Domain Finite Element Method Research Articles

Computational prediction of impact sound insulation of a timber floor excited by an ISO standard tapping machine

During the last decades, researchers have actively developed procedures to predict impact sound insulation of timber slabs and floors using the finite element method (FEM). Since the simulations have mainly been performed in the low frequencies, a full understanding of their suitability for research and development (R&D) purposes has not yet been created. The object of the study reported in this paper was to determine the applicability of a modern FEM simulation procedure for predicting the normalised impact sound pressure level Ln of a full timber floor, when information provided by material manufacturers is used as input data. Force excitation caused by the ISO standard tapping machine was determined utilizing explicit time integration and FEM. The modelling of sound radiation itself was performed in a frequency domain FEM analysis. The models of a timber floor in its construction stages were constructed before the laboratory measurements of impact sound insulation so that the set-up corresponded to a simulated R&D task. Based on the prediction results, the applied procedure was considered suitable for R&D purposes and needs for further studies were identified.

On the experimental determination and prediction of damage evolution in composites via cyclic testing

This study introduces a novel approach to obtaining and predicting damage evolution laws using quasi-static cyclic testing within the framework of continuum damage mechanics. To achieve this, a comprehensive set of characterization and parameter identification tests was performed. Carbon-epoxy specimens were manufactured using the filament-winding technique, and these laminates were tested using a universal testing machine. Digital image correlation was employed in all experiments to capture strain fields, and an alternative method utilizing the combined loading compression device is presented to obtain mechanical properties. Once the material was characterized, cyclic tests were conducted, including [Formula: see text], [Formula: see text], and [Formula: see text] tensile tests, and shear v-notch tests. These aim to determine damage evolution laws for both conditions, pure and coupled stress states. From these tests, values for damage onset and threshold were obtained and used to define four new parameters. These parameters permit the estimation of degradation relationships for any arbitrary orientation without requiring additional tests. This approach was tested as the proof-of-concept within the positive range of transverse tension and in-plane shear stress domain. The obtained results are promising, justifying its extension to other failure mechanisms. While acknowledging its limitations, this new approach holds potential for implementation in the analysis of progressive failure in fiber-reinforced composite materials, possibly in conjunction with established failure criteria and computational tools, mainly in the finite element method domain.

A unified-field monolithic fictitious domain-finite element method for fluid-structure-contact interactions and applications to deterministic lateral displacement problems

Based upon two overlapped, body-unfitted meshes, a type of unified-field monolithic fictitious domain-finite element method (UFMFD-FEM) is developed in this paper for moving interface problems of dynamic fluid-structure interactions (FSI), which is accompanied with high-contrast physical coefficients across the interface and with contacting collisions between the structure and fluidic channel wall in the immersed FSI case. In particular, the proposed novel numerical method consists of a monolithic, stabilized mixed finite element method within the frame of fictitious domain/immersed boundary method (FD/IBM) for generic fluid-structure-contact interaction (FSCI) problems in the Eulerian–updated Lagrangian description, while involving the no-slip type of interface conditions on the fluid-structure interface, and the repulsive contact force/stress on the structural surface when the immersed structure contacts the fluidic channel wall. The developed UFMFD-FEM for FSI/FSCI problems can deal with the structural motion with large rotational and translational displacements and/or large deformation in an accurate and efficient fashion, which is first validated by two benchmark FSI problems and one FSCI model problem, then by experimental results of a realistic FSCI scenario – the microfluidic deterministic lateral displacement (DLD) problem that is applied to isolate circulating tumor cells (CTCs) from blood cells in the blood fluid through a cascaded filter DLD microchip in practice, where a particulate fluid with the pillar obstacles effect in the fluidic channel, i.e., the effects of fluid-structure interaction and structure collision, play significant roles to sort particles (cells) of different sizes with tilted pillar arrays. The developed unified-field, monolithic fictitious domain-based mixed finite element method can be seamlessly extended to more sophisticated, high dimensional FSCI problems with contacting collisions between the moving elastic structure and fluidic channel wall.

Numerical study on the distance between the propeller with pre-swirl duct and rudder considering fatigue characteristics

Recently, there has been increasing awareness about greenhouse gases, resulting in considerable efforts to increase the fuel efficiency of ships and reduce the amount of gases they emit. Thus, pre-swirl ducts (PSDs) have been widely adopted in ships due to their high fuel efficiency. However, attaching PSDs induces a change in the fatigue characteristics of ship structures, as evidenced by the reported crack in the rudder of a ship with an attached PSD. Nevertheless, the arrangement of a ship’s rudder, which is a crucial factor in a rudder’s fatigue characteristics, continues to rely on the empirical rule without any consideration of fatigue characteristics. This study investigated a propeller–rudder interaction distance ensuring fatigue stability with the PSD attachment and developed a procedure for designing it considering fatigue characteristics. In the developed procedure, the fatigue characteristics of rudders due to the propeller wake were obtained through frequency domain finite element method (FEM) analysis utilizing computational fluid dynamics (CFD) analysis results of a rudder’s surface pressure fluctuations. In addition, the potential for fatigue failures in ship rudders was evaluated by employing damage factors. A comparative analysis of rudder fatigue characteristics considering the presence of PSDs revealed that attaching them increased the stresses in the rudder. Furthermore, the analysis results demonstrated that PSD attachment can result in the fatigue failure of rudders. Finally, the propeller–rudder interaction distance of ships with an attached PSD was newly proposed using the developed procedure. The proposed propeller–rudder interaction distance is expected to enable the design of appropriate rudder arrangements for ships with attached PSDs while ensuring fatigue stability.

An Efficient Goal-Oriented Adaptive Finite Element Method for Accurate Simulation of Complex Electromagnetic Radiation Problems

A goal-oriented adaptive frequency domain finite element method for solving electromagnetic radiation problems including complex structures is presented in this paper. Compared with the traditional adaptive finite element method, the goal-oriented method can flexibly control the refined regions according to the parameters of interest; therefore it has better convergence and has made significant progress in scattering problems and eigenvalue problems. To simulate complex antennas, this paper proposes an error indicator with high accuracy and low computational cost, and it uses the adjoint problem to weight element residuals without additional degrees of freedom. Moreover, high-quality mesh refinement algorithms adapted to this indicator are developed using a suitable point insertion strategy for multiscale structures. By simulating two practical antennas, comparisons with the traditional goal-oriented FEM and the well-developed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> -adaptive finite element method in commercial software demonstrate the accuracy and efficiency of the proposed method.

Using Computer Technique for Developing Method for Vibration Damage Estimation Under Combined Random and Deterministic Loading

Abstract This paper is focusses on developing a novel method for vibration damage estimation for military helicopters, fighter aircrafts and any other aircraft exposed to combined stochastic and deterministic loading. The first stage of the research focused on frequency domain damage prediction, which is the legacy method proposed by Bishop and developed by Sweitzer, Schlesinger, Woodward, Kerr, Murthy, Datta and, Atkins. The mentioned frequency domain-based method is used in commercial software, e.g., MSC CAE Fatigue. Frequency domain damage prediction is based on superposition of spectral moments and Dirlik method of Rainflow Cycle Counting algorithm in frequency domain. The first phase of the research showed the legacy algorithm based on transfer function developed using FEM (Finite Element Method) method in Abaqus environment and is very conservative. The second stage of the research aims to develop a novel method which allowing for more robust and accurate damage estimation. For this purpose, the Monte Carlo method for retrieving random signal in the time domain from signal in frequency domain was used. To obtain the system transfer function, – the 1 g load harmonic system response was obtained using FEM analysis. It was subsequently scaled linearly by the PSD input curve for random loading and sine wave, or sine sweep function for deterministic loading to calculate the cumulative system response of the linear system. The research allows the development of a novel method to precisely estimate vibration damage using combined time and frequency domains approach, based on effective frequency domain FEM analysis of the linear system. The new proposed method can be also used for precise replication of test conditions via considering signal clipping and frequency resolution used for real testing.

A basic study on presentation of improvement effect of sound environments by use of computational simulation

The purpose of this study is to propose a method of presenting information so that architectural designers who do not specialize in architectural acoustics can easily understand the problems of the sound environment. This paper focuses on presenting the effects of the sound absorbing material using the time domain finite element method (TDFEM) as a computational simulation method. First, the sound fields of different room shapes and sound absorption boundaries are analyzed using TDFEM, and the changes between the sound fields are confirmed by room acoustic parameters at each sound receiving point. Next, visualization and auralization of those sound fields are attempted. The visualization allowed for a detailed capture of changes in sound pressure distribution due to differences in room boundary conditions. As for auralization, subjective differences in sound fields with different boundary conditions were confirmed using the paired comparison method.

Modelling of bidirectional functionally graded plates with geometric nonlinearity: A comparative dynamic study using whole domain and finite element method

Present work attempts to study the nonlinear dynamic behaviour of bidirectional functionally graded plates (BFG) along with unidirectional functionally graded plates (UFG). For BFG plates the material is graded along the thickness and length simultaneously and two types of UFG plates are considered namely thickness-wise (TFG) and length-wise (AFG) plates. The dynamic problem is formulated using two different methods namely, whole domain method and finite element method. The constitutive relation for the former is generated using classical plate theory whereas Mindlin plate theory is used in the later. Geometric nonlinearity is addressed here by using Von Karman type strain-displacement relation. Both clamped and simply supported boundary conditions are considered and the plate is assumed to be under action of uniformly distributed external load. The results of free and forced vibration analyses are presented as backbone curves and frequency response curves respectively. The results show that all three plates exhibit hardening type nonlinearity. It is also seen that the effect of material gradation parameters is more profound in simply supported plates compared to clamped plates. Specifically, these parameters do not seem to have much effect on BFG clamped plates in free vibration. The outcome of the analysis is compared with those in existing literature and fair agreement is observed between them.

An atomistic-continuum concurrent statistical coupling technique for amorphous materials using anchor points

A generalized framework for anchor point based concurrent coupling of finite element method (FEM) and molecular dynamics (MD) domains, incorporating previous related methods, is presented. The framework is robust and is agnostic of material crystallinity and atomistic description. The method follows an iterative approach to minimize the total energy of the coupled FEM-MD system, while maintaining displacement constraints between the domains. Two distinct forms of the coupling method are discussed in detail, differing in the nature of the constraint, both of which are able to make use of specialized MD solvers such as LAMMPS with little or no modification. Both methods make use of springs that join groups of atoms in the MD to the FEM domain. Method 1, termed ‘Direct Coupling’, couples MD anchor points directly to the FEM domain in a force-based manner and has the added advantage of being able to couple to specialized FEM solvers such as ABAQUS. Method 2 couples the MD to the FEM domain in a more ‘soft’ manner using the method of Lagrange multipliers and least squares approximation. The relative performance of these two methods are tested against each other in a uniaxial tension test using a graphene monolayer at 300 K temperature and a block of thermosetting polymer EPON862 at low temperature, showing comparable results. Convergence behaviour of the two coupling methods are studied and presented. The methods are then applied to the fracture of a centre-cracked graphene monolayer and compared with results from an identical pure MD simulation. The results corroborate the effectiveness of the developed method and potential use as a plug-and-play tool to couple pre-existing specialized FEM and MD solvers. Future work will focus on applying these methods to simulate elevated-temperature amorphous polymer models and their brittle fracture.

An Interface-Fitted Fictitious Domain Finite Element Method for the Simulation of Neutrally Buoyant Particles in Plane Shear Flow

In this paper, an interface-fitted fictitious domain finite element method is developed for the simulation of fluid–rigid particle interaction problems in cases of rotated particles with small displacement, where an interface-fitted mesh is employed for the discrete scheme to capture the fluid–rigid particle interface accurately, thereby improving the solution accuracy near the interface. Moreover, a linearization and decoupling process is presented to release the constraint between velocities of fluid and rigid particles in the finite element space, and to make the developed numerical method easy to be implemented. Our numerical experiments are carried out using two different moving interface-fitted meshes; one is obtained by a rotational arbitrary Lagrangian–Eulerian (ALE) mapping, and the other one through a local smoothing process among interface-cut elements. A unified velocity is defined in the entire domain based on the fictitious domain method, making it easier to develop an interface-fitted mesh generation algorithm in a fixed domain. Both show that the proposed method has a good performance in accuracy for simulating a neutrally buoyant particle in plane shear flow. This approach can be easily extended to fluid–structure interaction problems involving fluids in different states and structures in different shapes with large displacements or deformations.

The sound radiation from a periodic array of railway sleepers using a wavenumber domain method

Rolling noise, radiated by the vibration of the wheels and the track, is an important source of noise from railway operations. In ballasted track the sleepers supporting the rails form an important source of noise at low frequencies. There are difficulties to calculate their sound radiation using numerical models due to their discrete periodic nature and the infinite extent of the track. For the rail, which has invariant geometry in the axial direction, the wavenumber domain (2.5D) finite element or boundary element method can be used to calculate the vibration and noise radiation. However, the 2.5D method cannot be used directly to predict the vibration and sound radiation of railway sleepers due to their discrete spacing. In this work, the discrete spacing of the sleepers in the spatial domain is introduced into the 2.5D method by applying a series of rectangular windows according to the sleeper width and spacing. The vibration of the sleepers in the wavenumber domain is obtained by applying a spatial Fourier transform to the product of these windows and the rail transfer mobility, also allowing for the ratio between the sleeper vibration and the rail vibration. The sleeper radiation obtained from the proposed approach is compared with the result obtained from the Rayleigh integral method, showing good agreement. The mobilities of the sleepers in the wavenumber domain are used to explain the effect of the sleeper spacing on the sound radiation. The spectrum of response in the wavenumber domain contains multiple waves, shifted in wavenumber by multiples of 2π/L, where L is the sleeper spacing. At low frequency, only the fundamental wave corresponding to the rail wavenumber radiates power to the far field; the ratio of the sound power of discrete sleepers to that of continuous sleepers is shown to be equal to the square of the width-to-spacing ratio. As the frequency increases, new wave branches enter the acoustic wavenumber range, leading to peaks in the radiation efficiency. At high frequency, the ratio of the sound powers converges to a constant value equal to the ratio of areas.

Tuning SERS Signal via Substrate Structuring: Valves of Different Diatom Species with Ultrathin Gold Coating.

The discovered light modulation capabilities of diatom silicious valves make them an excellent toolkit for photonic devices and applications. In this work, a reproducible surface-enhanced Raman scattering (SERS) enhancement was achieved with hybrid substrates employing diatom silica valves coated with an ultrathin uniform gold film. Three structurally different hybrid substrates, based on the valves of three dissimilar diatom species, have been compared to elucidate the structural contribution to SERS enhancement. The comparative analysis of obtained results showed that substrates containing cylindrical Aulacoseira sp. valves achieved the highest enhancement, up to 14-fold. Numerical analysis based on the frequency domain finite element method was carried out to supplement the experimental results. Our results demonstrate that diatom valves of different shapes can enhance the SERS signal, offering a toolbox for SERS-based sensors, where the magnitude of the enhancement depends on valve geometry and ultrastructure.

Electrothermal analysis of a TEC-less IR microbolometer detector including self-heating and thermal drift

ABSTRACT The article presents the results of modelling and experiments of the self-heating and thermal drift effects of microbolometric sensors of infrared radiation. The developed electrothermal model of the readout electronic circuit generates the power dissipated in the active microbolometer during row-by-row scanning implemented in the focal plane array (FPA) detector. Two approaches to thermal modelling are presented. Both 1D frequency domain and 2D time domain finite element method models allow estimation of the thermal behaviour of an FPA microbolometer. The modelling and presented experiment results lead to the estimation of the deterioration in FPA performance and allow definition of the basic limits of resistive bolometers in operation.

An advanced detection method for unfavorable geological boulder based on electrical source in drill holes under shield machine

Abstract In recent years, due to the increasingly complex terrain, geological conditions, and working environments in engineering, the accuracy requirements in explorations have been continuously growing. In this study, with the goal of high-resolution prospecting for unfavorable geological boulder under a complex detection environment (such as subway shield machine tunnel). A tunnel model with an unfavorable geological boulder was constructed, and a time domain finite element method was adopted for 3D transient electromagnetic forward modeling. To realize high resolution in the positioning of small-scaled boulders, a detection method in complex environments was explored. A hole was drilled from the central point of the tunnel face toward the tunnel construction direction. Then, an electrical source was placed into the hole and array data was collected on the tunnel face. Electromagnetic sounding was achieved through the movement of the source, and the plane positions of the geological bodies were determined through the electromagnetic field distribution characteristics on the tunnel face. It was observed that the Ex and Ey (horizontal components of the electric field) had a higher resolution for a high resistance geological boulder. Therefore, the results indicated that in complex environments, collecting the horizontal components of the electric fields on the tunnel face excited by the electrical source within a drill hole could be a feasible method for fine explorations of a small-scale high resistance boulder.

An Artificial Immune System Model Tightly Coupled to the Inverse Design of Photonic Crystals

We propose a model based on an Artificial Immune System (AIS) to be used in conjunction with any electromagnetic solver in order to solve inverse design problems of integrated photonics. The proposed AIS was inspired by the Opt-aiNET algorithm coupled to a homemade electromagnetic solver based on the frequency domain Finite Element Method (FEM), which was used for calculating the fitness function. To validate the proposed model, we evaluate the photonic bandgap (PBG) of photonic crystals by the inverse design approach by assuming triangular lattices comprised of Si and air, and compared the results with other metaheuristics. The proposed AIS model is tightly coupled to such type of problem when the photonic structure is discretized in the binary-valued domain. Interestingly, different from many bio-immune-inspired metaheuristics, this proposed model has one of its metaheuristics parameters highly related to the characteristics of the application, which allows the algorithm itself to get a better “learning” of the problem and, additionally, reveals the designer some features intrinsic to the application. We have obtained midgap ratios of the first PBGs in triangular lattices of 47.55% and 49.11% for transversal magnetic (TM) and transversal electric (TE) polarizations, respectively. Additionally, the proposed model was applied to achieve large PBGs assuming the TM polarization in PhCs based on silicon carbide, and a new structure presented a PBG equals to 33.94%.

Simulation of compound anchor intrusion in dry sand by a hybrid FEM+SPH method

The intrusion of deformable compound anchors in dry sand is simulated by coupling the Finite Element Method (FEM) with Smoothed Particle Hydrodynamics (SPH). This novel approach can calculate granular flows at lower computational cost than SPH alone. The SPH and FEM domains interact through reaction forces calculated from balance equations and are assigned the same soil constitutive model (Drucker–Prager) and the same constitutive parameters (measured or calibrated). Experimental force–displacement curves are reproduced for penetration depths of 8 mm or more (respectively, 20 mm or more) for spike-shaped (respectively, fan-shaped) anchors with 1 to 6 blades. As the number of blades increases, simulations reveal that the granular flow under the anchor deviates from the vertical and that the horizontal granular flow transitions from orthoradial to radial. We interpret the strain field distribution as the result of soil arching, i.e., the transfer of stress from a yielding mass of soil onto adjoining stationary soil masses. Arching is fully active when the radial distance between blade end points is less than a critical length. In that case, the normal stress that acts on the compound anchor at a given depth reaches the normal stress that acts on a disk-shaped anchor of same radius. A single-blade anchor produces soil deformation and failure similar to Prandtl’s foundation sliding model. Multiblade anchors produce a complex failure mechanism that combines sliding and arching.

Port Parameter Extraction-Based Self-Consistent Coupled EM-Circuit FEM Solvers

Self consistent solution to electromagnetic (EM)-circuit systems is of significant interest for a number of applications. This has resulted in exhaustive research on means to couple them. In time domain, this typically involves a tight integration (or coupling) with field and non-linear circuit solvers. This is in stark contrast to coupled analysis of linear/weakly non-linear circuits and EM systems in frequency domain. Here, one typically extracts equivalent port parameters that are then fed into the circuit solver. Such an approach has several advantages; (a) the number of ports is typically smaller than the number of degrees of freedom, resulting in cost savings; (b) is circuit agnostic; (c) can be integrated with a variety of device models. Port extraction is tantamount to obtaining impulse response of the linear EM system. In time domain, the deconvolution required to effect this is unstable. Recently, a novel approach was developed for time domain integral equations to overcome this bottleneck. We extend this approach to time domain finite element method, and demonstrate its utility via a number of examples; significantly, we demonstrate that self consistent solutions obtained using either a fully coupled or port extraction is identical to the desired precision for non-linear circuit systems. This is shown within a nodal network. We also demonstrate integration of port extracted data directly with drift diffusion equation to model device physics.

A self-aligned lithography method based on Fabry-Perot resonator effect

Fabry-Perot (F-P) resonator is widely applied in the field of optics such as micro-ring resonator and photonic crystal, but there are not yet relevant reports about optical imaging. We propose a self-aligned lithography method based on F-P resonator effect and realize self-aligned effect successfully by controlling film stack parameters. The self-aligned structure is composed of Ag/photoresist/Ag film stack and wafer layer which contains SiO2 layer and SiO2/Si gratings. A rapid simulation model based on Rigorous Coupled Wave Analysis algorithm is established to optimize the best parameters of the self-aligned structure. Then rigorous Finite Difference Time Domain model and Finite Element Method model are used to verify the self-aligned effect and the results show that such process has extremely large mask critical dimension (CD) and overlay variation. The mask CD could be tuned more than 50% of structure period while the wafer CD maintains in the range less than 10%, and the maximum mask overlay offset could be ± 25% of half pitch while the wafer pattern center maintains unchanged. All the results show that the proposed method has lots of process robustness and could increase the application area of imaging lithography technology.

Random geometries for optimal control PDE problems based on fictitious domain FEMs and cut elements

This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually computationally “forbidden” combination of poorly conditioned equation system matrices due to challenging geometries, optimal control searches with iterative methods, slow convergence to system solutions on deterministic and non-deterministic level, and expensive remeshing due to geometrical changes. We overcome all these difficulties, utilizing the advantages of proper preconditioners adapted to unfitted mesh methods, improved types of Monte Carlo methods, and mainly employing the advantages of embedded FEMs, based on a fixed background mesh computed once even if geometrical changes are taking place. The sensitivity of the control problem is introduced in terms of random domains, employing a Quasi Monte Carlo method and emphasizing on a deterministic target state. The variational discretization concept is adopted, optimal error estimates for the state, adjoint state and control are derived that confirm the efficiency of the cut finite element method in challenging geometries. The performance of a multigrid scheme especially developed for unfitted finite element discretizations adapted to the optimal control problem is also tested. Some fundamental preconditioners are applied to the arising sparse linear systems coming from the discretization of the state and adjoint state variational forms in the spatial domain. The corresponding convergence rates along with the quality of the prescribed preconditioners are verified by numerical examples.

A Detailed FEM Study on the Vibro-acoustic Behaviour of Crash and Splash Musical Cymbals

Advanced numerical simulations, that include modal and frequency response function finite element analysis, frequency domain and time domain finite element method – boundary element method analysis, are performed to study the vibro-acoustic behaviour of crash and splash musical cymbals. The results of the modal analysis agree well with experimental measurements found in literature. The frequency domain and time domain coupled finite – boundary element method simulations, despite their high computational resources and time demands, are used for the crucial comparison of the velocity spectrograms on the cymbal to the radiated sound pressure spectrograms in the air. The computational analysis results show that the splash cymbal is characterized by a faster decay and a higher frequency content compared to the crash cymbal. The advanced multiphysics vibro-acoustic simulations that correlate the displacements and velocities of the vibrated structure with the radiated sound pressure results demonstrate the future capability to synthesize the sounds of cymbal music instruments.