Time-domain Finite-element Simulation Research Articles

Direct integration of measured viscoelastic relaxation data in time-domain finite element simulations

The current approach to modeling viscoelastic materials in most commercial finite element packages is based on the General Maxwell Model, which views these materials as combinations of spring and dashpot elements. However, the data can be incorporated more directly into a transient finite element study by direct interpolation of the relaxation function. This work explores a linear interpolation scheme to the inclusion of viscoelastic relaxation functions on an example problem. The results show several benefits over the General Maxwell Model for transient studies. Included in the analysis are displacement solutions utilizing both approaches, relaxation function error calculations for both approaches, and parametric runtime studies comparing speed of calculation. The variation in computational flop counts is considered and an argument is made for the preference of the proposed approach.

Design and time-domain finite element simulation of multi-functional transformation optical device

In this paper, we first proposed mathematical model equations for wave propagation in a multi-functional transformation optical device, namely, an electromagnetic rotation concentrator. This device can concentrate electromagnetic energy while rotating electromagnetic waves. We also demonstrate the stability of the model equation in the continuous case. Next, we designed the multi-functional device with multiple layers. We then proposed a time-domain finite element method for simulating wave propagation in this device and conducted a stability analysis of the model equations in the discrete case. Finally, we implemented the proposed algorithm and obtained numerous numerical results that demonstrate the validity of our model equations. To the best of our knowledge, this is the first work on time-domain modeling and analysis of multi-functional electromagnetic devices.

Quantitative monitoring of icing on CFRP laminate with guided wave combining forward modeling and inverse characterization

Aircraft icing is one of the critical factors for flight safety. Timely and accurate monitoring of in-flight ice accretion is essential for flight systems to take immediate and effective action to significantly improve the efficiency of subsequent de-icing processes and ensure flight safety. Since carbon fiber reinforced polymer (CFRP) are now widely used in the aviation industry, the study of ice accretion on the surfaces of CFRP with anisotropic properties is of great importance. In this work, a three-dimensional frequency domain finite element model for icing CFRP laminate is first established, via which the mechanism of mode conversion of ultrasonic guided waves (UGWs) at different ice layer thicknesses is quantitatively analyzed. Then, the time-domain finite element simulation was performed, from which the time–frequency domain spectrogram of the acquired UGW signal is obtained by short-time Fourier transform (STFT). The extracted frequency–time-of-flight (ToF) curve of the signal via STFT shows high agreement with the theoretical results, which confirms the influence of icing on UGW propagation. Finally, numerous experiments with bonded lead zirconate titanate wafers to excite and acquire UGWs are conducted with different ice layer thicknesses and lengths on CFRP. The extracted frequency–ToF curves of UGW signals are used as input to a two-layer feedforward artificial neural network (ANN) to accurately evaluate the length and thickness of the ice layer. The high reliability of this method with ANN is confirmed, which shows the potential of the proposed UGW-based method for quantitative monitoring of icing length and thickness on aircraft CFRP laminate.

Fatigue Life Convergence of Offshore Wind Turbine Support Structure According to Wind Measurement Period

This paper investigated the fatigue life of offshore wind turbine (OWT) support structures. For this purpose, a 3 MW-capacity typical wind turbine is investigated using time-domain finite element simulations. In numerical simulations, different stochastic wind models corresponding to different accumulation periods are applied. Then, the stress-based fatigue life is estimated following the rain-flow counting algorithm and Palmgren-Miner linearly cumulative damage rule. The study also addresses the joint distribution of loads at the site of interest. Generally, the study emphasizes the significance of the long-term distribution of the applied environment loads and its influence on the fatigue life of OWT’s substructures. The results imply that the wind measurement period is directly linked to the fatigue life of offshore wind turbine support structures. Accordingly, its fatigue life is significantly reduced at the 25-year accumulative period of wind. Therefore, this study recommends that a sufficient number of accumulative periods of wind and other environmental loads should be considered appropriately.

Surface wave suppression in granular media using a partially embedded meta-barrier

Existing studies on meta-barrier designs for suppressing surface modes in inhomogeneous granular media are limited to meta-barriers comprising vertical or horizontal oscillators. However, a clear understanding of the surface mode hybridizations with the local resonances of the resonators is lacking and could help realize more realistic meta-barrier designs for surface wave control in granular media. In this work, we propose a meta-barrier comprising partially embedded rod-like resonators to study the hybridization of the fundamental surface modes: PSV1 and PSV2, with the longitudinal and flexural resonances of the resonators that enable surface mode suppression. The hybridized dispersion curves and frequency-domain finite element simulations with the meta-barrier demonstrate preferential hybridization of the PSV1 mode with the longitudinal resonance of the resonators, enabling PSV1 mode suppression above the hybridized longitudinal-resonance mode cut-off frequency. Unlike the PSV1 mode, PSV2 hybridizes with both longitudinal and flexural resonances, making it challenging to suppress the mode. However, we observe that enhancing the filling fraction of the meta-barrier promotes PSV2 mode suppression as the flexural-resonance hybridized modes are localized under the meta-barrier. The time-domain finite element simulation using a broadband excitation source further numerically validates the meta-barrier design for applications in vibration mitigation and seismic isolation of structures.

A snowman-like seismic metamaterial

A snowman-like seismic metamaterial is proposed in this study. The proposed model gives a lower and wider complete bandgap compared with the seismic metamaterials of the same volume in previous research. The vibration modes are investigated to clarify the mechanism of bandgap formation. Past studies used large amounts of steel to attenuate waves at low frequencies. On the contrary, to reduce the cost, this work only uses concrete. In addition, a set of geometric parameters is suggested through parametric studies. The shielding performance of the proposed seismic metamaterials against surface waves is also demonstrated using time domain finite element simulations. The results from the transient analysis are in good agreement with the dispersion curves, validating the accuracy of the numerical simulations.

Strongly nonlinear wave dynamics of continuum phononic materials with periodic rough contacts.

We investigate strongly nonlinear wave dynamics of continuum phononic material with discrete nonlinearity. The studied phononic material is a layered medium such that the elastic layers are connected through contact interfaces with rough surfaces. These contacts exhibit nonlinearity by virtue of nonlinear mechanical deformation of roughness under compressive loads and strong nonlinearity stemming from their inability to support tensile loads. We study the evolution of propagating Gaussian tone bursts using time-domain finite element simulations. The elastodynamic effects of nonlinearly coupled layers enable strongly nonlinear energy transfer in the frequency domain by activating acoustic resonances of the layers. Further, the interplay of strong nonlinearity and dispersion in our phononic material forms stegotons, which are solitarylike localized traveling waves. These stegotons satisfy properties of solitary waves, yet exhibit local variations in their spatial profiles and amplitudes due to the presence of layers. We also elucidate the role of rough contact nonlinearity on the interrelationship between the stegoton parameters as well as on the generation of secondary stegotons from the collision of counterpropagating stegotons. The phononic material exhibits strong acoustic attenuation at frequencies close to (and fractional multiples of) layer resonances, whereas it causes energy propagation as stegotons for other frequencies. This study sheds light on the wave phenomena achievable in continuum periodic media with local nonlinearity, and opens opportunities for advanced wave control through discrete and local contact nonlinearity.

Wave propagation in a continuum nonlinear phononic material with soft nonlinear elastic layers

This presentation discusses modeling the propagation of nonlinear waves in a continuum phononic material. This system is shown to exhibit amplitude-dependent response and energy transfer between frequencies, which are well studied phenomena of nonlinear discrete systems, but are relatively unexplored in fully elastic continuum models. The phononic material is composed of repeated layers of stiff and soft materials, and the nonlinearity is introduced through a nonlinear hyperelastic Gent model in the soft material. We analyze the dispersion of the linearized system using Bloch-wave analysis to identify band gaps in the system, and we use full-scale time-domainfinite element simulations to analyze the dynamic behavior of the system. Generation of zero frequency and second harmonic frequency amplitudes as well as their accumulation with distance are observed, and the influence of phononic band gaps on nonlinear wave propagation are described. We explore the influence of material nonlinearity in soft materials in continuum phononic materials as a mechanism for control of nonlinear wave propagation.

Purified nonlinear guided waves through a metamaterial filter for inspection of material microstructural changes

Nonlinear guided waves (NGWs) exhibit extraordinary sensitivity to microstructural changes in materials which are often considered as damage precursors in many structural health monitoring (SHM) applications. However, these changes are usually very small at the microstructural level, thus generating weak nonlinear wave components which are prone to or even overwhelmed by other deceptive and non-damage-related nonlinear sources present in a monitoring system. This may jeopardize the practical implementation of the NGW-based SHM methodology. To tackle this problem, this paper proposes a metamaterial filter (meta-filter (MF)), in the form of a patch to be surface-mounted over the structure under inspection. The MF is designed to purify the probing waves during propagation before reaching the inspection area through tactical elimination of non-damage-related nonlinear components from the actuation. Considering different bonding conditions and the lattice symmetry of the MF, two types of bandgaps, corresponding to Bragg scattering and local resonances, alongside their respective band properties are analyzed. Time-domain finite element simulations are carried out to assess the efficacy of the MF in terms of wave purification in the context of SHM, supported by experimental validations. The designed MF is deployed in an aluminum strip to detect the material microstructural changes induced by a thermal ageing treatment. Results demonstrate the designed MF significantly enhances the detection ability of NGW-based SHM system. Both locally resonant and Bragg bandgaps can, in principle, be used for wave purification. While the former requires precise control of the bonding quality of the MF, the latter relies on symmetrical installation of the MF to ensure a reasonably wide wave filtering range. Considering variability factors in the implementation of the MF and better immunity to the nonlinearity of the bonding layers, preference is given to Bragg bandgap for NGW-based SHM applications.

Wave self-interactions in continuum phononic materials with periodic contact nonlinearity

The existence of nonlinearity within materials manifests richer wave propagation compared to their linear counterpart in the form of amplitude-dependent material response and energy transfer between frequencies. While these properties have been extensively studied in the case of continuous and discrete nonlinear phononic materials (PMs), individually, the behavior of continuum PMs with discrete nonlinearities, which could open new opportunities for wave propagation control via discrete–continuum coupling, is relatively unexplored. In this article, we investigate nonlinear wave propagation through one-dimensional continuum PMs with periodic contacts. Specifically, the periodicity is in the form of pre-compressed rough contacts resulting in nonlinearly coupled linear finite thickness elastic layers. We analyze the system using full-scale time-domain finite element simulations by treating the contacts as spring-equivalent nonlinear thin elastic layers. The model considers a power-law pressure-gap relationship at the rough contacts. The evolution of propagating nonlinear waves within the weakly nonlinear regime is illustrated, emphasizing the generation of zero (DC), self-demodulated low, and second harmonic frequencies for excitation in different zones of the dispersion relation. The continuum between discrete contact nonlinearities exhibits local DC reduction and second harmonic increment, not observed in discrete PMs such as granular phononic crystals. The intertwined effects of nonlinearity, periodicity, and finiteness on nonlinear wave propagation are also explored, which results in maximum DC amplitude at the finite boundaries of the PMs and mode-based second harmonic characteristics. Finally, we demonstrate the flexibility of the proposed nonlinear PMs by characterizing the dependence of nonlinear wave propagation on different arrangements of embedded contacts. The concept of discretely embedding nonlinear interfaces, such as rough contacts, within an elastic continuum, opens opportunities to control the global nonlinear response of the PMs through local microstructural nonlinearities.

Numerical modeling for terahertz testing of non-metallic pipes

In the oil and gas industry, safety and operational efficiency at production sites are of paramount importance. A reliable non-destructive testing technology for non-metallic pipes has a high potential financial impact, since it may facilitate the replacement of metallic pipes with non-metallic ones. This article features a perspective and future trends in the field of terahertz sensing technology. Importantly, several numerical simulations that illustrate many exciting potential applications for this emerging technology are described. These range from underground detection of spilt liquids and the content of pipes to the detection of cracks in plastic pipes using both frequency-domain and time-domain finite-element simulations.

Wave interaction with nonlinear damage and generation of harmonics in composite structures

This work presents a generic Finite Element (FE) based computational scheme for quantifying guided wave interaction with Localised Nonlinear Structural Damage (LNSD) within structures of arbitrary layering and geometric complexity. The through-thickness mode-shape of the structure is obtained through a wave and finite element method. This is applied in a time domain FE simulation in order to generate time harmonic excitation for a specific wave mode. Interaction of the wave with LNSD within the system is computed through an element activation and deactivation iteration. The scheme is validated against experimental measurements and a WFE-FE methodology for calculating wave interaction with damage. Case studies for guided wave interaction with crack and delamination are presented to exhibit the robustness of the proposed method in classifying and identifying damage.

Design and Performance Analysis of Single-Phase Pre-Saturated Core Fault Current Limiters

The technology of a presaturated core fault current limiter (PCFCL) has particular importance due to its instantaneous limitation of the fault current in electric power grids and keeping its value below the ratings of the switchgear or circuit breakers with a reasonable safety margin. In this paper, a design methodology of single-phase, simple nonsuperconducting magnetic coils, PCFCL is proposed based on extensive electromagnetic time-domain finite-element simulations taking into account the relative performances of the constructive design parameters. These controlled finite-element simulations allow fine realistic details, such as the nonlinear magnetic saturation behavior of the iron core to be included, and studying the effect on general performance during dynamic reactions of the system. Moreover, the dynamic behavior of PCFCL is characterized in terms of steady-state voltage drop across its terminals, counter electromotive force induced on the dc coil terminals, and limitation factor of the fault current. Dual-core and single-core designs are investigated with a comparison of their ability of limiting the fault current. Results reveal that the dual-core design has superior performance than that of the single-core one. Finally, a design methodology flowchart has been proposed which depends on the extensive simulation results of different PCFCL topologies and published experimental results, where changing either the governing constructive parameters or the magnetic iron core design are considered.

Fatigue life sensitivity of monopile-supported offshore wind turbines to damping

Offshore wind energy is an important renewable electricity source in the UK and Europe. Monopiles are currently the most commonly used substructures to support offshore wind turbines. The fatigue life of offshore wind turbines is directly linked to the oscillatory bending stresses caused by wind and wave loading. The dynamic response of the structure is highly dependent on the combined aerodynamic, hydrodynamic, structural, and soil damping present. The fatigue life sensitivity of a reference 5 MW wind turbine under operational and non-operational conditions has been investigated using time-domain finite element simulations. The model uses beam elements for the monopile and tower and includes nonlinear p-y curves for soil-structure interaction. The effects of the wind turbine operation, environmental loads, and variable damping levels on the fatigue life were investigated systematically. The fatigue life increases significantly as a result of reductions in the bending stress caused by increased damping. From a practical point of view, significant cost-savings could be achieved in the design of a wind turbine by fitting supplemental damping devices. An efficient approximate method is proposed to assess the influence of damping, by scaling the vibration amplitudes around the first natural frequency of the system.

A multiband approach for accurate numerical simulation of frequency dependent ultrasonic wave propagation in the time domain.

Finite element (FE) simulations are popular for studying propagation and scattering of ultrasonic waves in nondestructive evaluation. For a large number of degrees of freedom, time domain FE simulations are much more efficient than the equivalent frequency domain solution. However, unlike frequency domain simulations, time domain simulations are often poor at representing the speed and the attenuation of waves if the material is strongly damping or highly dispersive. Here, the authors demonstrate efficient and accurate representation of propagated and scattered waves, achieved by combining a set of time domain solutions that are obtained for a set of frequency ranges known as bands, such that, in combination, the authors' multiband solution accurately represents the whole wave spectrum. Consequently, high accuracy is achieved, at minor computational cost, using a modest number of bands. The multiband technique is implemented for ultrasonic wave propagation in highly attenuating polyethylene material, using three frequency bands, and can yield a reduction in empirical acoustic properties fractional error compared with respective time domain simulations, in propagation duration, of a factor of 1.4, and in full-width-half-maximum, of a factor of 10. Last, the accuracy of this approach is further exemplified in a wave scattering simulation.

Influence of lips on the production of vowels based on finite element simulations and experiments

Three-dimensional (3-D) numerical approaches for voice production are currently being investigated and developed. Radiation losses produced when sound waves emanate from the mouth aperture are one of the key aspects to be modeled. When doing so, the lips are usually removed from the vocal tract geometry in order to impose a radiation impedance on a closed cross-section, which speeds up the numerical simulations compared to free-field radiation solutions. However, lips may play a significant role. In this work, the lips' effects on vowel sounds are investigated by using 3-D vocal tract geometries generated from magnetic resonance imaging. To this aim, two configurations for the vocal tract exit are considered: with lips and without lips. The acoustic behavior of each is analyzed and compared by means of time-domain finite element simulations that allow free-field wave propagation and experiments performed using 3-D-printed mechanical replicas. The results show that the lips should be included in order to correctly model vocal tract acoustics not only at high frequencies, as commonly accepted, but also in the low frequency range below 4 kHz, where plane wave propagation occurs.

Comparison of numerical and effective-medium modeling of porosity in layered media.

In this study, modeling approaches for porosity in layered media are presented and compared. First, an effective-medium model is used to account for the frequency-dependent attenuation of the elastic waves. The effective-medium model is based on a single-scattering approach, i.e., it neglects multiple-scattering effects. Then, the effective-medium model is compared in time-domain finite element simulations. The numerical model allows the study of the scattering of the elastic waves on randomly distributed spherical cavities and also accounts for multiple-scattering effects. The models are compared to investigate the validity of the effective-medium model approach. The calculated reflected laminate responses and transmission spectra from the two models show a good agreement.

Accelerated finite element elastodynamic simulations using the GPU

An approach is developed to perform explicit time domain finite element simulations of elastodynamic problems on the graphical processing unit, using Nvidia s CUDA. Of critical importance for this ...

Accelerated finite element elastodynamic simulations using the GPU

An approach is developed to perform explicit time domain finite element simulations of elastodynamic problems on the graphical processing unit, using Nvidiaʼs CUDA. Of critical importance for this problem is the arrangement of nodes in memory, allowing data to be loaded efficiently and minimising communication between the independently executed blocks of threads. The initial stage of memory arrangement is partitioning the mesh; both a well established ‘greedy’ partitioner and a new, more efficient ‘aligned’ partitioner are investigated. A method is then developed to efficiently arrange the memory within each partition. The software is applied to three models from the fields of non-destructive testing, vibrations and geophysics, demonstrating a memory bandwidth of very close to the cardʼs maximum, reflecting the bandwidth-limited nature of the algorithm. Comparison with Abaqus, a widely used commercial CPU equivalent, validated the accuracy of the results and demonstrated a speed improvement of around two orders of magnitude. A software package, Pogo, incorporating these developments, is released open source, downloadable from http://www.pogo-fea.com/ to benefit the community.

Effects of head geometry simplifications on acoustic radiation of vowel sounds based on time-domain finite-element simulations

One of the key effects to model in voice production is that of acoustic radiation of sound waves emanating from the mouth. The use of three-dimensional numerical simulations allows to naturally account for it, as well as to consider all geometrical head details, by extending the computational domain out of the vocal tract. Despite this advantage, many approximations to the head geometry are often performed for simplicity and impedance load models are still used as well to reduce the computational cost. In this work, the impact of some of these simplifications on radiation effects is examined for vowel production in the frequency range 0-10 kHz, by means of comparison with radiation from a realistic head. As a result, recommendations are given on their validity depending on whether high frequency energy (above 5 kHz) should be taken into account or not.