Time-domain Finite Element Research Articles

Site-specific seismic design of damage tolerant structural systems using a novel concept

Designing more seismic load-tolerant structures is one of the major challenges of the world communities. It is due to the inability of the profession to predict future design earthquake time histories at a site compounded by the failure to appropriately incorporate uncertainties in other design variables and structural behavior just before failure. A site-specific method is proposed to generate a suite of ground excitation time histories and a novel risk estimation is developed considering major sources of nonlinearity and uncertainty. For wider application and acceptance, the risk evaluation procedure essentially consists of few deterministic time domain finite element analyses. The procedure is verified and showcased by estimating risks associated with three buildings designed by professional experts in the Los Angeles area satisfying the post-Northridge design criteria for the overall lateral deflection and inter-story drift. The accuracy of the estimated risk is verified using the Monte Carlo simulation technique. In all cases, the probabilities of collapse are found to satisfy the current code requirements. The spread in the reliability indexes for each building for both limit states cannot be overlooked, indicating the significance of the frequency contents of the time histories. The inter-story drift is found to be more critical than the overall lateral displacement. The reliability indexes for both limit states are similar only for few cases. The authors believe that they proposed an alternative to the classical random vibration and simulation approaches. The proposed site-specific seismic safety assessment procedure can be used by practicing engineers for routine applications.

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.

Flexible and Accurate Simulation of Radiation Cooling with FETD Method

Thermal management and simulation are becoming increasingly important in many areas of engineering applications. There are three cooling routes for thermal management, namely thermal conduction, thermal convection and thermal radiation, among which the first two approaches have been widely studied and applied, while the radiation cooling has not yet attracted much attention in terrestrial environment because it usually contributes less to the total amount of thermal dissipation. Thus the simulation method for radiation cooling was also seldom noticed. The traditional way to simulate the radiation cooling is to solve the thermal conduction equation with an approximate radiation boundary condition, which neglects the wavelength and angular dependence of the emissivity of the object surface. In this paper, we combine the heat conduction equation with a rigorous radiation boundary condition discretized by the finite-element time-domain method to simulate the radiation cooling accurately and flexibly. Numerical results are given to demonstrate the accuracy, flexibilities and potential applications of the proposed method. The proposed numerical model can provide a powerful tool to gain deep physical insight and optimize the physical design of radiation cooling.

Anti-reflection coating design for metallic terahertz meta-materials.

We demonstrate a silicon-based, single-layer anti-reflection coating that suppresses the reflectivity of metals at near-infrared frequencies, enabling optical probing of nano-scale structures embedded in highly reflective surroundings. Our design does not affect the interaction of terahertz radiation with metallic structures that can be used to achieve terahertz near-field enhancement. We have verified the functionality of the design by calculating and measuring the reflectivity of both infrared and terahertz radiation from a silicon/gold double layer as a function of the silicon thickness. We have also fabricated the unit cell of a terahertz meta-material, a dipole antenna comprising two 20-nm thick extended gold plates separated by a 2 μm gap, where the terahertz field is locally enhanced. We used the time-domain finite element method to demonstrate that such near-field enhancement is preserved in the presence of the anti-reflection coating. Finally, we performed magneto-optical Kerr effect measurements on a single 3-nm thick, 1-μm wide magnetic wire placed in the gap of such a dipole antenna. The wire only occupies 2% of the area probed by the laser beam, but its magneto-optical response can be clearly detected. Our design paves the way for ultrafast time-resolved studies, using table-top femtosecond near-infrared lasers, of dynamics in nano-structures driven by strong terahertz radiation.

An Alternative Explicit and Unconditionally Stable Time-Domain Finite-Element Method for Electromagnetic Analysis

A new method for making an explicit time-domain finite-element method unconditionally stable is developed for general electromagnetic analysis, where the dielectrics and conductors can be inhomogeneous, lossless, or lossy. In this method, for a given time step, we find the unstable modes that are the root cause of instability, and deduct them directly from the system matrix resulting from a time-domain finite-element based analysis. The resultant explicit time-domain simulation is absolutely stable for the given time step no matter how large it is, and irrespective of the space step. The accuracy of the method is also guaranteed when the time step is chosen based on accuracy. In addition to a formulation for lossless problems, formulations for general lossy problems are also presented in detail. Numerical experiments have demonstrated the accuracy, efficiency, and unconditional stability of the proposed new explicit method.

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

The Role of the Photo-Generated Carrier in Surface Flashover of the GaAs Photoconductive Semiconductor Switch

The development of Gallium arsenide photoconductive semiconductor switch has been hampered by the surface flashover. The surface flashover threshold with the laser excitation is far lower than the one without the laser excitation. In this paper, the phenomena of surface flashover, including the infrared video, flashover spectrum, and the voltage waveforms are presented to research their work mechanism. The dynamic development process of surface flashover is divided into four typical states. Based on the 1-D time domain finite element method, the role of the photo-generated carrier in the surface flashover is analyzed. Our results suggest that the photo-activated charge domain (PACD) will enhance the local electric field and result in the surface flashover occurrence between the electrodes and semiconductors. So the atoms of GaAs semiconductors and electrodes are involved in the surface flashover. According to the PACD theory, the experimental phenomena can be explained reasonably.

Numerical time-domain modelling of hoof-ground interaction during the stance phase.

Hoof-ground interaction impacts on the health and performance characteristics of horses. Due to complex interactions between hoof and ground during the stance phase, previous experimentally dominated studies concentrated on subproblems of the phenomena observed. A multidisciplinary methodology with mathematical modelling, material testing and in vivo experimental measurements seems promising. With the help of a mathematical approach, this contribution aims to explain from a biomechanical point of view the phenomena observed during experimental investigations (hoof acceleration, interacting forces) and aims to contribute to an overall experimental-mathematical multidisciplinary approach. In silico modelling of hoof-ground interaction (limb, hoof and horizontally unbounded ground). Hoof-ground interaction is represented by a time-domain finite element model including the limb, the hoof and the unbounded representation of the ground via the scaled boundary finite element method to capture radiation damping during the stance phase. Motoric forces (driving forces) of the horse during locomotion are included. Numerical model results for acceleration-time relations (hoof) at different trotting velocities are compared with previously published acceleration-time relations and show qualitative agreement. From the model approach, power loss due to different ground properties and ground damping is computed in combination with the maximum limb force during the stance phase. Intentionally, a simplified model approach for the material and structural representation of the limb, the hoof and the ground in terms of material features and spatial resolution has been used for this study, which might be the basis for a model refinement in terms of contact properties as well as the integration of bone and joint structures. The comparison to experimentally obtained results demonstrates the applicability of the model, which, in turn, enables an insight into the processes taking place during hoof-ground interaction.

Interior Penalty Discontinuous Galerkin Time-Domain Method Based on Wave Equation for 3-D Electromagnetic Modeling

Built on the vector wave equation, an interior penalty discontinuous Galerkin time domain (IPDG-WE) method is presented for 3-D real-life electromagnetic modeling in this paper. We develop the interior penalty fluxes corresponding to different types of boundary conditions which are commonly used in electromagnetic modeling to construct the IPDG-WE system in local elements. In addition, to model the incident wave excitation, the total-field/scattered-field approach is incorporated into the proposed method. The stability of the IPDG-WE method is studied analytically and demonstrated numerically. We also compare the performance between wave equation-based finite-element time-domain method, the Maxwell’s equation-based discontinuous Galerkin time-domain method, and the proposed method, both in CPU time and memory usage, which demonstrates that the IPDG-WE method is very competitive among time-domain solvers. Besides, the presented method shows good characteristics including the energy conservation and the optimal convergence rate of $O( {h^{p+1}})$ . Numerical examples are presented to illustrate the validity, versatility, and potential of the proposed method in 3-D electromagnetic problems modeling.

Analytical and numerical investigation of site response due to vertical ground motion

Owing to the repeatedly observed strong vertical ground motions and compressional damage of engineering structures in recent earthquakes, the multi-directional site response analysis is increasingly critical for the seismic design of important structures, such as nuclear power plants and high earth dams. However, the site response to the vertical component of the ground motion has not been the subject of detailed investigation in the literature. Therefore, in this paper, the vertical site response due to vertical ground motion is investigated by employing both analytical and numerical methods. First, a one-dimensional frequency domain analytical solution, which can be employed for vertical site response analysis in practice, is studied and compared against time domain finite-element (FE) analyses for the two extreme soil state conditions (i.e. undrained and drained conditions). The vertical site response is further investigated with hydro-mechanically (HM) coupled FE analysis, considering solid–fluid interaction. The parametric studies undertaken show that the predicted vertical site response is strongly affected by the parameters characterising the hydraulic phase, namely, soil permeability and soil state conditions, both in terms of frequency content and amplification. The subsequent corresponding quantitative investigation, of the frequency content and amplification function of the vertical site response, shows that depending on the soil permeability the response is dominated by the two types of compressional waves (fast and slow waves). Notably, the parametric studies identify a range of permeability that significantly affects dynamic soil properties in terms of P-wave velocities, damping ratios and vertical site response, and this range is relevant for geotechnical earthquake engineering applications. It is therefore recommended that coupled consolidation analysis is necessary to simulate this effect accurately at such permeability-dependent intermediate transient states between fully undrained and drained conditions. Finally, this work suggests a simple modification of standard total-stress site response analysis to account for vertical ground motion and solid–pore fluid interaction. In order to simulate the attenuation of the response due to solid–pore fluid interaction effects, it is suggested to employ additional HM viscous damping in total-stress analysis, further to the one used to account for hysteretic material damping. This additional viscous damping can be quantified based on the empirical curves proposed in the paper.

3-D Domain Decomposition Based Hybrid Finite-Difference Time-Domain/Finite-Element Time-Domain Method With Nonconformal Meshes

A new 3-D domain decomposition based hybrid finite-difference time-domain (FDTD)/finite-element time-domain (FETD) method is introduced to facilitate electromagnetic modeling by exploiting both the computational efficiency of FDTD and the meshing flexibility of FETD. The proposed hybrid method allows the FETD mesh and the FDTD grid to be nonconformal based on domain decomposition technique. It implements the hybridization with a buffer zone, which functions as a transition region between FDTD and FETD. The buffer zone helps the proposed hybrid method obviate the interpolation approach for field coupling of the nonconformal mesh and hence overcome the late-time instability issue. The discontinuous Galerkin method is utilized to couple different regions, thus improving the coupling accuracy compared with that using the Dirichlet boundary condition. Moreover, the hybrid method allows further division of the FETD region into multiple subdomains when the degrees of freedom in this region are large. For temporal discretization, a global leapfrog time integration scheme is implemented to sequentially update the fields in the FDTD, buffer, and FETD regions. The numerical results are shown to demonstrate the meshing flexibility and computational efficiency of the proposed hybrid method inherited from FETD and FDTD methods.

Finite-element time-domain modeling of electromagnetic data in general dispersive medium using adaptive Padé series

The induced polarization (IP) method has been widely used in geophysical exploration to identify the chargeable targets such as mineral deposits. The inversion of the IP data requires modeling the IP response of 3D dispersive conductive structures. We have developed an edge-based finite-element time-domain (FETD) modeling method to simulate the electromagnetic (EM) fields in 3D dispersive medium. We solve the vector Helmholtz equation for total electric field using the edge-based finite-element method with an unstructured tetrahedral mesh. We adopt the backward propagation Euler method, which is unconditionally stable, with semi-adaptive time stepping for the time domain discretization. We use the direct solver based on a sparse LU decomposition to solve the system of equations. We consider the Cole-Cole model in order to take into account the frequency-dependent conductivity dispersion. The Cole-Cole conductivity model in frequency domain is expanded using a truncated Padé series with adaptive selection of the center frequency of the series for early and late time. This approach can significantly increase the accuracy of FETD modeling.

A Hybrid FETD-GSM Algorithm for Broadband Full-Wave Modeling of Resonant Waveguide Devices

An efficient hybrid algorithm that combines the finite-element time-domain (FETD) method with the generalized scattering matrix (GSM) technique is proposed to characterize the properties of wave propagation in highly resonant waveguide devices. To alleviate the problem of an extremely large number of time steps required for a highly resonant device, the algorithm first divides the device into several less resonant or resonant-free subdomains to reduce the number of time steps and the computational complexity of the FETD solver. The subdomain interfaces, which are assumed to be homogeneous, are modeled with an accurate waveguide port boundary condition (WPBC) to absorb any impinging waveguide modes. Each subdomain is then represented by a broadband GSM, which is computed by the fast Fourier transform of the FETD solutions. Finally, the subdomain GSMs are cascaded to form the global GSM of the original resonant device. The formulation and implementation of the FETD method with the WPBC, its required general waveguide modal analysis, and the cascading of GSMs are discussed in detail. Three numerical examples are presented to demonstrate the accuracy and efficiency of the proposed hybrid algorithm.

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.

A time-domain finite element boundary integral approach for elastic wave scattering

The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.

Design and modeling of highly tunable filters based on the linear electro-optic effect in strained silicon waveguides

Design and modeling of wavelength tunable filters based on the linear electro-optic (Pockels) effect in strained silicon waveguides is presented. The structure is based on the silicon grating-assisted contradirectional couplers. The basic idea is to utilize a silicon nitride (Si3N4) layer on top of the silicon waveguides to induce a relatively large Pockels effect in the waveguides by breaking the centrosymmetry of the Si crystal due to the surface strain. Wavelength tuning is obtained by applying DC voltages to the device contacts on top of the Si3N4 layer. Based on the presented structure, a wavelength tunable filter at the C-band communication window is designed and its characteristics were investigated by full-vectorial finite-element and finite-difference time-domain methods for electrostatic and optical responses. A 3.5-nm wavelength shift for an applied voltage of 1 V and a 7.5-nm shift for an applied voltage of 5 V are obtained with negligible loss. The presented device is superior to the previously reported structures in terms of tunability and loss.

U-DMA measurement and dynamic analysis of ultrasonic wave propagation in particulate composites

This work is dedicated to a high-precision ultrasonic testing technology for dynamic mechanical evaluation of particle reinforced composite materials. The detailed ultrasonic wave propagation due to multi-reflection and scattering waves by particles and matrix viscoelasticity, especially the mutual interactions among particles, are systematically clarified. Through a unique material evaluation method, Ultrasonic Dynamic Mechanical Analysis (U-DMA), the dynamic viscoelasticity of particulate composites with different types and contents of particles are measured directly in high frequency domain. Furthermore, based on the experiment data, the ultrasonic propagation behaviors are detailedly investigated by a newly developed time-domain finite element analysis code, Pzflex, for investigating the detailed mechanisms of particles. The results clarify that the particle interactions are playing a major role in ultrasonic wave propagation and attenuation properties, which can significantly affect the viscoelastic characteristics of developed particulate composite materials. And the feasibility and effectiveness of U-DMA are verified from both simulation and practical experiments.

Finite element time domain modeling of controlled-source electromagnetic data with a hybrid boundary condition

We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies.

Steel Catenary Riser-Seabed Interaction Due to Caspian Sea Environmental Conditions

This paper investigates the integrated riser/vessel system which is subjected to random waves. Riser pipelines are the main components of the oil and gas offshore platforms. Whereas Iran country has been located on the fringes of Caspian Sea deep water, therefore study and research in this area is increasingly essential. The fluctuation of floating production causes the intense response and greatest fatigue damage near the Touchdown Point (TDP) where the Steel Catenary Riser (SCR) first touches the seabed. Therefore, analysis the response of SCRs in the TDP is very important to approximate the behavior of the riser. In this study, initially, the structural parameters (wall thickness and diameter) according to design codes due to the intense climatic conditions are obtained. In the next step, Pipe-soil interaction is modelled using a linear model in the vertical direction and Coulomb friction models in the lateral direction. Also, the significance of SCR-seabed interaction in the global response of riser pipeline at TDP when subjected to random waves on soft clay is analyzed based on the Caspian Sea environmental conditions. A fully three-dimensional non-linear time domain finite element program with a robust meshing technique has been applied to simulate the haphazard large deflections of the flexible from the initial configuration by using the commercial software OrcaFlex.

Time-domain finite element analysis to nonlinear transient responses of generalized diffusion-thermoelasticity with variable thermal conductivity and diffusivity

Numerous experimental and theoretical studies indicate that thermal conductivity and diffusivity in materials cannot be viewed as constants in practical analysis. This provides us a motivation to capture the nonlinear transient responses of generalized diffusion-thermoelasticity problems with variable thermal conductivity and diffusivity. The nonlinear finite element governing equations are derived due to the consideration of variable thermal conductivity and diffusivity. By using time-domain finite element method, nonlinear solutions can be obtained. Numerical examples are given to investigate the transient responses of a slim strip and a half-space. Nonlinear transient responses are obtained and illustrated graphically. The results show that the variable thermal conductivity and diffusivity have significant effects on propagations of thermal wave and diffusive wave. Parametric analysis is also performed to predict their influences on nonlinear thermo-elasto-diffusive responses.