Time-domain Finite Element Research Articles

Effects of breathing cracks on the dynamic characteristics of a drilling riser under irregular waves and the crack identification

To investigate the effects of breathing cracks on the dynamic characteristics, i.e., natural frequencies, vibration displacement, slope angle, and bending moment, of a drilling riser, a time-domain finite element method based on the fracture mechanics theory is developed. The correctness of the proposed method is verified, and the performance of the different dynamic characteristics for crack identification is evaluated. First, the influence of the breathing and open cracks on natural frequencies is explored. The maximum frequency shifts vs crack location and water depth are studied. The results of the small difference of natural frequencies between intact and cracked risers illustrate that the traditional frequency-based crack-detection method is not applicable for the risers. Second, the time-domain motions, orbit plots, Poincaré maps, and fast Fourier transform diagrams are extracted for discussing the effects of the breathing and open cracks and crack depth and location. Finally, the second and fourth derivatives of the root-of-mean-square (RMS) of the dynamic response characteristics are defined for crack identification. It is found that the moment RMS has a good performance in single- and multiple-crack identifications and that not only locations but also degrees of the breathing cracks can be well detected by the proposed indices. In short, several conclusions drawn are a benefit for the safety of a serviced drilling riser system.

A Three-Dimensional Discontinuous Galerkin Time-Domain Finite Element Method for Electromagnetic Modeling of Wireless Power Transfer Coils

Inductive coupling based wireless power transfer (WPT) is a popular short-range power delivery mechanism for many industrial, biomedical, and home electronic appliances applications. A numerical methodology is needed for the analysis of the electromagnetic propagation, radiation, scattering and coupling of highly efficient WPT systems. This study is based on the discontinuous Galerkin time-domain (DGTD) finite element method. A brief survey of the DGTD method is given, which is a finite element method using discontinuous piecewise polynomials as basis functions and numerical fluxes based on up-winding for stability. DGTD method is characterized by the fact that no continuity is enforced between the elements, then it is easy to parallelize and results in fast solvers. Even though the finite element method is used by a few researchers to study WPT problems, we found no study using the DGTD method to study WPT problems, which is surprising given that this discretization technique seems particularly well suited for these problems. A design of two coils at the frequency of 3 MHz is introduced, and the effects of the distance and misalignment between two coils on the mutual coupling are studied. The numerical results are validated by experimental and analytical results.

Propagation of Johnson-Cook flow stress model uncertainty to milling force uncertainty using finite element analysis and time domain simulation

This paper describes the propagation of uncertainty in the parameters for a 6061-T6 aluminum Johnson-Cook flow stress model to, first, the uncertainty in the corresponding mechanistic cutting force model obtained by orthogonal cutting finite element simulation and, second, the milling force predicted by time domain simulation using the force model. The approach includes five key elements: 1) a literature review to identify the means and standard deviations for the 6061-T6 aluminum Johnson-Cook model parameters; 2) structured light scanning to measure an endmill’s cutting edge macro-geometry along the tool axis; 3) structured light scanning to identify the cutting edge cross-sectional rake and relief profiles for the same endmill; 4) orthogonal cutting finite element analysis to determine the mechanistic force model coefficients that relate the force components to chip area and width using the tool’s rake and relief profiles and random samples from the Johnson-Cook parameter distributions; and 5) time domain simulation with inputs that include the measured cutting edge macro-geometry, uncertain finite element-based force model, and measured structural dynamics. Distributions for milling force predictions are determined by Monte Carlo simulation and compared to in-process measurements for an indexable endmill-collet holder to demonstrate the approach. It is observed that 95% confidence intervals on the predicted forces bound the measured time-dependent force profile peaks in over half of the cases tested. It is also seen that the Johnson-Cook flow stress model-based force predictions performed as well as predictions based on a calibrated mechanistic force model.

Rayleigh-Bloch mode based monolayer bend waveguide

A monolayer bend waveguide is designed based on the features of Rayleigh-Bloch (RB) mode wave in one-dimensional diffraction grating. The feasibility that the RB mode wave can transmit along the bend waveguide is demonstrated by the time-domain and frequency-domain finite element method, respectively. The results show that two different modes of transmission wave exist because of employing the circled unit cells. They possess different acoustical energy localization positions. In mode-1, the energy is localized between unit cells. In mode-2, the energy is localized in the center of unit cell, therefore, acoustic wave transmits with nearly no loss. Modulated sinusoidal wave and Gaussian pulse wave are used in the time-domain investigation. Because only RB mode waves can transmit and different modes have different energy distributions, the bend waveguide acts as an acoustic filter for the broadband waves. This study is conducive to the acoustic wave directional transmission, acoustic signal detection and identification.

Nonlinear time-domain dynamic analysis of three-dimensional deepwater steep wave riser subjected to top motions with internal flow effects

ABSTRACT The nonlinear dynamic behaviour of steep wave riser (SWR) subjected to the top harmonic motions considering the effect of the internal flow is numerically investigated using a three-dimensional (3D) time-domain finite element method (FEM) based on the slender flexible rod theory. In this numerical model, the riser which satisfies geometric nonlinearity is divided into three segments: decline segment, buoyancy segment and hang-off segment and the effect of the internal flow is also incorporated into motion equation using plug flow. A Newmark-β integral method is applied to update the dynamic responses at each time step. The published results for the static/dynamic performance of the steel flexible riser are used to validate the present numerical method. Numerical simulations are conducted to investigate the dependence of the tension, displacement and bending moment on the design parameters. The top motion amplitude/period, buoyancy length and internal flow density/velocity/top pressure are discussed respectively.

Shear-Actuation and Vibrometer Reception of Penetrating Ultrasonic Guided Wave Modes in Human Tibia

The hollow long bones of the human appendicular skeleton are known to support the propagation of ultrasonic guided waves, whose potential for diagnosing bone health is being investigated. In this study, ultrasonic guided waves propagating in the diaphysis of human tibia are characterized experimentally and numerically in the frequency range around 200 kHz. The experiment involves a unique combination of omni-directional shear transducer-based excitation and detection using a 1D laser Doppler vibrometer. The cluster of phase velocities obtained from a linear array of time-history data using space-time Fourier transform is found to be in the non-dispersive low-phase velocity region of the dispersion curves obtained for a tibial cross-section. Time-domain finite element analysis revealed that the displacement components normal to the surface are significant, even though the loading is from a shear transducer. Furthermore, semi-analytical finite element analysis revealed that the wave structures of the wave modes contained within the cluster of low-phase velocity modes are consistent with the displacement profiles obtained from the time-domain analysis. The experimental results show that the low-phase velocity mode cluster has sufficient intensity to propagate axially at least 85 mm in the mid-diaphyseal region.

A Combination of Mixed FETD Method and SPICE to Simulate Nonlinear Multiport Circuits

A combination of the mixed finite-element time-domain method (MFETD) and SPICE solver is proposed in this letter to analyze the circuit response and crosstalk effects in complex microwave circuits with linear/nonlinear, passive/active components. The MFETD method in the EM part is adopted as an unconditionally stable time integration scheme to account for the low-frequency breakdown problem. SPICE is introduced to solve the nonlinear circuit equations in the circuit part by taking into account the coupling between multiport circuits. A microwave circuit based on an AD633 chip and an MCP3221 board is simulated to verify that this hybrid MFETD-SPICE method not only is superior in mesh flexibility to the finite-difference time-domain (FDTD)-based method but also exploits the well-developed open-source software SPICE to solve the nonlinear equations.

Response of a plate in turbulent channel flow: Analysis of fluid–solid coupling

The paper performs simulation of a rectangular plate excited by turbulent channel flow at friction Reynolds numbers of 180 and 400. The fluid–structure interaction is assumed to be one-way coupled, i.e, the fluid affects the solid and not vice versa. We solve the incompressible Navier–Stokes equations using finite volume direct numerical simulation in the fluid domain. In the solid domain, we solve the dynamic linear elasticity equations using a time-domain finite element method. The obtained plate averaged displacement spectra collapse in the low frequency region in outer scaling. However, the high frequency spectral levels do not collapse in inner units. This spectral behavior is reasoned using theoretical arguments. The resonant vibration is stronger at the third natural frequency than at the first natural frequency. We explain this behavior by comparing the fluid and solid length scales. We further study the sources of plate excitation using a novel formulation. This formulation expresses the average displacement spectrum of the plate as an integrated contribution from the fluid sources within the channel. Analysis of the sources reveals that at the plate natural frequencies, the contribution of the fluid sources to the plate excitation peaks in the buffer layer. The corresponding wall-normal width is found to be ≈0.75δ. The integrated contribution of the overlap and outer regions together to the plate response is comparable to that from the buffer region for Reτ=180 and exceeds the buffer region contribution for Reτ=400. We analyze the decorrelated features of the sources using spectral Proper Orthogonal Decomposition (POD) of the net displacement source. We enforce the orthogonality of the modes in an inner product with a symmetric positive definite kernel. The dominant spectral POD mode contributes to the entire plate excitation. The contribution of the remaining modes from the different wall-normal regions undergo destructive interference resulting in zero net contribution. The envelope of the dominant mode further shows that the intensity of the sources peaks in the buffer region and the wall-normal width of the sources extend well into the outer region of the channel.

Time-domain finite element formulation of porous sound absorbers based on an equivalent fluid model

Time-domain finite element formulation of porous sound absorbers based on an equivalent fluid model

Implementation of a frequency-dependent impedance boundary model into a room acoustic solver with time-domain finite element method

Implementation of a frequency-dependent impedance boundary model into a room acoustic solver with time-domain finite element method

Numerical analysis of a finite element method for the electromagnetic concentrator model

In this paper, we consider the electromagnetic concentrator model obtained through transformation optics. This model is formed by a system of coupled time-dependent Maxwell’s equations with three unknowns, which makes the analysis and simulation much more challenging compared to the standard Maxwell equations. In our previous work (W. Yang, J. Li, Y. Huang, and B. He, Commun. Comput. Phys., 25(1), pp. 135–154, 2019), we proposed a finite element time-domain (FETD) method with edge elements for solving this model efficiently without any theoretical analysis. Here, we provide a rigorous analysis for the mathematical modelling equations and the FETD method proposed there.

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.

Research and application of finite-element time-domain method for transient response of buried cable excited by an electromagnetic wave

To analyze electromagnetic (EM) transient responses of a buried cable, an accurate and reliable time-domain method is proposed in this paper. The approach is based on the transmission line (TL) second-order telegrapher’s current equation, and the expressions of ground impedance and admittance at higher frequencies are used to obtain the discrete finite-element time-domain (FETD) equations for the cable. Finally, transient responses at termination loads of the buried cable are obtained based on the global FETD equation, which is assembled using discrete FETD equations on all intervals. The accuracy and effectiveness of the proposed FETD method are demonstrated by comparing numerical results to those of the finite-difference time-domain (FDTD) method. The proposed method is also employed to investigate the effects of numerous parameters on transient currents of the buried cable, including the soil conductivity, buried cable depth, and incident and polarization angles of the external EM wave.

Time-domain finite element method and analysis for modeling of surface plasmon polaritons

In this paper, we formulate a time-dependent model for simulating surface plasmon polaritons (SPPs) in graphene. The stability for the governing equations of the model is established. Then we propose a time-domain finite element method for solving the system of the governing equations. The discrete stability similar to the continuous level is proved. Numerical results are presented to demonstrate the effectiveness of our model for simulating SPPs along graphene slabs. To the best of our knowledge, this is the first time-domain finite element analysis and simulation obtained for SPPs in graphene.

Hybrid method for transient responses of transmission line in an apertured enclosure based on FETD method and transmission line equations

A hybrid method combining the finite-element time-domain (FETD) method and transmission line (TL) equations (FETD-TL) is presented for evaluating the transient responses of a lossy TL in an apertured rectangular enclosure excited by electromagnetic pulses. First, the electric fields in the enclosure without the TL are calculated based on the Bethe's small holes theory and the mirror procedure. Then, the enclosure's electric fields are introduced into the second-order TL equation for current as the equivalent distributed sources. The transient currents induced on the TL are obtained by solving the second-order TL equation for current based on the FETD method with a single iteration variable. Finally, the transient voltages induced on the TL are computed by discretising the first-order TL equation. Compared with the method based on finite-difference time-domain (FDTD) method and TL (FDTD-TL) via several examples, the proposed hybrid method is proved to be correct and effective, which possesses much higher convenience and efficiency than FDTD-TL method in dealing with TL model terminated by complex lumped parametric networks.

Performance change of a semi-submersible production platform system with broken mooring line or riser

Under high sea states, positioning mooring lines or production risers could be led to failure. Such an accident will change the watching circle of the platform or even cause production to shut down. The present paper is aimed at investigating the transient/unsteady response of a semi-submersible platform, tension variation of the remaining lines, and evaluate the risk of risers clashing after mooring lines or risers failure. The fully coupled time-domain analysis is set up for the whole system which including a semi-submersible platform, 12 mooring lines, and 22 production risers. One or several mooring lines and risers are intentionally disconnected from the fairleads at a certain time. Combined environmental loads are selected from irregular waves and the steady current varying from very rough to phenomenal sea conditions. Hydrodynamic response of the semi-submersible with regarding first-order and second-order wave forces is calculated with the combination of three-dimension radiation/diffraction theories and Morison's equation. Nonlinear time-domain finite element methods are employed to analyze the behavior of mooring lines and risers. Results indicated that the platform has a large horizontal offset with the lost positioning forces. This will lead to the successive failure of the neighboring objects. The tension of the rest lines is also increased accordingly. Remaining lines that are closer to the failed lines will have larger tension increase to compensate. A practical methodology for investigating the risk of risers collision is also provided in this paper.

New Mixed SETD and FETD Methods to Overcome the Low-Frequency Breakdown Problems by Tree-Cotree Splitting

Traditional time-domain finite-element and spectral-element methods are known to suffer from the so-called low-frequency breakdown problem, where the system matrix can become ill-conditioned, and results can be unstable for electrically fine structures. In this article, a new mixed spectral-element time-domain (SETD) and finite-element time-domain (FETD) methods are proposed to overcome this low-frequency breakdown problem by constraint equations and tree-cotree splitting. Two forms of gradient matrices or the null space of the stiffness matrix of high-order basis functions are calculated to construct the constraint equations. Then, the constraint equations are directly applied in the time-stepping matrix equation by tree-cotree splitting to improve the properties of system matrices when the implicit Newmark-beta algorithm is adopted in two different forms. In the calculation of the first form of gradient matrix, the electric field is expanded by high-order edge basis functions; in the second form of gradient matrix, high-order edge basis functions associated with cotree edges and nodal basis functions defined on the free nodes are both employed to expand the electric field. Several numerical examples demonstrate that the new mixed SETD and mixed FETD methods can effectively overcome the low-frequency breakdown with high accuracy and without increasing the number of degrees of freedom over the conventional SETD and FETD methods.

Locally implicit time-domain finite element method for sound field analysis including permeable membrane sound absorbers

Locally implicit time-domain finite element method for sound field analysis including permeable membrane sound absorbers

Wideband Low-Frequency Design of Inductors and Wireless Power Transfer Coils Using the Mixed Finite-Element Time-Domain Method

Wideband low-frequency designs of inductors and wireless power transfer (WPT) coils are challenging because of the low-frequency breakdown in traditional numerical methods. In this letter, we apply a recently developed mixed finite-element time-domain (mixed FETD) method to overcome such low-frequency breakdown difficulties in designing inductors and WPT coils and verify the feasibility of the mixed FETD method for such models at low frequencies. This letter provides a demonstration for the design of the low-frequency electrically small electromagnetic devices.

Time Domain Room Acoustic Solver with Fourth-Order Explicit FEM Using Modified Time Integration

This paper presents a proposal of a time domain room acoustic solver using novel fourth-order accurate explicit time domain finite element method (TD-FEM), with demonstration of its applicability for practical room acoustic problems. Although time domain wave acoustic methods have been extremely attractive in recent years as room acoustic design tools, a computationally efficient solver is demanded to reduce their overly large computational costs for practical applications. Earlier, the authors proposed an efficient room acoustic solver using explicit TD-FEM having fourth-order accuracy in both space and time using low-order discretization techniques. Nevertheless, this conventional method only achieves fourth-order accuracy in time when using only square or cubic elements. That achievement markedly impairs the benefits of FEM with geometrical flexibility. As described herein, that difficulty is solved by construction of a specially designed time-integration method for time discretization. The proposed method can use irregularly shaped elements while maintaining fourth-order accuracy in time without additional computational complexity compared to the conventional method. The dispersion and dissipation characteristics of the proposed method are examined respectively both theoretically and numerically. Moreover, the practicality of the method for solving room acoustic problems at kilohertz frequencies is presented via two numerical examples of acoustic simulations in a rectangular sound field including complex sound diffusers and in a complexly shaped concert hall.