Versatile Finite Element Method Research Articles

A Finite Element-Based Characteristic Mode Analysis

A novel Green’s function-free characteristic modes formulation is introduced in this work. The desired impedance or admittance matrix is obtained utilizing and appropriately modifying the versatile finite element method. For this purpose, the generalized eigenvalue problem of the electric or magnetic field vector wave equation is formulated. In the case of the electric field wave equation, using the Schur complement, the system is reformulated and expressed only in terms of the tangential electric field over the radiating apertures, retaining the equivalent magnetic currents. Similarly, in the case of the magnetic field wave equation, the electric current density on radiating metallic surfaces is isolated using the Schur complement. In both cases, the obtained matrix is split into its real and imaginary part to yield the characteristic modes eigenvalue problem. Key advantage of the proposed formulation is that it does not require the evaluation of Green’s function, thereby the study of any arbitrarily shaped, multilayered geometry loaded with anisotropic and inhomogeneous materials is feasible. To prove the validity of the proposed methodology various classical structures, with both homogeneous, and inhomogeneous and anisotropic materials, published in the bibliography are studied. Both the eigenvalues and eigenvectors compared with the published results show good agreement.

The compressive failure analysis of rock-like materials by experimental and numerical methods

Investigating the crack propagation mechanism is of paramount importance in analyzing the failure process of most materials. This process may be exposed during each kind of loading on the materials. In this work, the cracking mechanism in rock-like materials is studied using the numerical methods and compared with the experimental test results. However, the mechanism of crack growth in brittle materials such as rocks is influenced by different parameters. This research work focuses on the effect of the initial crack angles on the crack growth paths of these materials. Some cubic samples containing pre-existing cracks are tested in compression by considering different flaw orientations. The specimens are made of cement, water, and sand. Moreover, the mentioned process is numerically simulated using three different methods: the finite difference method for discontinuous bodies or discrete element method, the displacement discontinuity method, and the versatile finite element method. The micro-parameters for simulation are gained by the trial-and-error procedure for the discrete element method. Eventually, the crack growth paths observed in the experiments are compared with the numerically simulated models. The results obtained show that these central cracks propagate in two ways, which are dependent on their initial angle. By increasing the initial crack angle to greater than 30° (α > 30°), the wing crack path moves further away from the initial crack, and by decreasing α to smaller than 30° (α < 30°), only the shear cracks are initiated. Therefore, the validity and accuracy of the results are manifested by comparing all the corresponding results obtained by different methods. Based on these results, it can generally be concluded that the strength of the cubic (rock material) specimens increases with increase in the crack angles with respect to the applied loading direction.

Second Law Analysis of MHD Micropolar Fluid Flow through a Porous Microchannel with Multiple Slip and Convective Boundary Conditions

The impact of space dependent heat source in the transport of micropolar fluid in the existence of magnetic dipole, Joule heating, viscous heating, thermal radiation, hydrodynamic slips and convective condition effects has been numerically investigated. The dimensioned governing equations are non-dimensionlzed by using dimensionless variables then non-dimensional forms of the corresponding equations are than tackled by the versatile Finite Element Method (FEM). The effects of pertinent physical parameters characterize the flow phenomena are presented through graphs and discussed. It is found that, the impact of thermal based heat source advances the heat transfer characteristics significantly than exponential to space dependent. The thermal performance can be improved through the effects of magnetic dipole, viscous heating, Joule heating and convective condition. Further, the present numerical results are compared with previously published results in the literature as a limiting case of the considered problem and found to be in good agreement with the existing results.

A new approach for measurement of the fracture toughness using the edge cracked semi-cylinder disk (ECSD) concrete specimens

In this paper, a new approach for measurement of the fracture toughness of concrete using the edge cracked semi-cylinder disk (ECSD) specimens has been rendered. The critical stress intensity factor (fracture toughness) of concretes was determined by using the edge cracked semi-cylinder disk (ECSCD) type specimens. The normalized Mode I stress intensity factor of concrete was measured and estimated through a new formula. The versatile finite element method (FEM) was used to derive this appropriate formula and the Mode I fracture toughness of the specimens determined with a reasonable accuracy. In the laboratory, the notched Brazilian disks (NBD) were tested to evaluate the accuracy of the ECSCD method. A discrete element analysis of the ECSCD tests was also carried out to numerically simulate these experiments and validate the accuracy of the fracture toughness values. Finally, very good agreements gained by comparing the crack extension patterns obtained from the experimental tests with the numerical simulations’ results. However, the toughness values obtained through ECSCD experiments were lower than those measured from the NBD tests. This is due to the smooth distribution of tensile stress around the notch in the ECSCD concrete specimens.

A facile, robust and versatile finite element implementation to study the time-dependent behaviors of responsive gels

Though there are significant efforts to develop numerical platforms to simulate the dynamic behaviors of responsive gels, several challenges were not successfully resolved, including truly robust method to handle time-dependent and coupled mass diffusion and deformation fields particularly at very short-time and complicated instability. In this Letter, a facile, robust and versatile finite element method was developed to resolve these challenges by adopting ramping boundary conditions, viscous damping, and damped Newton–Raphson method. This method can be readily implemented in a commercial platform COMSOL Multiphysics. The finite element method was showcased to study several dynamic examples that possess very short-time surface wrinkles, wrinkle evolutions, and incorporation with other physics field. Given the fact that the implementation is through a commercial platform, this method can have significant contributions to the studies of gels.

Skeletonization, Geometrical Analysis, and Finite Element Modeling of Nanoporous Gold Based on 3D Tomography Data

Various modeling approaches simplify and parametrize the complex network structure of nanoporous gold (NPG) for studying the structure&ndash;property relationship based on artificially generated structures. This paper presents a computational efficient and versatile finite element method (FEM) beam model that is based on skeletonization and diameter information derived from the original 3D focused ion beam-scanning electron microscope (FIB-SEM) tomography data of NPG. The geometrical skeleton network is thoroughly examined for a better understanding of the NPG structure. A skeleton FEM beam model is derived that can predict the macroscopic mechanical behavior of the material. Comparisons between the mechanical response of this skeleton beam model and a solid FEM model are conducted. Results showed that the biggest-sphere diameter algorithm implemented in the open-source software FIJI, commonly used for geometrical analysis of microstructural data, overestimates the diameter of the curved NPG ligaments. The larger diameters lead to a significant overestimation of macroscopic stiffness and strength by the skeleton FEM beam model. For a parabolic shaped ligament with only 20% variation in its diameter, a factor of more than two was found in stiffness. It is concluded that improved algorithms for image processing are needed that provide accurate diameter information along the ligament axis.

Numerical simulation of parafoil inflation via a Robin–Neumann transmission-based approach

In this paper, a partitioned coupled iterative approach based on the Robin–Neumann transmission condition is proposed for the fluid–structure interaction simulation of the inflation process of a parafoil. The Reynold-averaged Navier–Stokes equations and the versatile finite element method are employed to solve the fluid flow field and the structural deformation, respectively. The generalized-α time integration scheme for the structure and the second order back Euler scheme for the fluid are incorporated in the Robin-Neumann method. A modified spring-transfinite interpolation hybrid method is exploited to detect the deformation of the grid and regenerate the grid for the fluid architecture. Both a two-dimensional case and a three-dimensional case are studied to examine the feasibility of the present approach. The simulation results reveal the evolution of the flow regime during the inflation process when the air pours into the parafoil. The whole inflation process can be concluded as two stages: the span-wise deployment and the longitudinal expansion. The numerical aerodynamic performance agrees well with that obtained by wind-tunnel experiment, suggesting the effectiveness of this method in handling such a highly nonlinear fluid–structure interaction in parachute inflation.

A Versatile Method for Analyzing the Influence of Track Irregularity on Vehicle-track-bridge Coupled System

A versatile finite element method is applied to analyze the dynamic responses of railway track and bridges under moving railway vehicles. The whole system is divided into two subsystems. The vehicle and railway track are regarded as an integrated subsystem while the railway track and bridge are regarded as the other subsystem. The equations of motion for the two elements are directly derived by means of Hamilton principle. After by assembling the stiffness, damping, mass matrices and the vectors of nodal loads of all elements, the global equations of motion are obtained and solved by Newmark-β method. Numerical examples demonstrate that the method is versatile and correct while dealing with the dynamic responses of vehicle-track-bridge coupled system. These examples also demonstrate that the influence of the track irregularities on the intergraded system is very significant and that the case of several different track irregularities existing at the same time plays more significant on the dynamics responses than the case of one track irregularity.

Flexural stress analysis of uniform slender functionally graded material beams using non-linear finite element method

Functionally graded material (FGM) typically consists of two constituent materials combined together with a particular distribution. A non-linear flexural stress analysis of through-thickness functionally graded uniform slender beam, subjected to a uniformly distributed load, is studied using the versatile finite element method based on Euler–Bernoulli beam hypothesis. The von-Karman strain–displacement relations are used to account for geometric non-linearity. Simply supported and clamped FGM beams with axially immovable ends are considered. Governing non-linear equations are obtained using the principle of virtual work. Numerical results are provided to show the effect of boundary conditions and volume fraction exponent on the non-linear structural behaviour, in terms of the strains and stresses, of the FGM beams, for the first time. A shift in the neutral axis, from the mid-thickness of the beam, is observed due to the large transverse deflections, for the homogenous as well as the FGM beams. The throu...

Optimal control of a nonlinear induction heating system using a proper orthogonal decomposition based reduced order model

This paper considers the problem of obtaining control inputs for induction heating processes involving nonlinearities and nontrivial geometries. The considered system falls within the much broader class of multiphysics or coupled, distributed parameter systems that are well known for the challenges they pose towards modeling, simulation and control. The approach is based on the versatile finite element method (FEM) widely popular in industry for modeling of such systems. The large dynamic model obtained through FEM is reduced using proper orthogonal decomposition (POD) technique, applicable to nonlinear systems, while preserving the input–output characteristics almost exactly. In the present work, using the reduced model, an optimal control input current for the induction heating system is obtained, for transferring the temperature profile over an axi-symmetric work piece from any initial temperature profile to any other desired temperature profile. The reduced model enables application and numerical implementation of established optimal control techniques based on Hamilton–Jacobi–Bellman theory for the system. Further, although the controller is developed using the reduced model, it is shown to perform perfectly well when used with the original unreduced model as well. Results of the numerical implementation are presented to evaluate the overall proposed approach.

Plasma wave simulation based on a versatile finite element method solver

The possibility of plasma wave simulation based on the finite element method (FEM) was explored, and a new full wave simulation code of the lower hybrid (LH) wave, Lower Hybrid wavE Analysis based on FEM (LHEAF), was developed. The efficient iterative solver for the LH wave [O. Meneghini, S. Shiraiwa, and R. Parker, Phys. Plasmas 16, 090701 (2009)] was coupled to one-dimensional Fokker–Planck calculation to obtain the self-consistent distribution function. In LHEAF, seamless handling of the core, scrape off layer, and antenna regions were realized and the wave launching structure were naturally included into the simulation. Simulation results of a Maxwellian tokamak plasma showed good agreement with ray tracing calculations and the TORIC-LH spectral solver [J. C. Wright, P. T. Bonoli, A. E. Schmidt et al., Phys. Plasmas 16, 072502 (2009)]. Compared to spectral domain solvers, the computational requirements are reduced significantly, allowing an Alcator C [M. Porkolab, J. J. Schuss, B. Lloyd et al., Phys. Rev. Lett. 53, 450 (1984)] scale plasma simulation on a desktop computer. Also, the LH full wave simulation of an ITER scale plasma was demonstrated for the first time with moderate increase in the problem size. In addition, the flexibility of the FEM approach has been exploited to address issues of antenna-plasma coupling in the LH and ion cyclotron range of frequencies (ICRF). Techniques using the FEM package for this purpose were validated on the traditional grill antenna and have been applied to the interdigital-line antenna of LH wave. Application to the near field analysis of the new Alcator C-Mod [I. H. Hutchinson, R. Boivin, F. Bombarda et al., Phys. Plasmas 1, 1511 (1994)] ICRF antenna is in progress.

Panel Flutter Detection and Control Using the Eigenvector Orientation Method and Piezoelectric Layers

A basic eigenvector orientation approach has been used to evaluate the possibility of controlling the onset of panel flutter using a simple flat panel (wide beam) as an illustrative example. The use of the eigenvector orientation method for prediction of the flutter boundary (indicated by a gradual loss of orthogonality between two eigenvectors) was developed in a previous study and can thus provide a lead time for possible flutter control. As a first step, piezoelectric layers are assumed to be bonded to the top and bottom surfaces of the panel in order to provide counterbending moments at joints between elements. The standard linear quadratic control theory is used for controller design and full state feedback is considered for simplicity. The controllers are designed to restabilize the system at the onset of flutter; as a result, flutter occurrence can be offset to a higher flutter speed. To illustrate the applicability and effectiveness of the developed method, several simple wide-beam examples are studied and presented. The effects of control moment locations are studied so as to fulfill the objective of adjusting the flutter speed to be within a desirable range. Potential applications of this basic method may be straightforwardly applied to plate and shell structures of laminated composites using the versatile finite element method.

Analysis of polarization conversion in AlGaAs/GaAs electrooptic polarization converter

A numerical simulation study of the polarization conversion phenomenon in deeply etched semiconductor electrooptic polarization converter is presented. Based on a powerful and versatile finite element method, the effects of various parameters on the polarization conversion in electrooptic semiconductor polarization converter are reported.

Efficient finite-element-based time-domain beam propagation analysis of optical integrated circuits

In this paper, a novel numerically efficient time-domain beam propagation method based on the versatile finite element method (FETDBPM) is presented for the analysis of arbitrarily shaped optical integrated circuits. Lumping the global mass matrix into a diagonal matrix, an explicit full band finite-element time-domain propagation algorithm that needs only matrix-vector multiplication at each time step is derived. The accuracy and efficiency of the proposed FETDBPM is demonstrated through the analysis of propagation in different photonic integrated structures.

Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator

A rigorous numerical study of a deeply etched semiconductor electrooptic modulator is presented. A Laplace equation solver followed by a full-vectorial modal solution technique for general anisotropic optical waveguides, all based on the versatile finite-element method, is used to find the potential distribution, the modulating electric fields, the changes in the permittivity tensor associated with the electrooptic effect, and the different modes of propagation. In particular, the optimization of the optical properties of the modulator structure such as the half-wave voltage length product V/sub π/L and the optical losses due to the imperfectly conducting electrodes has been carefully carried out and results reported. In addition, the effect of the waveguide parameters on the microwave properties such as the microwave index n/sub m/ and characteristic impedance Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> is explained.

Analysis of polarisation rotation in cascaded optical waveguide bends

The design of a polarisation rotator which is based on the use of cascaded and oppositely-curved optical semiconductor waveguide bends is presented. Using the versatile finite element method, both modal solution and beam propagation analyses are adopted in order to analyse and optimise the rotator performance in terms of polarisation conversion ratio, device length, and scattering losses. A sensitivity analysis of the rotator performance with respect to various fabrication tolerances is also performed.

New full-vectorial numerically efficient propagation algorithm based on the finite element method

A new full-vectorial beam propagation algorithm based on the versatile finite element method, in order to accurately characterize three-dimensional (3-D) optical guided-wave devices, is presented. The computationally efficient formulation is based on the two transverse components of the magnetic field without destroying the sparsity of the matrix equation. The robust perfectly matched layer (PML) boundary condition is incorporated into the formulation so as to effectively absorb the unwanted radiation out of the computational domain. The efficiency and precision of the proposed full-vectorial propagation approach is demonstrated through the analysis of single optical waveguide, directional couplers, and electrooptic modulator.

Finite Element Simulation of Twin-Roll Casting Process with an Implementation of Slip/Friction Boundary Condition

The twin-roll casting process is simulated by a general thermomechanical model by using a versatile finite element method. The multidomain method is employed to deal with the solid and liquid phases separately. This includes treating the liquid phase as an Newtonian fluid and the solid phase as a viscoplastic metal. Furthermore, a friction model is proposed to analyze the rolling effect of the completely solidified metal. From the results of this study, the implementation of the friction model can produce a reasonable flow field of the solidified metal. In addition, the non-slip condition severely restricts the motion of the solidified metal and introduces inaccuracy on the temperature, velocity and stress fields as compared to the current approach.

Analysis of flow and heat transfer in twin-roll strip casting process

The twin-roll process is modeled by a coupled fluid flow and phase change model by means of a versatile finite element method. The multidomain method is employed to deal with the solid and liquid phases separately, which includes treating the liquid phase as an Newtonian fluid and the solid phase as a viscoplastic metal. Furthermore, a simple and efficient method is used for overcoming the difficulty of remesh phase encountered during iteration. From the results of this study, the inlet region must be included in the analysis for obtaining the reliable flow field within the strip. In addition, the circulation occurs in the molten region and it is driven mainly by the rotating rollers. Finally, the interface position and shape are both influenced by the inlet flow rate and angular speed of rollers.

NUMERICAL MODELLING OF TWIN-ROLL CASTING BY THE COUPLED FLUID FLOW AND HEAT TRANSFER MODEL

The twin-roll process is modelled by a coupled fluid flow and phase change model by means of a versatile finite element method. Here, a simple numerical scheme is proposed to solve the problem of determining the interface shape under the thermal equilibrium condition. The procedure is based on a finite element method using a transform technique. The simple numerical method provides an efficient and accurate way to find the interface position and shape with arbitrary boundary geometry. This method can easily be implemented on the existing finite element program, and provides a simple and efficient tool to simulate the solidification as well as the fluid flow problem of the twin-roll casting process. © 1997 by John Wiley & Sons, Ltd.