FAT-luokkien määritys hitsatuille levyliitoksille käyttämällä lineaarisen murtumismekaniikan särönkasvun simulointia

Työssä tutkittiin hitsattujen levyliitosten väsymiskestävyyden mitoitusarvoja. Hitsien väsymiskestävyyden mitoitusarvot määritettiin lineaarista murtumismekaniikkaa soveltavalla 2D FEM-laskentaohjelmalla. Murtumismekaanisen laskennan tuloksista määriteltiin, eri liitosgeometrioiden ja kuormitustyyppien mukaisia, nimellisen jännityksen väsymismitoitusmenetelmää vastaavia FAT-luokkia, joissa on huomioitu rakenteellinen jännitys hitsiä vastaan kohtisuorassa suunnassa. Tutkittujen liitosten geometriat olivat pääsääntöisesti poikkeavia mitoitusstandardien ja ohjeiden sisältämistä taulukkotapauksista. Laskennassa otettiin huomioon hitsien liittymiskulma perusaineeseen, rajaviivan pyöristykset ja vajaa hitsautumissyvyys. Kuormitustyyppien vaihtelua tutkittiin rakenteellisen jännityksen taivutusosuuden muutoksilla ja kuormaa kantavien X-liitosten risteävien kuormituksien suhteellisilla suuruuksilla. Väsymiskestävyydet määritettiin kuormituskohtaisille kalvo- ja taivutusjännityksille sekä näiden jännitysjakaumien keskiarvoille. Työssä saatuja FAT-luokkia voidaan hyödyntää vastaavien geometrioiden ja kuormitusten yhteydessä, sekä interpoloimalla myös tuloksien väliarvoissa. Työssä käytetyillä menetelmillä voidaan parantaa nimellisen jännityksen mitoitusmenetelmän tarkkuutta ja laajentaa sitä koskemaan myös taulukkotapausten ulkopuolisia liitoksia. Työn tuloksissa on esitetty FAT-luokkia T-, X- ja päittäisliitoksille ja näiden eri kuormitusyhdistelmille.

Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Computational modeling of stented coronary arteries

The application of computational fluid dynamics (CFD) and finite element analysis (FEA) has been growing rapidly in the various fields of science and technology. One of the areas of interest is in biomedical engineering. The altered hemodynamics inside the blood vessels plays a key role in the development of the arterial disease called atherosclerosis, which is the major cause of human death worldwide. Atherosclerosis is often treated with the stenting procedure to restore the normal blood flow. A stent is a tubular, flexible structure, usually made of metals, which is driven and expanded in the blocked arteries. Despite the success rate of the stenting procedure, it is often associated with the restenosis (re-narrowing of the artery) process. The presence of non-biological device in the artery causes inflammation or re-growth of atherosclerotic lesions in the treated vessels. Several factors including the design of stents, type of stent expansion, expansion pressure, morphology and composition of vessel wall influence the restenosis process. Therefore, the role of computational studies is crucial in the investigation and optimisation of the factors that influence post-stenting complications. This thesis focuses on the stent-vessel wall interactions followed by the blood flow in the post-stenting stage of stenosed human coronary artery. Hemodynamic and mechanical stresses were analysed in three separate stent-plaque-artery models. Plaque was modeled as a multi-layer (fibrous cap (FC), necrotic core (NC), and fibrosis (F)) and the arterial wall as a single layer domain. CFD/FEA simulations were performed using commercial software packages in several models mimicking the various stages and morphologies of atherosclerosis. The tissue prolapse (TP) of stented vessel wall, the distribution of von Mises stress (VMS) inside various layers of vessel wall, and the wall shear stress (WSS) along the luminal surface of the deformed vessel wall were measured and evaluated. The results revealed the role of the stenosis size, thickness of each layer of atherosclerotic wall, thickness of stent strut, pressure applied for stenosis expansion, and the flow condition in the distribution of stresses. The thicknesses of FC, and NC and the total thickness of plaque are critical in controlling the stresses inside the tissue. A small change in morphology of artery wall can significantly affect the distribution of stresses. In particular, FC is the most sensitive layer to TP and stresses, which could determine plaque’s vulnerability to rupture. The WSS is highly influenced by the deflection of artery, which in turn is dependent on the structural composition of arterial wall layers. Together with the stenosis size, their roles could play a decisive role in controlling the low values of WSS (<0.5 Pa) prone to restenosis. Moreover, the time dependent flow altered the percentage of luminal area with WSS values less than 0.5 Pa at different time instants. The non- Newtonian viscosity model of the blood properties significantly affects the prediction of WSS magnitude. The outcomes of this investigation will help to better understand the roles of the individual layers of atherosclerotic vessels and their risk to provoke restenosis at the post-stenting stage. As a consequence, the implementation of such an approach to assess the post-stented stresses will assist the engineers and clinicians in optimizing the stenting techniques to minimize the occurrence of restenosis.

Development of finite elements for analysis of biomechanical structures using flexible multibody formulations

The absolute nodal coordinate formulation was originally developed for the analysis of structures undergoing large rotations and deformations. This dissertation proposes several enhancements to the absolute nodal coordinate formulation based finite beam and plate elements. The main scientific contribution of this thesis relies on the development of elements based on the absolute nodal coordinate formulation that do not suffer from commonly known numerical locking phenomena. These elements can be used in the future in a number of practical applications, for example, analysis of biomechanical soft tissues. This study presents several higher-order Euler–Bernoulli beam elements, a simple method to alleviate Poisson’s and transverse shear locking in gradient deficient plate elements, and a nearly locking free gradient deficient plate element. The absolute nodal coordinate formulation based gradient deficient plate elements developed in this dissertation describe most of the common numerical locking phenomena encountered in the formulation of a continuum mechanics based description of elastic energy. Thus, with these fairly straightforwardly formulated elements that are comprised only of the position and transverse direction gradient degrees of freedom, the pathologies and remedies for the numerical locking phenomena are presented in a clear and understandable manner. The analysis of the Euler–Bernoulli beam elements developed in this study show that the choice of higher gradient degrees of freedom as nodal degrees of freedom leads to a smoother strain field. This improves the rate of convergence.

The Fluid Structure Interaction Analysis of a Peristaltic Pump

The thesis work models the squeezing of the tube and computes the fluid motion of a peristaltic pump. The simulations have been conducted by using COMSOL Multiphysics FSI module. The model is setup in axis symmetric with several simulation cases to have a clear understanding of the results. The model captures total displacement of the tube, velocity magnitude, and average pressure fluctuation of the fluid motion. A clear understanding and review of many mathematical and physical concepts are also discussed with their applications in real field. In order to solve the problems and work around the resource constraints, a thorough understanding of mass balance and momentum equations, finite element concepts, arbitrary Lagrangian-Eulerian method, one-way coupling method, two-way coupling method, and COMSOL Multiphysics simulation setup are understood and briefly narrated.

Sähkökoneessa esiintyvien voimien yksityiskohtainen mittausjärjestelmä

Hissiteollisuudessa nostokoneistoina käytettyjen sähkömoottoreiden laatuvaatimukset ovat tiuken-tuneet viime vuosina. Erityisesti koneistojen tuottama ääni ja mekaaninen värähtely ovat olleet jat-kuvasti tiukentuneen tarkastelun alaisena. Hissikoriin ja hissiä ympäröiviin rakenteisiin välittyvästä värähtelystä johtuva ääni on yksi hissin laatuvaikutelmaan merkittävimmin vaikuttavia tekijöitä. Nostokoneisto on yksi tärkeimmistä äänen ja värähtelyn lähteistä hissijärjestelmässä. Koneiston suunnittelulla edellä mainittuja tekijöitä voidaan minimoida. Sähkökoneiden suunnittelussa finiit-tielementtimenetelmien (FEM) käyttö on vakiintunut haastavimmissa sovelluksissa. Kone Oyj:llä nostokoneistoina käytetään aksiaalivuokestomagneettitahtikoneita (AFPMSM), joiden FEM simu-lointiin käytetään yleisesti kolmea eri tapaa. Kukin näistä vaihtoehdoista pitää sisällään omat hyö-tynsä, että haittansa. Suunnittelun kannalta tärkeää on oikean menetelmän valinta ai-ka/informatiivisuus suhteen maksimoimiseksi. Erittäin tärkeää on myös saatujen tulosten oikeelli-suus. Tämän diplomityön tavoite on kehittää järjestelmä, jonka avulla AFPMS-koneen voimia voidaan mitata yksityiskohtaisella tasolla. Järjestelmän avulla voidaan tarkastella käytössä olevien FE-menetelmien tulosten oikeellisuutta sekä äänen että värähtelyn syntymekanismeja. Järjestelmän tarkoitus on myös syventää Kone Oyj tietotaitoa AFPMS-koneiden toiminnasta. Tässä työssä esitellään AFPMS-koneen epäideaalisuuksia, jotka voivat vaikuttaa mittajärjestelmän suunnitteluun. Myös koneen epäideaalisuuksiin lukeutuvaa ääntä on tarkasteltu tässä työssä. Jotta työn tavoitteiden mukaista FE-menetelmien vertailua ja tulosten oikeellisuuden tarkastelua voitai-siin tehdä, myös yleisimpiä AFPMS-koneen FE-menetelmiä tarkastellaan. Työn tuloksena on mittajärjestelmän suunnitelma, jonka avulla voidaan toteuttaa kuuden vapausas-teen voimamittaus jokaiselle koneistomagneetille alle 1N resoluutiolla. Suunnitellun järjestelmän toimivuutta on tarkasteltu FE-menetelmiä käyttäen ja järjestelmässä käytettävän voima-anturin ky-vykkyyttä on todennettu referenssimittauksin. Suunniteltu mittajärjestelmä mahdollistaa sähkömoottorin useiden eri epäideaalisuuksien tarkaste-lun yksityiskohtaisella tasolla. Mittausajatuksen soveltaminen myös muiden koneiden tutkimiseen tarjoaa mahdollisuuksia jatkotutkimuksille.

Mechanical simulation of the endovascular repair of abdominal aortic aneurysms

Ce travail de thèse porte sur la simulation du déploiement des prothèses vasculaires de type stent-graft (SG) lors de la réparation endovasculaire (EVAR) des anévrismes de l’aorte abdominale (AAA). Cette étude se présente en trois parties: (i) tests mécaniques en flexion et compression de SG couramment utilisés (corps et jambage de marque Cook) ainsi que la simulation numérique desdits tests, (ii) développement d’un modèle numérique d’anévrisme, (iii) stratégie de simulation du déploiement des SG. La méthode numérique employée est celle des éléments finis. Dans un premier temps, une vérification du modèle éléments finis (MEF) des SG est realisée par comparaison des différents cas de charge avec leur pendant expérimental. Ensuite, le MEF vasculaire (AAA) est lui aussi vérifié lors d’une comparaison des niveaux de contraintes maximales principales dans la paroi avec des valeurs de la littérature. Enfin, le déploiement est abordé tout en intégrant les cathéters. Les tests mécaniques menés sur les SG ont été simulés avec une différence maximale de 5,93%, tout en tenant compte de la pré-charge des stents. Le MEF de la structure vasculaire a montré des contraintes maximales principales éloignées de 4,41% par rapport à un modèle similaire précédemment publié. Quant à la simulation du déploiement, un jeu complet de SG a pu être déployé avec un bon contrôle de la position relative et globale, dans un AAA spécifique pré-déformé, sans toutefois inclure de thrombus intra-luminal (TIL). La paroi du AAA a été modélisée avec une loi de comportement isotropique hyperélastique. Étant donné que la différence maximale tolérée en milieu clinique entre réalité et simulation est de 5%, notre approche semble acceptable et pourrait donner suite à de futurs développements. Cela dit, le petit nombre de SG testés justifie pleinement une vaste campagne de tests mécaniques et simulations supplémentaires à des fins de validation.

Field Equilibrium Finite Elements for Structural Analysis

Many finite elements used in structural analysis possess deficiencies like shear locking, incompressibility locking, poor stress predictions within the element domain, violent stress oscillation, poor convergence etc. An approach that can probably overcome many of these problems would be to consider elements in which the assumed displacement functions satisfy the equations of stress field equilibrium. In this method, the finite element will not only have nodal equilibrium of forces, but also have inner stress field equilibrium. The displacement interpolation functions inside each individual element are truncated polynomial solutions of differential equations. Such elements are likely to give better solutions than the existing elements.In this thesis, a new family of finite elements in which the assumed displacement function satisfies the differential equations of stress field equilibrium is proposed. A general procedure for constructing the displacement functions and use of these functions in the generation of elemental stiffness matrices has been developed. The approach to develop field equilibrium elements is quite general and various elements to analyse different types of structures can be formulated from corresponding stress field equilibrium equations. Using this procedure, a nine node quadrilateral element SFCNQ for plane stress analysis, a sixteen node solid element SFCSS for three dimensional stress analysis and a four node quadrilateral element SFCFP for plate bending problems have been formulated.For implementing these elements, computer programs based on modular concepts have been developed. Numerical investigations on the performance of these elements have been carried out through standard test problems for validation purpose. Comparisons involving theoretical closed form solutions as well as results obtained with existing finite elements have also been made. It is found that the new elements perform well in all the situations considered. Solutions in all the cases converge correctly to the exact values. In many cases, convergence is faster when compared with other existing finite elements. The behaviour of field consistent elements would definitely generate a great deal of interest amongst the users of the finite elements.

Development and Analysis of a Novel Isosceles Trapezoidal Dielectric Resonator Antenna For Wireless Communication

This thesis describes the development and analysis of an Isosceles Trapezoidal Dielectric Resonator Antenna (ITDRA) by realizing different DR orientations with suitable feed configurations enabling it to be used as multiband, dual band dual polarized and wideband applications. The motivation for this work has been inspired by the need for compact, high efficient, low cost antenna suitable for multi band application, dual band dual polarized operation and broadband operation with the possibility of using with MICs, and to ensure less expensive, more efficient and quality wireless communication systems. To satisfy these challenging demands a novel shaped Dielectric Resonator (DR) is fabricated and investigated for the possibility of above required properties by trying out different orientations of the DR on a simple microstrip feed and with slotted ground plane as well. The thesis initially discusses and evaluates recent and past developments taken place within the microwave industry on this topic through a concise review of literature. Then the theoretical aspects of DRA and different feeding techniques are described. Following this, fabrication and characterization of DRA is explained. To achieve the desired requirements as above both simulations and experimental measurements were undertaken. A 3-D finite element method (FEM) electromagnetic simulation tool, HFSSTM by Agilent, is used to determine the optimum geometry of the dielectric resonator. It was found to be useful in producing approximate results although it had some limitations. A numerical analysis technique, finite difference time domain (FDTD) is used for validating the results of wide band design at the end. MATLAB is used for modeling the ITDR and implementing FDTD analysis. In conclusion this work offers a new, efficient and relatively simple alternative for antennas to be used for multiple requirements in the wireless communication system.

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.

Non-linear mechanical behavior of the elastomer polydimethylsiloxane (PDMS) used in the manufacture of microfluidic devices

Polydimethylsiloxane (PDMS) is the elastomer of choice to create a variety of microfluidic devices by soft lithography techniques (eg., [1], [2], [3], [4]). Accurate and reliable design, manufacture, and operation of microfluidic devices made from PDMS, require a detailed characterization of the deformation and failure behavior of the material. This paper discusses progress in a recently-initiated research project towards this goal. We have conducted large-deformation tension and compression experiments on traditional macroscale specimens, as well as microscale tension experiments on thin-film (≈ 50µm thickness) specimens of PDMS with varying ratios of monomer:curing agent (5:1, 10:1, 20:1). We find that the stress-stretch response of these materials shows significant variability, even for nominally identically prepared specimens. A non-linear, large-deformation rubber-elasticity model [5], [6] is applied to represent the behavior of PDMS. The constitutive model has been implemented in a finite-element program [7] to aid the design of microfluidic devices made from this material. As a first attempt towards the goal of estimating the non-linear material parameters for PDMS from indentation experiments, we have conducted micro-indentation experiments using a spherical indenter-tip, and carried out corresponding numerical simulations to verify how well the numerically-predicted P(load-h(depth of indentation) curves compare with the corresponding experimental measurements. The results are encouraging, and show the possibility of estimating the material parameters for PDMS from relatively simple micro-indentation experiments, and corresponding numerical simulations.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

How to save a bad element with weak boundary conditions

The P-1-P-1 finite element pair is known to allow the existence of spurious pressure (surface elevation) modes for the shallow water equations and to be unstable for mixed formulations. We show that this behavior is strongly influenced by the strong or the weak enforcement of the impermeability boundary conditions. A numerical analysis of the Stommel model is performed for both P-1-P-1 and P-1(NC)-P-1 mixed formulations. Steady and transient test cases are considered. We observe that the P-1-P-1 element exhibits stable discrete solutions with weak boundary conditions or with fully unstructured meshes. (c) 2005 Elsevier Ltd. All rights reserved.