastic pulse theory. Then, the Von Karman theory is applied to model the nonlinear vibration of membrane with geometric nonlinearity, which is then used to derive and solve the corresponding fokker–plank–kolmogorov (FPK). The theoretical model developed is validated by means of experiment study and monte carlo simulation (MCS) analysis. The effects of variables like pretension force, velocity of impact load, and material features on stochastic dynamic behavior of membranes are discussed in detail. This exposition provides theoretical framework for stochastic vibration control and design of membranes subjected to random dynamic load.

Quantifying Chaos by Various Computational Methods. Part 2: Vibrations of the Bernoulli-Euler Beam Subjected to Periodic and Colored Noise

In this part of the paper, the theory of nonlinear dynamics of flexible Euler-Bernoulli beams (the kinematic model of the first-order approximation) under transverse harmonic load and colored noise has been proposed. It has been shown that the introduced concept of phase transition allows for further generalization of the problem. The concept has been extended to a so-called noise-induced transition, which is a novel transition type exhibited by nonequilibrium systems embedded in a stochastic fluctuated medium, the properties of which depend on time and are influenced by external noise. Colored noise excitation of a structural system treated as a system with an infinite number of degrees of freedom has been studied.

Modeling bistable behaviors in morphing structures through finite element simulations

Bistable structures, exemplified by the Venus flytrap and slap bracelets, can transit between different configurations upon certain external stimulation. Here we study, through three-dimensional finite element simulations, the bistable behaviors in elastic plates in the absence of terminate loads, but with pre-strains in one (or both) of the two composite layers. Both the scenarios with and without a given geometric mis-orientation angle are investigated, the results of which are consistent with recent theoretical and experimental studies. This work can open ample venues for programmable designs of plant/shell structures with large deformations, with applications in designing bio-inspired robotics for biomedical research and morphing/deployable structures in aerospace engineering.