Integrating open source codes for solid modeling and automatic mesh generation in FEM applications

The applications of the Finite Element Method (FEM) for three-dimensional domains are already well documented in the framework of Computational Electromagnetics. However, despite the power and reliability of this technique for solving partial differential equations, there are only a few examples of open source codes available and dedicated to the solid modeling and automatic constrained tetrahedralization, which are the most time consuming steps in a typical three-dimensional FEM simulation. Besides, these open source codes are usually developed separately by distinct software teams, and even under conflicting specifications. In this paper, we describe an experiment of open source code integration for solid modeling and automatic mesh generation. The integration strategy and techniques are discussed, and examples and performance results are given, specially for complicated and irregular volumes which are not simply connected. © 2011 IEEE.

Accuracy of FEM and BEM for electromagnetic flux calculations in high power applications

The development and design of electric high power devices with electromagnetic computer-aided engineering (EM-CAE) software such as the Finite Element Method (FEM) and Boundary Element Method (BEM) has been widely adopted. This paper presents the analysis of a Fault Current Limiter (FCL), which acts as a high-voltage surge protector for power grids. A prototype FCL was built. The magnetic flux in the core and the resulting electromagnetic forces in the winding of the FCL were analyzed using both FEM and BEM. An experiment on the prototype was conducted in a laboratory. The data obtained from the experiment is compared to the numerical solutions to determine the suitability and accuracy of the two methods.

The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

Impact and energy absorption of road safety barriers by coupled SPH/FEM

Road safety barriers are used to minimise the severity of road accidents and protect lives and property. There are several types of barrier in use today. This paper reports the initial phase of research carried out to study the impact response of portable water-filled barrier (PWFB) which has the potential to absorb impact energy and hence provide crash mitigation under low to moderate speeds. Current research on the impact and energy absorption capacity of water-filled road safety barriers is limited due to the complexity of fluid-structure interaction under dynamic impact. In this paper, a novel fluid-structure interaction method is developed based on the combination of Smooth Particle Hydrodynamics (SPH) and Finite Element Method (FEM). The sloshing phenomenon of water inside a PWFB is investigated to explore the energy absorption capacity of water under dynamic impact. It was found that water plays an important role in energy absorption. The coupling analysis developed in this paper will provide a platform to further the research in optimising the behaviour of the PWFB. The effect of the amount of water on its energy absorption capacity is investigated and the results have practical applications in the design of PWFBs.

A novel free floating accelerometer force balance system for shock tunnel applications

In order to overcome the interference of the model mounting system with the external aerodynamics of the body during shock tunnel testing, a new free floating internally mountable balance system that ensures unrestrained model motion during testing has been designed, fabricated and tested. Minimal friction ball bearings are used for ensuring the free floating condition of the model during tunnel testing. The drag force acting on a blunt leading edge flat plate at hypersonic Mach number has been measured using the new balance system. Finite element model (FEM) and CFD are exhaustively used in the design as well as for calibrating the new balance system. The experimentally measured drag force on the blunt leading edge flat plate at stagnation enthalpy of 0.7 and 1.2 MJ/kg and nominal Mach number of 5.75 matches well with FEM results. The concept can also be extended for measuring all the three fundamental aerodynamic forces in short duration test facilities like free piston driven shock tunnels.

Calculating transport AC losses in stacks of high temperature superconductor coated conductors with magnetic substrates using FEM

In this paper, the authors investigate the electromagnetic properties of stacks of high temperature superconductor (HTS) coated conductors with a particular focus on calculating the total transport AC loss. The cross-section of superconducting cables and coils is often modeled as a two-dimensional stack of coated conductors, and these stacks can be used to estimate the AC loss of a practical device. This paper uses a symmetric two dimensional (2D) finite element model based on the H formulation, and a detailed investigation into the effects of a magnetic substrate on the transport AC loss of a stack is presented. The number of coated conductors in each stack is varied from 1 to 150, and three types of substrate are compared: non-magnetic weakly magnetic and strongly magnetic. The non-magnetic substrate model is comparable with results from existing models for the limiting cases of a single tape (Norris) and an infinite stack (Clem). The presence of a magnetic substrate increases the total AC loss of the stack, due to an increased localized magnetic flux density, and the stronger the magnetic material, the further the flux penetrates into the stack overall. The AC loss is calculated for certain tapes within the stack, and the differences and similarities between the losses throughout the stack are explained using the magnetic flux penetration and current density distributions in those tapes. The ferromagnetic loss of the substrate itself is found to be negligible in most cases, except for small magnitudes of current. Applying these findings to practical applications, where AC transport current is involved, superconducting coils should be wound where possible using coated conductors with a non-magnetic substrate to reduce the total AC loss in the coil. © 2011 Elsevier B.V. All rights reserved.

Fem modeling of periodic arrays of multi-walled carbon nanotubes

Multiwalled carbon nanotubes display dielectric properties similar to those of graphite, which can be calculated using the well known Drude-Lorentz model. However, most computational softwares lack the capacity to directly incorporate this model into the simulations. We present the finite element modeling of optical propagation through periodic arrays of multiwalled carbon nanotubes. The dielectric function of nanotubes was incorporated into the model by using polynomial curve fitting technique. The computational analysis revealed interesting metamaterial filtering effects displayed by the highly dense square lattice arrays of carbon nanotubes, having lattice constants of the order few hundred nanometers. The curve fitting results for the dielectric function can also be used for simulating other interesting optical applications based on nanotube arrays.

Dynamic load-balancing of finite element applications with the DRAMA library

The DRAMA library, developed within the European Commission funded (ESPRIT) project DRAMA, supports dynamic load-balancing for parallel (message-passing) mesh-based applications. The target applications are those with dynamic and solution-adaptive features. The focus within the DRAMA project was on finite element simulation codes for structural mechanics. An introduction to the DRAMA library will illustrate that the very general cost model and the interface designed specifically for application requirements provide simplified and effective access to a range of parallel partitioners. The main body of the paper will demonstrate the ability to provide dynamic load-balancing for parallel FEM problems that include: adaptive meshing, re-meshing, the need for multi-phase partitioning.

Modelling the Performance of Flexible Substrates for Lead-Free Applications

In this paper, the performance of flexible substrates for lead-free applications was studied using finite element method (FEM). Firstly, the thermal induced stress in the flex substrate during the lead free solder reflow process was predicted. The shear stress at the interface between the copper track and flex was plotted. This shear stress increases with the thickness of the copper track. Secondly, an ACF flip chip was taken as a typical lead-free application of the flex substrate. The reflow effect on the reliability of ACF interconnections was analyzed. Higher stress was identified along the interface between the conductive particle and the metallization, and the interfacial stress increases with the reflow peak temperature and the coefficient of thermal expansion (CTE) of the adhesive. The moisture effect on the reliability of ACF joints were studied using a macro-micro modeling technique, the predominantly tensile stress found at the interface between the conductive particle and metallization could reduce the contact area and even cause the electrical failure. Modeling results are consistent with the findings in the experimental work

Analyzing the performance of flexible substrates for lead-free applications

The performance of flexible substrates for lead-free applications was studied using finite element method (FEM). Firstly, the thermal induced stress in the flex substrate during the lead free solder reflow process was predicted. The shear stress at the interface between the copper track and flex was plotted. This shear stress increases with the thickness of the copper track and the thickness of the flex. Secondly, an anisotropic conductive film (ACF) flip chip was taken as a typical lead-free application of the flex substrate and the moisture effect on the reliability of ACF joints were studied using a 3D macro-micro modeling technique. It is found that the time to be saturated of an ACF flip chip is much dependent on the moisture diffusion rate in the polyimide substrate. The majority moisture diffuses into the ACF layer from the substrate side rather than the periphery of the ACF. The moisture induced stress was predicted and the predominant tensile stress was found at the interface between the conductive particle and metallization which could reduce the contact area and even cause the electrical failure

FEM based Virtual Prototyping and Design of Third Harmonic Excitation System for Low Voltage Brushless Alternators

Salient pole brushless alternators coupled to IC engines are extensively used as stand-by power supply units for meeting in- dustrial power demands. Design of such generators demands high power to weight ratio, high e ciency and low cost per KVA out- put. Moreover, the performance characteristics of such machines like voltage regulation and short circuit ratio (SCR) are critical when these machines are put into parallel operation and alterna- tors for critical applications like defence and aerospace demand very low harmonic content in the output voltage. While designing such alternators, accurate prediction of machine characteristics, including total harmonic distortion (THD) is essential to mini- mize development cost and time. Total harmonic distortion in the output voltage of alternators should be as low as possible especially when powering very sophis- ticated and critical applications. The output voltage waveform of a practical AC generator is replica of the space distribution of the ux density in the air gap and several factors such as shape of the rotor pole face, core saturation, slotting and style of coil disposition make the realization of a sinusoidal air gap ux wave impossible. These ux harmonics introduce undesirable e ects on the alternator performance like high neutral current due to triplen harmonics, voltage distortion, noise, vibration, excessive heating and also extra losses resulting in poor e ciency, which in turn necessitate de-rating of the machine especially when connected to non-linear loads. As an important control unit of brushless alternator, the excitation system and its dynamic performance has a direct impact on alternator's stability and reliability. The thesis explores design and implementation of an excitation i system utilizing third harmonic ux in the air gap of brushless al- ternators, using an additional auxiliary winding, wound for 1=3rd pole pitch, embedded into the stator slots and electrically iso- lated from the main winding. In the third harmonic excitation system, the combined e ect of two auxiliary windings, one with 2=3rd pitch and another third harmonic winding with 1=3rd pitch, are used to ensure good voltage regulation without an electronic automatic voltage regulator (AVR) and also reduces the total harmonic content in the output voltage, cost e ectively. The design of the third harmonic winding by analytic methods demands accurate calculation of third harmonic ux density in the air gap of the machine. However, precise estimation of the amplitude of third harmonic ux in the air gap of a machine by conventional design procedures is di cult due to complex geome- try of the machine and non-linear characteristics of the magnetic materials. As such, prediction of the eld parameters by conven- tional design methods is unreliable and hence virtual prototyping of the machine is done to enable accurate design of the third har- monic excitation system. In the design and development cycle of electrical machines, it is recognized that the use of analytical and experimental methods followed by expensive and in exible prototyping is time consum- ing and no longer cost e ective. Due to advancements in com- putational capabilities over recent years, nite element method (FEM) based virtual prototyping has become an attractive al- ternative to well established semi-analytical and empirical design methods as well as to the still popular trial and error approach followed by the costly and time consuming prototyping. Hence, by virtually prototyping the alternator using FEM, the important performance characteristics of the machine are predicted. Design of third harmonic excitation system is done with the help of results obtained from virtual prototype of the machine. Third harmonic excitation (THE) system is implemented in a 45 KVA ii experimental machine and experiments are conducted to validate the simulation results. Simulation and experimental results show that by utilizing third harmonic ux in the air gap of the ma- chine for excitation purposes during loaded conditions, triplen harmonic content in the output phase voltage is signi cantly re- duced. The prototype machine with third harmonic excitation system designed and developed based on FEM analysis proved to be economical due to its simplicity and has the added advan- tage of reduced harmonics in the output phase voltage.

Geostatistics for constrained variables: positive data, compositions and probabilities. Applications to environmental hazard monitoring

Aquesta tesi estudia com estimar la distribució de les variables regionalitzades l'espai mostral i l'escala de les quals admeten una estructura d'espai Euclidià. Apliquem el principi del treball en coordenades: triem una base ortonormal, fem estadística sobre les coordenades de les dades, i apliquem els output a la base per tal de recuperar un resultat en el mateix espai original. Aplicant-ho a les variables regionalitzades, obtenim una aproximació única consistent, que generalitza les conegudes propietats de les tècniques de kriging a diversos espais mostrals: dades reals, positives o composicionals (vectors de components positives amb suma constant) són tractades com casos particulars. D'aquesta manera, es generalitza la geostadística lineal, i s'ofereix solucions a coneguts problemes de la no-lineal, tot adaptant la mesura i els criteris de representativitat (i.e., mitjanes) a les dades tractades. L'estimador per a dades positives coincideix amb una mitjana geomètrica ponderada, equivalent a l'estimació de la mediana, sense cap dels problemes del clàssic kriging lognormal. El cas composicional ofereix solucions equivalents, però a més permet estimar vectors de probabilitat multinomial. Amb una aproximació bayesiana preliminar, el kriging de composicions esdevé també una alternativa consistent al kriging indicador. Aquesta tècnica s'empra per estimar funcions de probabilitat de variables qualsevol, malgrat que sovint ofereix estimacions negatives, cosa que s'evita amb l'alternativa proposada. La utilitat d'aquest conjunt de tècniques es comprova estudiant la contaminació per amoníac a una estació de control automàtic de la qualitat de l'aigua de la conca de la Tordera, i es conclou que només fent servir les tècniques proposades hom pot detectar en quins instants l'amoni es transforma en amoníac en una concentració superior a la legalment permesa.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.