Finite Element Method In Order Research Articles

Electrodynamic Forces in Main Three-Phase Busbar System of Low-Voltage Switchgear—FEA Simulation

This paper concerns the effects of electrodynamic forces that act on current paths that are part of high-grade industrial distribution switchgear. This work is composed of experimental and simulation sections. In the experimental section, the short-circuit tests are presented and the occurrence of electrodynamic forces are shown in a visible way. The formation of electrodynamic forces in the current circuits of electrical energy distribution systems is related to the flow of high currents, but mostly it is related to short-circuit currents. In order to highlight these phenomena, the detailed specification of the parameters during tests is displayed. In the simulation section, the physical phenomenon of electrodynamic forces is being captured by employing a detailed real-scale model of switchgear and current paths. Therefore, the authors proposed employment of the FEM (finite element method) in order to obtain values of electrodynamic forces acting on the current paths by executing the detailed 3D coupled simulation. The analysis of the results and aftermath effects of their interactions provided interesting conclusions that concerned the operation of such power distribution layouts in critical short-circuit conditions.

A Comparative Study on the Structural Response of Multi-Linked Floating Offshore Structure between Digital Model and Physical Model Test for Digital Twin Implementation

A digital twin is a virtual model of a real-world structure (such as a device or equipment) which supports various problems or operations that occur throughout the life cycle of the structure through linkage with the actual structure. Digital twins have limitations as a general simulation method because the characteristic changes (motion, stress, vibration, etc.) that occur in the actual structure must be acquired through installed sensors. Additionally, it takes a huge computing cost to output changes in the structure’s characteristics in real time. In particular, in the case of ships and offshore structures, simulation requires a lot of time and resources due to the size of the analysis model and environmental conditions where the wave load acts irregularly, so the application of a different simulation methodology from existing ones is required. The order reduction method, which accurately represents the system’s characteristics and expresses them in a smaller model, can significantly reduce analysis time and is an effective option. In this study, to analyze the applicability of the order reduction method to the development of digital twins for offshore structures, the structural responses of a multi-connected floating offshore structure were estimated by applying the order reduction method based on distortion base mode. The order reduction method based on the distortion base mode predicts the responses by constructing an order-reduced conversion matrix consisting of the selected distortion base mode, based on the mode vector’s orthogonality and autocorrelation coefficients. The predicted structural responses with the reduced order model (ROM) were compared with numerical analysis results derived using the higher order boundary element method and finite element method with in-house code owned by the Korea Research Institute of Ship & Ocean Engineering and measured responses with a model test. When compared with the numerical analysis results, the structural responses were predicted with high accuracy in the wave direction and wave frequency band of the selected distortion base mode, but there are differences due to changed characteristics of the structure when compared with the results of the model test. In addition, differences were also seen in reduced order model evaluation with different sensor locations, and it was confirmed that the more similar the extracted distortion base modes of input sensor location set is to the distortion base modes of predicted location set, the higher accuracy is in predicting the structural responses. As a result, the performance of the reduced order model is determined by the distortion base mode selection method, the locations of the sensor, and the prediction for the structural response.

Fatigue crack propagation near a corrosion pit in a HSS specimen

Corrosion and fatigue are very common forms of metal degradation, and thus an aspect of the complex issues involved is analysed within this work. A rectangular specimen with a surface fatigue crack and a surface corrosion pit subjected to remote tensile loading was modelled via the finite element method in order to assess the crack behaviour for various configurations of both the crack and the pit. A perpendicular crack was considered along with an angled crack, and the basic fracture parameters have been determined and discussed regarding the influence of the corrosion pit on further crack propagation. Additionally, selected fracture criteria have been applied in their classical one-parameter as well as generalised multi-parameter form to estimate the angle of further crack propagation. The results obtained are discussed thoroughly, and it is proved that the larger the corrosion pit, and the closer it is to the crack, the higher its effect on the fatigue crack behaviour is.

A split-explicit second order Runge–Kutta method for solving 3D hydrodynamic equations

Numerical models of marine hydrodynamics have to deal with processes exhibiting a wide range of timescales. These processes include fast external gravity waves and slower internal fully three-dimensional motions. In order to be both time-efficient and numerically stable, the time stepping scheme has to be chosen carefully to cope with the characteristic time scale of each phenomenon. An usual approach is to split the fast and slow dynamics into separate modes. The fast waves are modeled with a two-dimensional system through depth averaging while the other motions, where characteristic times are much longer, are dealt with in three dimensions. However, if the splitting is inexact, for instance in projecting the fields in a new 3D mesh, this procedure can lead to improper results regarding to the physical properties such as mass conservation and tracer consistency. In this work, a new split-explicit Runge–Kutta scheme is adapted and developed for the Discontinuous-Galerkin Finite Element method in order to obtain a new second-order time stepping, yielding to more accurate results. This method combines a three-stage low-storage Runge–Kutta for the slow processes and a two-stage low-storage for the fast ones. The 3D iterations are not affecting the surface elevation, hence an Arbitrary Lagrangian Eulerian implementation is straightforward. Water volume and tracers are conserved. A set of test cases for baroclinic flows as well as a laboratory application demonstrate the performance of the scheme. They suggest that the new scheme has little numerical diffusion.

Isogeometric multi-resolution full waveform inversion based on the finite cell method

Full waveform inversion (FWI) is an iterative identification process that serves to minimize the misfit of model-based simulated and experimentally measured wave field data. Its goal is to identify a field of parameters for a given physical object. For many years, FWI is very successful in seismic imaging to deduce velocity models of the earth or of local geophysical exploration areas. FWI has also been successfully applied in various other fields, including non-destructive testing (NDT) and biomedical imaging. The inverse optimization process of FWI relies on forward and backward solutions of the (elastic or acoustic) wave equation, as well as on efficient computations of adequate optimization directions. Many approaches employ (low order) finite element or finite difference methods, using parameterized material fields whose resolution is chosen in relation to the elements or nodes of the discretized wave field. In our previous paper (Bürchner et al., 2023), we investigated the potential of using the finite cell method (FCM) as the wave field solver. The FCM offers the advantage that highly complex geometric models can be incorporated easily. Furthermore, we demonstrated that the identification of the model’s density outperforms that of the velocity — particularly in cases where unknown voids characterized by homogeneous Neumann boundary conditions need to be detected. The paper at hand extends this previous study in the following aspects: The isogeometric finite cell analysis (IGA-FCM) – a combination of isogeometric analysis (IGA) and FCM – is applied as the wave field solver, with the advantage that the polynomial degree and subsequently also the sampling frequency of the wave field can be increased quite easily. Since the inversion efficiency strongly depends on the accuracy of the forward and backward wave field solutions and of the gradients of the functional, consistent, and lumped mass matrix discretization are compared. The resolution of the grid describing the unknown material density – thus allowing to identify voids in a physical object – is then decoupled from the knot span grid. Finally, we propose an adaptive multi-resolution algorithm that locally refines the material grid using an image processing-based refinement indicator. The developed inversion framework allows fast and memory-efficient wave simulations and object identification. While we study the general behavior of the proposed approach using 2D benchmark problems, a final 3D problem shows that it can also be used to identify void regions in geometrically complex spatial structures.

Custom Transient Finite Element Method and Ray Tracing Hybridization Strategies for Ultrasonic Testing Modelling

The transient spectral element method (SEM) is a specific high order finite element method that is particularly accurate and fast with a low memory footprint, hence enabling 3D ultrasonic testing simulations on a standard PC. However, particular care in its settings and hybridization with a semi-analytical solution remains a major challenge when seeking for both practicality and performance. A natural hybrid strategy consists of coupling a field calculated by ray tracing in the defect-free object to a SEM subdomain wherein the perturbation is enclosed, then synthesizing the signal with a reciprocity argument. The difficulty is to define the suited coupling strategy when the flaw response interacts with the back wall. In a highly heterogeneous medium, it may even become necessary to widen the numerical domain to the entire thickness of the inspected object and, therefore, to ensure the performance of the SEM through a custom discretization strategy. Here we present different customized uses of the SEM for practical ultrasonic inspection applications and discuss how they complement the ray tracing solution.

Analysis of effects of moving wall direction in a one sided semi-circular porous cavity on mixed magneto-bioconvection in the presence of hybrid nanofluid with oxytactic bacteria

A computational analysis on the effects of direction of wall movement in a one sided semi-circular porous cavity on mixed magneto-bioconvection of hybrid nanofluid in the presence of oxytactic bacteria has been performed. The working fluid is the hybrid nanofluid. The enclosure is cooled from semi-circle side and heated from moving lid under the effect of uniform magnetic field in the horizontal direction. The numerical solution of governing equations is obtained by using the higher order finite element method (FEM). The reliability of designed solver is tested through the experimental and numerical data available in the literature. Two cases of the boundary conditions are considered related to the tendency of right vertical lid of the cavity. Other parameters are Richardson number, Darcy number, Hartmann number, Peclet number and porosity. It is found that moving lid direction is the most effective parameter for the flow field, isotherms, oxygen and microorganism distributions. Moreover, higher heat transfer rate is obtained in Case-I for different values of Darcy number. Around 10% increment is occurred on mass transfer with different Pe number in case of downward moving lid due to increment of convection mode of heat transfer inside the cavity.

Improving the convergence rate of Newman’s battery model using 2nd order finite element method

While battery cycling experiments last for years, battery modelling can save time and is environment friendly, to study the degradation mechanisms of lithium-ion batteries. However, battery models are being challenged by issues of long-time calculation, poor accuracy and bad convergence. In this work, a Julia-based framework (Jubat) has been developed for Newman’s battery model. This framework benefits from the high execution efficiency of Julia language, so the mean computational time is lower than its counterpart PyBaMM written in Python. Governing equations are solved by the finite element method, and good accuracy is obtained. The convergence rate is improved by 2nd order elements, which capture better flux variation within elements than the finite volume method and the finite element method using linear elements, with slightly higher computation cost. Numerical examples show easy use of this framework and ability to solve practical problems like drive cycles. This work provides a compact, readable and fast framework for battery modelling and is useful for the rapid development of advanced battery management system. The code is open-source at https://github.com/weilongai/JuBat.

FEM simulation of thixo‐viscoplastic flow problems: Error analysis

AbstractThis note is concerned with the essential part of Finite Element Methods (FEM) approximation of error analysis for quasi‐Newtonian modelling of thixo‐viscoplastic (TVP) flow problems. The developed FEM settings for thixotropic generalized Navier‐Stokes equations is based on a constrained monotonicity and continuity for the coupled system, which is a cornerstone for an efficient monolithic Newton‐multigrid solver. The manifested coarseness in the energy inequality by means of proportional dependency of its constants on regularization, nonoptimal estimate for microstructure, and extra regularity requirement for velocity, is due to the weak coercivity of microstructure operator on one hand and the modelling approach on the other hand, which we dealt with stabilized higher order FEM. Furthermore, we show the importance of taking into consideration the thixotropy inhabited in material by presenting the numerical solutions of TVP flow problems in a 4:1 contraction configuration.

High-order, unconditionally maximum-principle preserving finite element method for the Allen–Cahn equation

In this paper, based on the mass-lumping finite element space discretization, we incorporate the integrating factor Runge–Kutta method and stabilization technique to develop a class of temporal up to the fourth-order unconditionally structure-preserving schemes for the Allen–Cahn equation and its conservative forms. The proposed methods are linear, without requiring any post-processing or limiters, and unconditionally preserve the maximum principle and mass conservation law. Several numerical experiments verify the high-order temporal accuracy of the proposed schemes, as well demonstrate the ability to preserve the maximum principle, mass conservation, and energy stability over long periods. Moreover, by the aid of numerical simulation, we show that the proposed schemes also have good performances in terms of structure-preserving with high order finite element method.

Nonlinear interactions between solitary waves and structures in a steady current

Interactions between solitary waves and structures in a steady current are studied based on a fully nonlinear wave potential theory, and a higher order finite element method (FEM) with a mesh of 8-node quadrilateral isoperimetric elements is employed to simulate the interaction in two-dimensions. Numerical examples are given by solitary waves propagating over an underwater rectangular cylinder in a steady current in a tank and solitary waves acting on single- and twin-rectangular cylinders in a steady current on free surface. Waves and hydrodynamic forces are obtained at different current speeds. It is found that the peak of diffracted wave due to the first and second reflections by an underwater cylinder clearly increase in following current. Furthermore, a packet of periodic waves with constant peak and trough are found to appear when the absolute value of the Froude number becomes large enough in single- and twin-cylinder cases. For the twin-cylinder cases, the maximum wave and horizontal force are clearly affected by the current especially in larger incident wave amplitudes and smaller spacings. In addition, the nonlinearity of wave or force becomes stronger at larger Froude numbers and larger incident wave amplitudes.

Evaluation of macroscopic yield surfaces of periodic porous microstructures employing transformation field analysis and high order finite element method

Evaluation of macroscopic yield surfaces of periodic porous microstructures employing transformation field analysis and high order finite element method

Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems

In this paper, third-order compact and fourth-order finite element methods (FEMs) based on simple modifications of traditional FEMs are proposed for solving one-dimensional Sturm-Liouville boundary value problems (BVPs). The key idea is based on interpolation error estimates. A simple posterior error analysis of the original piecewise linear finite element space leads to a third-order accurate solution in the L2 norm, second-order in the H1, and the energy norm. The novel idea is also applied to obtain a fourth-order FEM based on the quadratic finite element space. The basis functions in the new fourth-order FEM are more compact compared with that of the classic cubic basis functions. Numerical examples presented in this paper have confirmed the convergence order and analysis. A generalization to a class of nonlinear two-point BVPs is also discussed and tested.

Numerical analysis of a singularly perturbed convection diffusion problem with shift in space

We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high order finite element method on layer adapted meshes. We also apply a new idea of using a coarser mesh in places where weak layers appear. Numerical experiments confirm our theoretical results.

Impact of wavy porous layer on the hydrodynamic forces and heat transfer of hybrid nanofluid flow in a channel with cavity under the effect of partial magnetic field

Abstract This computational analysis focuses on the effects of porous layer on the flow dynamics, heat transfer and hydrodynamic forces of hybrid nanofluid in a channel having an open cavity fixed with bottom wall in the presence of partial magnetic field. The set of PDEs governing the dynamics has been transformed to dimensionless form and simulated using higher order finite element method. In particular, P 3 / P 2 ${\mathbb{P}}_{3}/{\mathbb{P}}_{2}$ finite element pair is employed for the spatial discretization and Crank–Nicolson approach is utilized for the temporal discretization. The obtained equations has been linearized with adaptive Newtons method and linearized systems have been computed using the geometric multi-grid technique. The impact of parameters, for instance, Richardson number, thickness of porous layer and nanoparticle fraction is analyzed in the presence of partial magnetic field and porous layer on the hydrodynamic forces like lift and drag forces on the submerged bodies, being the important part of the fluid flow and heat transfer are also be analysed. It is noticed that the drag and lift coefficients are reduced as the nanoparticle fraction is altered while the local- and average-Nusselt number get higher values.

Study, simulation and detection of glucose concentrations through a biochip based on two-dimensional photonic crystals

A biochip is made from a two-dimensional photonic crystal waveguide and a rhombus shape that acts as a resonator. This biochip is a sensor that can detect different concentrations of glucose with amounts of 10, 20 and 60% in water. Here, we studied and simulated the concentrations of glucose, which have a refractive index n of 1.3477, 1.3635 and 1.4394, respectively. To identify these quantities, we have proposed a square lattice structure formed by silicon rods with a n = 3.46. With the help of these dielectric rods immersed in the air, it was possible to analyze the detection characteristics. Our results are examined according to COMSOL software by using the PWE method and the finite element method in order to have the PBG and which helped us to create the structure and extract the propagation at resonance, the field norm, the total energy density (TED), the power flow norm (PFN), the transmission and the sensitivity. The concentrations of glucose in water answered yes to the variations for each of the E-field, the TED, the PFN and the sensitivity. These variations are due to the radius r and refractive index n of each concentration used. This structure can help with diabetes self-monitoring.

Dynamic Phasor Finite-Element Modeling of a DFIG for Grid Connection Studies

Co-simulation studies of electric power systems and electric machines have been always a challenge. In order to reduce the simulation time to a reasonable value, lumped-parameter Electric-Machines models are commonly used in electric power system modeling software packages to avoid the heavy computational burden of more accurate modeling methods especially Finite Element Method (FEM) on the expense of less accuracy. The proposed technique in this paper combines the Dynamic Phasor Modeling technique for power system simulations with FEM to accurately model the DFIG while connected to the grid. The utilization of dynamic phasors enables adopting large simulation time-steps resulting in a significant reduction in the simulation time compared to the conventional time-domain FEM modeling. The mathematical foundation of the proposed modeling method is presented including the generator's core saturation. Custom-written C++ codes have been developed by the authors to execute the new dynamic phasor FEM algorithm and the conventional time-domain FEM in order to fairly compare their accuracy and numerical performances. As the proposed method combines time and frequency domains, a unique capability of modeling the rotor movement can be achieved. The rotation can be represented by physically incrementing the rotor and airgap mesh as in regular time-domain solvers, by mathematically representing the rotation using the Virtual Blocked Rotor method as in frequency-domain solvers, and the proposed method of combining the two aforementioned approaches. The three methods of modeling rotor rotation are discussed and their simulation results are compared to give a guide to choose the proper method for the different modeling targets. The results show that the proposed dynamic phasor FEM is capable of producing comparable results to the traditional time-domain solver at a substantially reduced simulation time.

High-order finite element method on a Vulanović–Bakhvalov mesh for a singularly perturbed convection–diffusion problem

A kth order (k≥1) finite element method on a Vulanović–Bakhvalov mesh is proposed for a singularly perturbed convection–diffusion problem. Some properties of the Vulanović–Bakhvalov mesh are derived. Based on these estimations and a new Lagrange interpolation technique, an optimal order of uniform convergence with respect to the perturbation parameter is proved. Numerical results are provided to demonstrate the theoretical findings.

Fast solution of elasto-plastic problems by reduced order finite element method with manifold learning

Solution of elasto-plastic problems is often computationally intensive. The most effective way to accelerate the computation is to reduce the number of the degree of freedom of the model. Considering the fact that constitutive relations of solid materials are very diverse and usually quite complicated, the paper investigates a model order reduction technique which can be embedded into existing finite element frameworks and reuse their constitutive models. The semi-intrusive technique can thus be used to solve nontrivial problems. Two typical models, i.e., the perforated plate under tensile load and the pressure vessel head under cyclic load, are tested to evaluate the accuracy and the efficiency of the reduced order model. It is shown that a speedup of around two orders of magnitude can be achieved by the reduced order model while maintaining the same level of accuracy. Moreover, the requirements for processor and memory of the computer are also significantly reduced.

Experimental facility for studying the physical properties of materials in a plane stress state

An original experimental facility for studying the physical properties of materials during elastic-plastic deformation along two axes has been created. The facility has no ferromagnetic parts in the working area, thus enabling us to make more accurate magnetic measurements. Biaxial deformation is simulated by the finite element method in order to optimize the geometry of the specimen and to determine the stress state in the central zone of the specimen. Test experiments on the effect of biaxial tension on the coercive force of the 12G2S are performed.