Finite Element Method Calculations Research Articles

Moving least-squares aided finite element method (MLS-FEM): A powerful means to predict pressure discontinuities of multi-phase flow fields and reduce spurious currents

A technique based on the finite element method (FEM) is developed to precisely predict the pressure jump due to the surface tension forces in two-phase flow problems. In this method, the FEM shape functions of the active elements (the elements containing both phases) are enhanced by the aid of the moving least-squares (MLS) interpolation functions and used in the FEM calculations. Therefore, this technique is named as moving least-squares aided finite element method (MLS-FEM).The enhanced shape function correlates the value of any unknown parameters (e.g., the velocity, pressure, or stress values) at any arbitrary point inside an active element to its surrounding nodes. When the enhancement is performed only for the pressure (P) shape functions, we briefly name the MLS-FEM as the PMLS method (pressure shape function enhanced by the MLS technique). In this case, it would be possible to predict the pressure discontinuities in a two-phase flow domain.To assess the performance of the PMLS method in the calculation of the velocity components and pressure values in two-phase flow fields, the stationary drop problem is investigated. The results show that by employing the PMLS method, not only the magnitude of the spurious current is significantly reduced but also the pressure jump approaches toward its analytical value, without any pressure fluctuation at the interface. It is also explained that the method can be used to evaluate the extent of the drop deformation in a structured or an unstructured meshing system. Finally, the limitation of the introduced method is discussed, which is the basis for further developments.

Theoretical analysis and experimental measurement of coupling dynamic characteristics for transversely isotropic rectangular plate based on modified FSDT assumption

The theoretical analysis of thick plate vibration behavior has been investigated in the literature, but most of the studies were focused on flexural dynamic characteristics and lack experimental verification. In this study, the analytical solutions based on the superposition method for both the flexural and extensional vibrations are presented to obtain resonant frequencies and associated mode shapes for a transversely isotropic thick rectangular plate. The displacement equilibrium equations and boundary conditions of the modified first-order shear deformation theory (FSDT) are derived by utilizing Hamilton’s principle and the variation method. To verify the validity of the theoretical model, the finite-element method (FEM) and impact experiment results for thick plates are employed in this work. Excellent agreement of resonant frequencies and associated mode shapes is obtained for FEM calculation and theoretical analysis. To excite vibrations of a thick rectangular plate, a steel ball controlled by an electromagnet is utilized. A steel ball is dropped freely from a height of 231 mm on the top of the plate surface, and a transient wave will be generated after the ball impact on the specimen. The frequency spectrum of the thick rectangular plate is constructed by using the fast Fourier transform of the time-domain transient response. The excited resonant frequencies obtained from experimental measurement are compared with theoretical results. The comparisons show that the modified FSDT provides an excellent prediction of the resonant frequencies and mode shapes for the dynamic characteristics of thick rectangular plates.

Intracranial alternating current stimulation facilitates neurogenesis in a mouse model of Alzheimer\u2019s disease

BackgroundNeurogenesis is significantly impaired in the brains of both human patients and experimental animal models of Alzheimer’s disease (AD). Although deep brain stimulation promotes neurogenesis, it is an invasive technique that may damage neural circuitry along the path of the electrode. To circumvent this problem, we assessed whether intracranial electrical stimulation to the brain affects neurogenesis in a mouse model of Alzheimer’s disease (5xFAD).Methods and resultsWe used Ki67, Nestin, and doublecortin (DCX) as markers and determined that neurogenesis in both the subventricular zone (SVZ) and hippocampus were significantly reduced in the brains of 4-month-old 5xFAD mice. Guided by a finite element method (FEM) computer simulation to approximately estimate current and electric field in the mouse brain, electrodes were positioned on the skull that were likely to deliver stimulation to the SVZ and hippocampus. After a 4-week program of 40-Hz intracranial alternating current stimulation (iACS), neurogenesis indicated by expression of Ki67, Nestin, and DCX in both the SVZ and hippocampus were significantly increased compared to 5xFAD mice who received sham stimulation. The magnitude of neurogenesis was close to the wild-type (WT) age-matched unmanipulated controls.ConclusionOur results suggest that iACS is a promising, less invasive technique capable of effectively stimulating the SVZ and hippocampus regions in the mouse brain. Importantly, iACS can significantly boost neurogenesis in the brain and offers a potential treatment for AD.

High‐frequency modelling of permanent magnet synchronous motor for conducted EMI studies

In this work, a high-frequency model of permanent magnet synchronous motor (PMSM) is proposed for using in conducted electromagnetic interference (EMI) modelling and simulation of variable speed drive systems. The presented model covers the defined frequency range for the conducted emissions, based on MIL-STD-461 and FCC/CISPR standards from 10 kHz to 30 MHz. Common-mode (CM) and differential-mode (DM) impedance characteristics of PMSM are measured; the proposed method is based on the behavioural method using the measurement data. However, in order to improve the mid-frequency representation, the model is enhanced by physics-based methods with parameters extracted directly from the physical properties of the motor using a three-dimensional finite element method and analytical calculations. This approach enables us to avoid the trial and error method and fine-tuning the model parameters. In order to validate the calculated CM and DM impedances of the PMSM, simulation results are compared with the experimental measurements. Root mean squared relative error is introduced to measure the accuracy of the proposed model and also to compare the given results with the models previously presented in the literature.

Large-Area Arrays of Quasi-3D Au Nanostructures for Polarization-Selective Mid-Infrared Metasurfaces

Metasurfaces are two-dimensional patterns that are used to manipulate the propagation of light by controlling the resultant transmittance, reflectance, or absorption at specific wavelengths. Metasurfaces are typically composed of metallic or dielectric components arranged in single or multiple layers and with sizes significantly less than the wavelength of incident light. While considerable advances have been made in the design of these surfaces, there are significant challenges with high-throughput parallel fabrication over large areas which limits their applicability. Here, we demonstrate the design and characterization of mid-IR metasurfaces fabricated using a combination of photo and nanoimprint lithography (NIL). We fabricate arrays over millimeter scales with a variety of 3D nanoscale designs including asymmetric disjointed shapes and symmetric accordion-like shapes with widths of 400–600 nm, thicknesses of 30–50 nm, and lengths of 5–6 μm. We characterize the mid-IR optical response of these metasurfaces in reflection using Fourier transform infrared (FTIR) microscopy, and simulate the spectral response using finite element method (FEM) calculations with good agreement between simulations and experiments. Also, we demonstrate that the metasurfaces exhibit characteristic and significantly different plasmonic resonance modes based on the polarization of the incoming light. Our large-area fabrication methodology allows cost-effective manufacturing of large-area metasurfaces with 3D micro- and nanoelements for scalable photonic and plasmonic devices with significant tunability in geometry and optical characteristics.

Practical Application of the Galerkin Finite Element Method with a Mass Conservation Scheme under Dirichlet Boundary Conditions to Solve Groundwater Problems

The Galerkin finite element method (FEM) has long been used to solve groundwater flow equations and compute the mass balance in a region. In this study, we proposed a simple, new computational FEM procedure for global mass balance computations that can simultaneously obtain boundary fluxes at Dirichlet boundary nodes and finite element hydraulic heads at all nodes in only one step, whereas previous approaches usually require two steps. In previous approaches, the first step obtains the Galerkin finite element hydraulic heads at all nodes, and then, the boundary fluxes are calculated using the obtained Galerkin finite element hydraulic heads in a second step. Comparisons between the new approach proposed in this study and previous approaches, such as Yeh’s approach and a conventional differential approach, were performed using two practical groundwater problems to illustrate the improved accuracy and efficiency of the new approach when computing the global mass balance or boundary fluxes. From the results of the numerical experiments, it can be concluded that the new approach provides a more efficient mass balance computation scheme and a much more accurate mass balance computation compared to previous approaches that have been widely used in commercial and public groundwater software.

A coupled mode model for omnidirectional three-dimensional underwater sound propagation.

A fully three-dimensional (3D) omnidirectional numerical coupled mode model of acoustic propagation is detailed. A combination of normal mode and finite element computational methods is applied to produce the numerical results. The technique is tested in a strongly range-dependent ocean environment modeled after the Hudson Canyon. Modeled sound from three source locations selected over different bathymetric depths is examined to determine capabilities and difficulties associated with varying numbers of propagating vertical modes across the horizontal domain, and variable amounts of mode coupling. Model results are compared to those from a unidirectional Cartesian 3D parabolic equation simulation, and from adiabatic (uncoupled) simulations to illustrate the capabilities of the techniques to study the influences of coupling, strong refraction, and reflection.

Stress-strain state of wooden beams with external reinforcement

The stress-strain state of wood-composite beams was studied numerically. Numerical studies were performed on wood-composite floor beams with a cross-section size of 100×240 mm and a length of 4.8 m. it was Experimentally proved that the deformability of wood-glued beams is reduced by 1.8…2.1 times, compared to conventional wooden beams. For wooden beams in the elastic design stage, the limiter is the calculation of the 2nd group of limit States (for stiffness), for composite beams, the calculation of the 1st group of limit States (for strength. The calculation proved that the deformability of wood composite beams is reduced by 1.8…2.1 times, compared to conventional wooden beams. The high efficiency of the finite element method calculation for evaluating the criteria of load-bearing capacity of wood-composite beams up to their destruction is proved.

SIMULATION OF WOOD BURNING PROCESS BY FINITE ELEMENT METHOD

The concept of laboratory or field research is increasingly being replaced by computer simulations. It is already common for every engineer to simulate the static and dynamic operation of a structure using the finite element method. Another question arises in the simulation of emergency effects such as fire. If for materials which possess ability to keep the geometrical characteristics for a long time the decision is realized, then for such material as wood for which during a fire burnout and variable section is characteristic, realization of simulation of such settlement situation by means of a method of final elements is a difficult enough task. This article presents the results of modeling and calculation of the loaded wooden column by the finite element method, as well as theoretical calculations of the column in case of one-sided local damage of the section as a result of fire. The aim of the work is to compare the results of calculations by the theoretical method of DSTU-N-P B V.2.6-157: 2010 with the results obtained by the finite element method. Calculation of a design by a method of finite elements are realised in software complex Lira. The calculation is done in a flat production. The results of calculation are obtained and conclusions about expediency of using the finite element method for calculation of tasks, for which reduction of construction cross-section in time is characteristic.

Simulation assisted process chain design for the manufacturing of bulk hybrid shafts with tailored properties

To manufacture semi-finished hybrid workpieces with tailored properties, a finite element simulation assisted process chain design was investigated. This includes the process steps of cross wedge rolling, hot geometry inspection, induction hardening, and fatigue testing. The process chain allows the utilisation of material combinations such as high-strength steels with low-cost and easy to process steels. Here, plasma transferred arc welding is applied to supply the process chain with hybrid specimen featuring different steel grades. An overview of the numerical approaches to consider the various physical phenomena in each of the process steps is presented. The properties of the component behaviour were investigated via the finite element method (FEM) and theoretical approaches. At first, the manufacturing of a hybrid workpiece featuring a near net shape geometry with improved mechanical properties due to recrystallising the weld was computed, using the example of a cross wedge rolling process. The rolling process was designed by means of FEM to determine suitable process parameters and to reduce experimental testing. An optical multi-scale geometry inspection of the hot workpiece is meant to be carried out after each manufacturing step to detect potential undesired forming or cooling-induced deformations. Due to the heat transfer from the hot component to the ambient medium, an optical measurement is affected by the developing inhomogeneous refractive index field in air. To gain a basic understanding of the refractive index field and induced light deflection effects, computations were conducted using heat transfer and ray tracing simulations. According to the proposed process route, a subsequent local heat treatment of the hybrid component is required to adapt the mechanical properties by a spray cooling assisted induction hardening. The heat treatment step was computed via a 2D FEM calculation. After finishing by machining, the hybrid material shafts are examined in fatigue tests under load conditions. To predict the component’s lifetime under rolling contact fatigue, a damage accumulation model was combined with an FE simulation. The resulting residual stress state after quenching and the geometry after the finishing process were used as input data for the fatigue life calculations.

A Method for Evaluating the Worst-Case Cogging Torque Under Manufacturing Uncertainties

Permanent-magnet (PM) motors have been widely used in industrial applications and automobiles. However, owing to the design tolerances, manufacturing uncertainties, and material inconsistency, deviations from the ideal motor inevitably occur with parasitic effects, such as additional cogging torque and vibration. One of the most significant obstacles for evaluating these uncertainties is the large computational burden caused by the countless uncertain combinations, which must be computed via the finite-element method (FEM). Herein, a worst-uncertain-combination-analyze (WUCA) method is proposed to significantly reduce the computational cost. A widely used analytical method is modified to identify the origin of additional cogging-torque harmonics caused by uncertainties. Different types of uncertainties for the surface-mounted PM machine and interior PM machine can be analyzed simultaneously. With the WUCA method, the worst-case combinations can be confirmed theoretically; thus, FEM calculations for only a few combinations of uncertainties are required, rather than thousands. Compared with the widely adopted design of experiments based uncertain combining methods, the worst-case cogging torque obtained from the WUCA is higher. FEM verification of different pole/slot configurations revealed that the WUCA method was a general and effective method for quickly estimating the worst-case cogging torque under manufacturing uncertainties.

An Explicit Coupled Method of FEM and Meshless Particle Method for Simulating Transient Heat Transfer Process of Friction Stir Welding

Friction stir welding (FSW) is a favorable welding technology for aluminum alloys. The FSW process involves complex heat and mass transfer. Explicit meshless particle methods are currently popular methods for simulating the process, but they require expensive computational cost. Coupling explicit finite element method (FEM) and meshless particle methods can ease the problem by making use of high efficiency of FEM and advantages of meshless particle methods. Though many efforts have been made to couple FEM and meshless particle methods for transient dynamics problems, coupling them for transient heat transfer problems is seldom addressed. In this work, we focus on treating this problem. We developed an explicit coupled method of FEM and the meshless particle method presented in a previous work and used it to simulate the thermal process during FSW. In the method, FEM using lumped heat capacity matrix and low-order numerical integration is constructed to obtain high efficiency. A new coupling algorithm is proposed to link thermal calculations of the weak-form FEM and the strong-form meshless particle method. Forward Euler method is used for time integration to achieve an explicit algorithm. The coupled method is used to calculate a numerical example having analytical solution. Calculated results show that it can achieve a good accuracy. The method is employed to simulate FSW of Al 6061-T6 plates. It predicts thermal cycles in good agreement with experimental results. It shows an accuracy comparable to that of the meshless particle method while having a higher efficiency than the latter.

A bicomplex finite element method for wave propagation in homogeneous media

PurposeThe purpose of this paper is to present the advantageous applicability of the bicomplex analysis in the context of the Finite Element Method (FEM). This method can be applied for wave propagation problems in various environments.Design/methodology/approachIn this paper, the bicomplex number system is introduced and accordingly the differential equation for time-harmonic Maxwell’s equations in homogeneous media is derived in detail. Besides that, numerical simulations of wave propagation are performed and compared to the traditional approach based on classical FEM related to the Helmholtz equation. The appropriate error norm is investigated for different discretizations.FindingsThe results show that the use of bicomplex analysis in FEM leads to the higher accuracy of the electromagnetic field determination compared to the traditional Helmholtz approach. By using the bicomplex-valued formulation, the complex-valued electric and magnetic fields can be found directly and no additional FEM calculations are necessary to get the whole field.Originality/valueThe direct bicomplex formulation overcomes the use of the second order derivatives, which leads to the higher accuracy. In general, accurate calculations of the wave propagation in FEM is still an open problem and the approach described in this paper is a contribution to this class of problems.

On the Performance and Structural Stability of Cathodic Electrocatalysts with Complex Nanoscale Morphology

Increasing complexity of nanosynthesis has produced a variety of intricate nanoparticle shapes which have attracted significant attention for applications in electrocatalysis. These complex nanoelectrocatalyst shapes not only introduce high surface areas and high energy active sites, but also improve electrocatalytic performance by altering electric field at the surface thereby concentrating reagents and accelerating electrocatalysis. However, long-term structural stability of complex nanoelectrocatalysts necessary for their industrial implementation often remains unknown and difficult to predict. Here, we study structural stability in cathodic reactions (CO2 and water electrolysis) of noble metal nanoparticles with star- and core-cage structures that collectively cover major structural nanoscale features including extrusions, holes, voids, and nanogaps. Based on structural and surface analysis, density functional theory and finite element method calculations, we demonstrate that uneven electric field and current density distributions in these morphologies influence metal mobility resulting in their structural degradation. Our results revealed that extrusions and holes facing the anode form electric field hot spots for electrolysis, that also facilitate surface reconstruction. The holes and voids perpendicular to the direction facing the anode form current crowding spots within the metal that facilitate electromigration via local Joule heating, while being blind spots for electrolysis due to low local electric field in these areas. Finally, structural features within nanocages are electrically shielded resulting in them being blind spots for both electrolysis and electromigration. This study provides guidelines for the structural design of electrocatalysts, highlighting that it should not only be dictated by the surface atomic organization and the generation of electric field hotspots, but also by current distribution within the electrode itself, to ensure not only high material performance but also improved stability.

Parameter sensitivity analysis of stability of T-shaped rigid frame bridge by adopting swivel construction method

PurposeIn order not to affect the highway and railway traffic under the bridge during the construction process, bridges adopting swivel construction method are increasingly used at areas where the traffic is heavy. Previous studies are mostly conducted by assuming that the bridge is under its own stability conditions, without considering the impact of construction error, changes of external condition and wind-induced vibration on the stability of the bridge, which poses serious challenges to the bridge construction process. This paper aims to analyze the extent to which static load and fluctuating wind effect influence structural stability and to test the credibility of the structure.Design/methodology/approachA finite element calculation method is used to analyze a T-shaped rigid frame swivel bridge. A full bridge model was built, and a local model of the turntable structure established; the two are then combined means of node coupling. Subsequently, the three sensitivity indexes – deflection rate, stress change rate and the change rate of spherical hinges – are used to evaluate in what way the bridge stability is influenced under various factors.FindingsIt is found that the stability of the swivel bridge is quite sensitive to unilateral overweight, steel beam tension and wind-induced vibration effects but less sensitive to the change of bulk density. Also found is that the change of elastic modulus exerts some effects on deflection but has negligible effects on other stability indexes. Furthermore, the transverse unbalanced torque on the bridge generated by wind-induced vibration is an important factor in determining the size of the turntable, indicating that it is not just controlled by the weight of the bridge.Originality/valueAll factors affecting the stability of swivel construction are analyzed, and solutions to reduce the influence are proposed. The influence of wind-induced vibration effects on swivel construction is analyzed for the first time. It is pointed out that wind-induced vibration effects have great influence on the structure, and its influence could not be neglected.

An Optically Tunable THz Modulator Based on Nanostructures of Silicon Substrates.

Nanostructures can induce light multireflection, enabling strong light absorption and efficient photocarrier generation. In this work, silicon nanostructures, including nanocylinders, nanotips, and nanoholes, were proposed as all-optical broadband THz modulators. The modulation properties of these modulators were simulated and compared with finite element method calculations. It is interesting to note that the light reflectance values from all nanostructure were greatly suppressed, showing values of 26.22%, 21.04%, and 0.63% for nanocylinder, nanohole, and nanotip structures, respectively, at 2 THz. The calculated results show that under 808 nm illumination light, the best modulation performance is achieved in the nanotip modulator, which displays a modulation depth of 91.63% with a pumping power of 60 mW/mm2 at 2 THz. However, under shorter illumination wavelengths, such as 532 nm, the modulation performance for all modulators deteriorates and the best performance is found with the nanohole-based modulator rather than the nanotip-based one. To further clarify the effects of the nanostructure and wavelength on the THz modulation, a graded index layer model was established and the simulation results were explained. This work may provide a further theoretical guide for the design of optically tunable broadband THz modulators.

Optically tunable microresonator using an azobenzene monolayer

Photoswitchable organic molecules can undergo reversible structural changes with an external light stimulus. These optically controlled molecules have been used in the development of “smart” polymers, optical writing of grating films, and even controllable in vivo drug release. Being the simplest class of photoswitches in terms of structure, azobenzenes have become the most ubiquitous, well-characterized, and implemented organic molecular switches. Given their predictable response, they are ideally suited to create an all-optically controlled switch. However, fabricating a monolithic optical device comprised solely of azobenzene while maintaining the photoswitching functionality is challenging. In this work, we combine integrated photonics with optically switchable organic molecules to create an optically controlled integrated device. A silica toroidal resonant cavity is functionalized with a monolayer of an azobenzene derivative. After functionalization, the loaded cavity Q is above 105. When 450 nm light is coupled into cavity resonance, the azobenzene isomerizes from trans isomer to cis isomer, inducing a refractive index change. Because the resonant wavelength of the cavity is governed by the index, the resonant wavelength changes in parallel. At a probe wavelength of 1300 nm, the wavelength shift is determined by the duration and intensity of the 450 nm light and the density of azobenzene functional groups on the device surface, providing multiple control mechanisms. Using this photoswitchable device, resonance frequency tuning as far as 60% of the cavity’s free spectral range in the near-IR is demonstrated. The kinetics of the tuning are in agreement with spectroscopic and ellipsometry measurements coupled with finite element method calculations.

Assessment of the use of FEM for computation of Electromagnetic Forces, Losses and Design of Transformers

This paper reviews the published work on power transformers for assessment of the electrical, magnetic losses, and electromagnetic forces produced during normal and short circuit conditions. The different methods used are analytical method, integral equation method, boundary element method, and finite element method (FEM). The copper losses and eddy currents within the copper conductors/windings need to be assessed to estimate the heat generate and compute the efficiency. The knowledge of the eddy current losses in the core and stray losses in each component of the transformer can help in the design improvement. Earlier 2D FEM and now 3D FEM has been used to evaluate the electromagnetic flux under normal conditions, the effect of the in-rush phenomenon, assessment of mechanical strength of windings, insulation, computation of short circuit forces and need of the mechanical support components during fault conditions. This paper gives an overview of the work done on the computation of electromagnetic forces, losses, and design of transformers using FEM to assess the scope for further work.

Assessing artificial neural network performance for predicting interlayer conditions and layer modulus of multi-layered flexible pavement

The objective of this study is to evaluate the performance of the artificial neural network (ANN) approach for predicting interlayer conditions and layer modulus of a multi-layered flexible pavement structure. To achieve this goal, two ANN based back-calculation models were proposed to predict the interlayer conditions and layer modulus of the pavement structure. The corresponding database built with ANSYS based finite element method computations for four types of a structure subjected to falling weight deflectometer load. In addition, two proposed ANN models were verified by comparing the results of ANN models with the results of PADAL and double multiple regression models. The measured pavement deflection basin data was used for the verifications. The comparing results concluded that there are no significant differences between the results estimated by ANN and double multiple regression models. PADAL modeling results were not accurate due to the inability to reflect the real pavement structure because pavement structure was not completely continuous. The prediction and verification results concluded that the proposed back-calculation model developed with ANN could be used to accurately predict layer modulus and interlayer conditions. In addition, the back-calculation model avoided the back-calculation errors by considering the interlayer condition, which was barely considered by former models reported in the published studies.

Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform

The following article presents a computation procedure that enables us to simulate the dynamic states of electric machines with a laminated magnetic core, with direct consideration of the eddy current losses. The presented approach enables a significant reduction of the simulation process computational complexity. The verification of the obtained data correctness is based on a detailed balance of energy and power in the investigated system. The correctness of the obtained results was also confirmed by comparing them with the results included in norms that describe the losses in laminated sheets. The presented approach is based on expressing the equivalent permeability of transformer metal sheets by using RC or RL circuits. The impedances of these circuits are treated as the transmittance of Infinite Impulse Response filters (IIR) of the Laplace s variable. In this form they are implemented in direct calculations of the dynamics of electric machines based on field-circuital models, using the Finite Element Method (FEM). In this way, we present the method of including eddy current losses in laminated metal circuits of chokes or transformers, during calculations using the finite element method, with the IIR filter in the domain of the variable s of the Laplace transform. Eddy current losses are directly included in the calculation process. Therefore, they have a direct impact on the transient state waveforms. However, the use of the Laplace variable s caused an excessive increase in the number of state variables, and the overall computational efficiency of the presented method is sufficiently low so as to be used in the simulation process of electrical machine dynamic states with a relatively large number of elements in the FE Model.