Impact of the Femoral Head Position on Moment Arms in Total Hip Arthroplasty: A Parametric Finite Element Study.

BACKGROUND: Although the importance of accurate femoral reconstruction to achieve a good functional outcome is well documented, quantitative data on the effects of a displacement of the femoral center of rotation on moment arms are scarce. The purpose of this study was to calculate moment arms after nonanatomical femoral reconstruction. METHODS: Finite element models of 15 patients including the pelvis, the femur, and the gluteal muscles were developed. Moment arms were calculated within the native anatomy and compared to distinct displacement of the femoral center of rotation (leg lengthening of 10 mm, loss of femoral offset of 20%, anteversion ±10°, and fixed anteversion at 15°). Calculations were performed within the range of motion observed during a normal gait cycle. RESULTS: Although with all evaluated displacements of the femoral center of rotation, the abductor moment arm remained positive, some fibers initially contributing to extension became antagonists (flexors) and vice versa. A loss of 20% of femoral offset led to an average decrease of 15% of abductor moment. Femoral lengthening and changes in femoral anteversion (±10°, fixed at 15°) led to minimal changes in abductor moment arms (maximum change of 5%). Native femoral anteversion correlated with the changes in moment arms induced by the 5 variations of reconstruction. CONCLUSION: Accurate reconstruction of offset is important to maintaining abductor moment arms, while changes of femoral rotation had minimal effects. Patients with larger native femoral anteversion appear to be more susceptible to femoral head displacements.

Design and Control of Permanent Magnet Synchronous Machine for Hybrid Electric Vehicle

This master’s thesis mainly focuses on the design requirements of an Electric drive for Hybrid car application and its control strategy to achieve a wide speed range. It also emphasises how the control and performance requirements are transformed into its design variables. A parallel hybrid topology is considered where an IC engine and an electric drive share a common crank shaft. A permanent magnet synchronous machine (PMSM) is used as an electric drive machine. Performance requirements are converted into Machine design variables using the vector model of PMSM. Main dimensions of the machine are arrived using analytical approach and Finite Element Analysis (FEA) is used to verify the design and performance. Vector control algorithm was used to control the machine. The control algorithm was tested in a low power PMSM using an embedded controller. A prototype of 10 kW PMSM was built according to the design values. The prototype was tested in the laboratory using a high power converter. Tests were carried out to verify different operating modes. The results were in agreement with the calculations.

Be-Fe coupled method for the analysis of 3D elastodynamic problems in the time domain

By coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM) an algorithm that combines the advantages of both numerical processes is developed. The main aim of the work concerns the time domain analysis of general three-dimensional wave propagation problems in elastic media. In addition, mathematical and numerical aspects of the related BE-, FE- and BE/FE-formulations are discussed. The coupling algorithm allows investigations of elastodynamic problems with a BE- and a FE-subdomain. In order to observe the performance of the coupling algorithm two problems are solved and their results compared to other numerical solutions.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

An Hp-Adaptive Hierarchical Formulation for the Boundary Element Method Applied to Elasticity in Two Dimensions

This paper presents an HP-Adaptive Procedure with Hierarchical formulation for the Boundary Element Method in 2-D Elasticity problems. Firstly, H, P and HP formulations are defined. Then, the hierarchical concept, which allows a substantial reduction in the dimension of equation system, is introduced. The error estimator used is based on the residual computation over each node inside an element. Finally, the HP strategy is defined and applied to two examples.

Cost Reduction of Permanent Magnet Synchronous Machines

Electrical machine drives are the most electrical energy-consuming systems worldwide. The largest proportion of drives is found in industrial applications. There are, however many other applications that are also based on the use of electrical machines, because they have a relatively high efficiency, a low noise level, and do not produce local pollution. Electrical machines can be classified into several categories. One of the most commonly used electrical machine types (especially in the industry) is induction motors, also known as asynchronous machines. They have a mature production process and a robust rotor construction. However, in the world pursuing higher energy efficiency with reasonable investments not every application receives the advantage of using this type of motor drives. The main drawback of induction motors is the fact that they need slipcaused and thus loss-generating current in the rotor, and additional stator current for magnetic field production along with the torque-producing current. This can reduce the electric motor drive efficiency, especially in low-speed, low-power applications. Often, when high torque density is required together with low losses, it is desirable to apply permanent magnet technology, because in this case there is no need to use current to produce the basic excitation of the machine. This promotes the effectiveness of copper use in the stator, and further, there is no rotor current in these machines. Again, if permanent magnets with a high remanent flux density are used, the air gap flux density can be higher than in conventional induction motors. These advantages have raised the popularity of PMSMs in some challenging applications, such as hybrid electric vehicles (HEV), wind turbines, and home appliances. Usually, a correctly designed PMSM has a higher efficiency and consequently lower losses than its induction machine counterparts. Therefore, the use of these electrical machines reduces the energy consumption of the whole system to some extent, which can provide good motivation to apply permanent magnet technology to electrical machines. However, the cost of high performance rare earth permanent magnets in these machines may not be affordable in many industrial applications, because the tight competition between the manufacturers dictates the rules of low-cost and highly robust solutions, where asynchronous machines seem to be more feasible at the moment. Two main electromagnetic components of an electrical machine are the stator and the rotor. In the case of a conventional radial flux PMSM, the stator contains magnetic circuit lamination and stator winding, and the rotor consists of rotor steel (laminated or solid) and permanent magnets. The lamination itself does not significantly influence the total cost of the machine, even though it can considerably increase the construction complexity, as it requires a special assembly arrangement. However, thin metal sheet processing methods are very effective and economically feasible. Therefore, the cost of the machine is mainly affected by the stator winding and the permanent magnets. The work proposed in this doctoral dissertation comprises a description and analysis of two approaches of PMSM cost reduction: one on the rotor side and the other on the stator side. The first approach on the rotor side includes the use of low-cost and abundant ferrite magnets together with a tooth-coil winding topology and an outer rotor construction. The second approach on the stator side exploits the use of a modular stator structure instead of a monolithic one. PMSMs with the proposed structures were thoroughly analysed by finite element method based tools (FEM). It was found out that by implementing the described principles, some favourable characteristics of the machine (mainly concerning the machine size) will inevitable be compromised. However, the main target of the proposed approaches is not to compete with conventional rare earth PMSMs, but to reduce the price at which they can be implemented in industrial applications, keeping their dimensions at the same level or lower than those of a typical electrical machine used in the industry at the moment. The measurement results of the prototypes show that the main performance characteristics of these machines are at an acceptable level. It is shown that with certain specific actions it is possible to achieve a desirable efficiency level of the machine with the proposed cost reduction methods.

Sekaelementit absoluuttisten solmukoordinaattien menetelmässä

Tässä lisensiaatintyössä käsitellään sekaelementtien sovellusmahdollisuuksia absoluuttisten solmukoordinaattien menetelmässä. Absoluuttisten solmukoordinaattien menetelmä on uudentyyppinen lähestymistapa elementtimenetelmän elementtien koordinaattien määrittämiseksi ja sen yhtenä tavoitteena on tehostaa suuria siirtymiä tai kiertymiä sisältävien elementtien laskentatehokkuutta. Tässä työssä absoluuttisten solmukoordinaattien menetelmä esitellään pääpiirteittäin sekä annetaan esimerkkejä muutamista tyypillisimmistä elementeistä lausuttuna edellä mainittujen koordinaattien perusteella. Sekaelementeiksi kutsutaan elementtityyppejä, missä tuntemattomien muuttujien joukkoja on aina enemmän kuin yksi. Sekaelementit erottavat redusoitumattomista elementeistä siirtymäkentän sisältyminen muuttujaryhmään ja hybridielementeistä muuttujien identtiset ulottuvuudet. Sekaelementtejä käytetään esimerkiksi kokoonpuristumattomien materiaalien rakenneanalyyseissä, alentamaan elementiltä vaadittavia jatkuvuusehtoja tai mallintamaan ilmiöitä, missä fysikaaliset ominaisuudet ovat jostain syystä voimakkaasti toisistaan riippuvaisia. Tämän lisensiaatintyön kirjoittamiseksi on tehty tutkimusta sekaelementtien mahdollisuuksista toimia absoluuttisten solmukoordinaattien menetelmässä. Tutkimuksen tuloksena on saatu aikaan kaksi tässä työssä esiteltävää, varsin rajatun toimintakyvyn omaavaa sekaelementtityyppiä, joiden siirtymäkentät on määritelty globaalien koordinaattien suhteen sisältäen myös orientaatiotermit. Tutkimusaihe vaatii kuitenkin vielä paljon lisätyötä, ennen kuin sekaelementtityyppejä voidaan kauttaaltaan soveltaa absoluuttisten solmukoordinaattien menetelmällä toteutetuissa rakenneanalyyseissä.

Finite Element Analysis of Warship Structures

Warships are generally sleek, slender with V shaped sections and block coefficient below 0.5, compared to fuller forms and higher values for commercial ships. They normally operate in the higher Froude number regime, and the hydrodynamic design is primarily aimed at achieving higher speeds with the minimum power. Therefore the structural design and analysis methods are different from those for commercial ships. Certain design guidelines have been given in documents like Naval Engineering Standards and one of the new developments in this regard is the introduction of classification society rules for the design of warships.The marine environment imposes subjective and objective uncertainties on ship structure. The uncertainties in loads, material properties etc.,. make reliable predictions of ship structural response a difficult task. Strength, stiffness and durability criteria for warship structures can be established by investigations on elastic analysis, ultimate strength analysis and reliability analysis. For analysis of complicated warship structures, special means and valid approximations are required.Preliminary structural design of a frigate size ship has been carried out . A finite element model of the hold model, representative of the complexities in the geometric configuration has been created using the finite element software NISA. Two other models representing the geometry to a limited extent also have been created —- one with two transverse frames and the attached plating alongwith the longitudinal members and the other representing the plating and longitudinal stiffeners between two transverse frames. Linear static analysis of the three models have been carried out and each one with three different boundary conditions. The structural responses have been checked for deflections and stresses against the permissible values. The structure has been found adequate in all the cases. The stresses and deflections predicted by the frame model are comparable with those of the hold model. But no such comparison has been realized for the interstiffener plating model with the other two models.Progressive collapse analyses of the models have been conducted for the three boundary conditions, considering geometric nonlinearity and then combined geometric and material nonlinearity for the hold and the frame models. von Mises — lllyushin yield criteria with elastic-perfectly plastic stress-strain curve has been chosen. ln each case, P-Delta curves have been generated and the ultimate load causing failure (ultimate load factor) has been identified as a multiple of the design load specified by NES.Reliability analysis of the hull module under combined geometric and material nonlinearities have been conducted. The Young's Modulus and the shell thickness have been chosen as the variables. Randomly generated values have been used in the analysis. First Order Second Moment has been used to predict the reliability index and thereafter, the probability of failure. The values have been compared against standard values published in literature.

Finite-Elemente-Mehrgitter von Molekülen

Im Rahmen der Dichtefunktionaltheorie wurden Orbitalfunktionale wie z.B. B3LYP entwickelt. Diese lassen sich mit der „optimized effective potential“ – Methode selbstkonsistent auswerten. Während sie früher nur im 1D-Fall genau berechnet werden konnte, entwickelten Kümmel und Perdew eine Methode, bei der das OEP-Problem unter Verwendung einer Differentialgleichung selbstkonsistent gelöst werden kann. In dieser Arbeit wird ein Finite-Elemente-Mehrgitter-Verfahren verwendet, um die entstehenden Gleichungen zu lösen und damit Energien, Dichten und Ionisationsenergien für Atome und zweiatomige Moleküle zu berechnen. Als Orbitalfunktional wird dabei der „exakte Austausch“ verwendet; das Programm ist aber leicht auf jedes beliebige Funktional erweiterbar. Für das Be-Atom ließ sich mit 8.Ordnung –FEM die Gesamtenergien etwa um 2 Größenordnungen genauer berechnen als der Finite-Differenzen-Code von Makmal et al. Für die Eigenwerte und die Eigenschaften der Atome N und Ne wurde die Genauigkeit anderer numerischer Methoden erreicht. Die Rechenzeit wuchs erwartungsgemäß linear mit der Punktzahl. Trotz recht langsamer scf-Konvergenz wurden für das Molekül LiH Genauigkeiten wie bei FD und bei HF um 2-3 Größenordnungen bessere als mit Basismethoden erzielt. Damit zeigt sich, dass auf diese Weise benchmark-Rechnungen durchgeführt werden können. Diese dürften wegen der schnellen Konvergenz über der Punktzahl und dem geringen Zeitaufwand auch auf schwerere Systeme ausweitbar sein.

Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite-element velocity/surface-elevation pairs that are used to approximate the linear shallow-water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P0-P1, RT0 and P-P1 pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?