A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

A novel procedure for establishing clinching parameters for high strength steel sheet

The building industry has a particular interest in using clinching as a joining method for frame constructions of light-frame housing. Normally many clinch joints are required in joining of frames.In order to maximise the strength of the complete assembly, each clinch joint must be as sound as possible. Experimental testing is the main means of optimising a particular clinch joint. This includes shear strength testing and visual observation of joint cross-sections. The manufacturers of clinching equipment normally perform such experimental trials. Finite element analysis can also be used to optimise the tool geometry and the process parameter, X, which represents the thickness of the base of the joint. However, such procedures require dedicated software, a skilled operator, and test specimens in order to verify the finite element model. In addition, when using current technology several hours' computing time may be necessary. The objective of the study was to develop a simple calculation procedure for rapidly establishing an optimum value for the parameter X for a given tool combination. It should be possible to use the procedure on a daily basis, without stringent demands on the skill of the operator or the equipment. It is also desirable that the procedure would significantly decrease thenumber of shear strength tests required for verification. The experimental workinvolved tests in order to obtain an understanding of the behaviour of the sheets during clinching. The most notable observation concerned the stage of the process in which the upper sheet was initially bent, after which the deformation mechanism changed to shearing and elongation. The amount of deformation was measured relative to the original location of the upper sheet, and characterised as the C-measure. By understanding in detail the behaviour of the upper sheet, it waspossible to estimate a bending line function for the surface of the upper sheet. A procedure was developed, which makes it possible to estimate the process parameter X for each tool combination with a fixed die. The procedure is based on equating the volume of material on the punch side with the volume of the die. Detailed information concerning the behaviour of material on the punch side is required, assuming that the volume of die does not change during the process. The procedure was applied to shear strength testing of a sample material. The sample material was continuously hot-dip zinc-coated high-strength constructional steel,with a nominal thickness of 1.0 mm. The minimum Rp0.2 proof stress was 637 N/mm2. Such material has not yet been used extensively in light-frame housing, and little has been published on clinching of the material. The performance of the material is therefore of particular interest. Companies that use clinching on a daily basis stand to gain the greatest benefit from the procedure. By understanding the behaviour of sheets in different cases, it is possible to use data at an early stage for adjusting and optimising the process. In particular, the functionality of common tools can be increased since it is possible to characterise the complete range of existing tools. The study increases and broadens the amount ofbasic information concerning the clinching process. New approaches and points of view are presented and used for generating new knowledge.

Design of User Authentication System for Multi-operator wireless LANs

Langattomat lähiverkot ovat viime vuosikymmeninä saavuttaneet suuren suosion. Tässä työssä käsitellään käyttäjien todentamisjärjestelmän suunnittelua ja kehitystä langattomaan monioperaattoriverkkoon. Langattomassa monioperaattoriverkossa käyttäjillä on mahdollisuus käyttää eri operaattoreiden palveluita. Aluksi käsitellään olemassa olevia todentamismenetelmiä ja -järjestelmiä. minkä jälkeen kuvaillaan todentamisjärjestelmä langattomille monioperaattoriverkoille. Todentamisjärjestelmän ratkaisuvaihtoehtoja esitellään kaksi, niin sanotut moni- istunto - ja yksittäisistuntomalli. Moni-istuntomalli on normaali lähestymistapa käyttäjien todentamiseen tietokonejärjestelmissä. Siinä käyttäjän pitää tunnistautua ja todentaa itsensä jokaiselle verkon palvelulle erikseen. Yksittäisistuntomallissa pyritään parempaan luotettavuuteen ja käytettävyyteen. Siinä käyttäjä todentaa itsensä vain kerran ja voi sen jälkeen päästä useisiin palveluihin. Työn loppuosassa kuvaillaan suunnitellun järjestelmän toteutusta. Lisäksi ehdotetaan vaihtoehtoisia toteutustapoja, analysoidaan järjestelmän heikkouksia ja kerrotaan jatkokehitysmahdoillisuuksista.

Development of beam and plate finite elements based on the absolute nodal coordinate formulation

The focus of this dissertation is to develop finite elements based on the absolute nodal coordinate formulation. The absolute nodal coordinate formulation is a nonlinear finite element formulation, which is introduced for special requirements in the field of flexible multibody dynamics. In this formulation, a special definition for the rotation of elements is employed to ensure the formulation will not suffer from singularities due to large rotations. The absolute nodal coordinate formulation can be used for analyzing the dynamics of beam, plate and shell type structures. The improvements of the formulation are mainly concentrated towards the description of transverse shear deformation. Additionally, the formulation is verified by using conventional iso-parametric solid finite element and geometrically exact beam theory. Previous claims about especially high eigenfrequencies are studied by introducing beam elements based on the absolute nodal coordinate formulation in the framework of the large rotation vector approach. Additionally, the same high eigenfrequency problem is studied by using constraints for transverse deformation. It was determined that the improvements for shear deformation in the transverse direction lead to clear improvements in computational efficiency. This was especially true when comparative stress must be defined, for example when using elasto-plastic material. Furthermore, the developed plate element can be used to avoid certain numerical problems, such as shear and curvature lockings. In addition, it was shown that when compared to conventional solid elements, or elements based on nonlinear beam theory, elements based on the absolute nodal coordinate formulation do not lead to an especially stiff system for the equations of motion.

FLASH-OFDM System Performance Studies for Wireless Broadband Network Operator Services

@450 wireless broadband service is Digita’s mobile wireless broadband network service. In @450 network Digita acts as the network operator offering network capacity to service operators. For Digita it is important to know what kind of services its network is capable of and what are the network’s service parameters. The knowledge of the network parameters and the behaviour can be used in advance in the development of new service products. Before a new service product can be offered to service operators a lot of work has to be done. The basic testing is necessary to get an understanding of the basic functionality. The requirement specification has to be done and a new product has to be created. The new product has to be tested. The test results have to be analysed in order to find out if the new product is suitable for real use and with which limitations. The content of this Thesis is the development of wireless technologies, @450 service and network, FLASH-OFDM technology, FLASH-OFDM performance testing and the development of a new service product.

Simulation of structural stress history based on dynamic analysis

Modern machine structures are often fabricated by welding. From a fatigue point of view, the structural details and especially, the welded details are the most prone to fatigue damage and failure. Design against fatigue requires information on the fatigue resistance of a structure’s critical details and the stress loads that act on each detail. Even though, dynamic simulation of flexible bodies is already current method for analyzing structures, obtaining the stress history of a structural detail during dynamic simulation is a challenging task; especially when the detail has a complex geometry. In particular, analyzing the stress history of every structural detail within a single finite element model can be overwhelming since the amount of nodal degrees of freedom needed in the model may require an impractical amount of computational effort. The purpose of computer simulation is to reduce amount of prototypes and speed up the product development process. Also, to take operator influence into account, real time models, i.e. simplified and computationally efficient models are required. This in turn, requires stress computation to be efficient if it will be performed during dynamic simulation. The research looks back at the theoretical background of multibody dynamic simulation and finite element method to find suitable parts to form a new approach for efficient stress calculation. This study proposes that, the problem of stress calculation during dynamic simulation can be greatly simplified by using a combination of floating frame of reference formulation with modal superposition and a sub-modeling approach. In practice, the proposed approach can be used to efficiently generate the relevant fatigue assessment stress history for a structural detail during or after dynamic simulation. In this work numerical examples are presented to demonstrate the proposed approach in practice. The results show that approach is applicable and can be used as proposed.

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.

Numerical simulation of two-chamber plasma sources using finite element method

Numerical simulation of plasma sources is very important. Such models allows to vary different plasma parameters with high degree of accuracy. Moreover, they allow to conduct measurements not disturbing system balance.Recently, the scientific and practical interest increased in so-called two-chamber plasma sources. In one of them (small or discharge chamber) an external power source is embedded. In that chamber plasma forms. In another (large or diffusion chamber) plasma exists due to the transport of particles and energy through the boundary between chambers.In this particular work two-chamber plasma sources with argon and oxygen as active mediums were onstructed. This models give interesting results in electric field profiles and, as a consequence, in density profiles of charged particles.

Finite size effects in superconducting nanocomposites

The present Master’s thesis presents theoretical description of the extraodinary behavior of the confined Indium nanoparticles. Superconducting properties of nanoparticles and nanocomposites are extensively reviewed. Special attention has been paid to phase fluctuation, shell and disordered effects. The experimental data has been obtained and provided by Dmitry Shamshur from Ioffe Physical Technical Institute. The investigated material represents a highly ordered system of silicate spheres filled with indium metal, where the In nanoparticles are interconnected between each other. Bulk indium is a superconductor with crititcal superconducting temperature Tc0 = 3:41 K. But indium nanoparticles exhibit different behavior, the critical temperature rise by approximately 20% up to 4.15 K. As well as transition of the indium particles to type-II superconductivity with high critical magnetic fields. Such diversity is explained by finite size effects which originate from nanosize of the samples.

Simulation and material calibration of ultra high strength steel (UHSS) S960 welded joint under static tensile test utilizing finite element method (FEM)

The aim of this work was to calibrate the material properties including strength and strain values for different material zones of ultra-high strength steel (UHSS) welded joints under monotonic static loading. The UHSS is heat sensitive and softens by heat due to welding, the affected zone is heat affected zone (HAZ). In this regard, cylindrical specimens were cut out from welded joints of Strenx® 960 MC and Strenx® Tube 960 MH, were examined by tensile test. The hardness values of specimens’ cross section were measured. Using correlations between hardness and strength, initial material properties were obtained. The same size specimen with different zones of material same as real specimen were created and defined in finite element method (FEM) software with commercial brand Abaqus 6.14-1. The loading and boundary conditions were defined considering tensile test values. Using initial material properties made of hardness-strength correlations (true stress-strain values) as Abaqus main input, FEM is utilized to simulate the tensile test process. By comparing FEM Abaqus results with measured results of tensile test, initial material properties will be revised and reused as software input to be fully calibrated in such a way that FEM results and tensile test results deviate minimum. Two type of different S960 were used including 960 MC plates, and structural hollow section 960 MH X-joint. The joint is welded by BöhlerTM X96 filler material. In welded joints, typically the following zones appear: Weld (WEL), Heat affected zone (HAZ) coarse grained (HCG) and fine grained (HFG), annealed zone, and base material (BaM). Results showed that: The HAZ zone is softened due to heat input while welding. For all the specimens, the softened zone’s strength is decreased and makes it a weakest zone where fracture happens while loading. Stress concentration of a notched specimen can represent the properties of notched zone. The load-displacement diagram from FEM modeling matches with the experiments by the calibrated material properties by compromising two correlations of hardness and strength.

Hierarchy and Expansiveness in Two-Dimensional Subshifts of Finite Type

Subshifts are sets of configurations over an infinite grid defined by a set of forbidden patterns. In this thesis, we study two-dimensional subshifts offinite type (2D SFTs), where the underlying grid is Z2 and the set of for-bidden patterns is finite. We are mainly interested in the interplay between the computational power of 2D SFTs and their geometry, examined through the concept of expansive subdynamics. 2D SFTs with expansive directions form an interesting and natural class of subshifts that lie between dimensions 1 and 2. An SFT that has only one non-expansive direction is called extremely expansive. We prove that in many aspects, extremely expansive 2D SFTs display the totality of behaviours of general 2D SFTs. For example, we construct an aperiodic extremely expansive 2D SFT and we prove that the emptiness problem is undecidable even when restricted to the class of extremely expansive 2D SFTs. We also prove that every Medvedev class contains an extremely expansive 2D SFT and we provide a characterization of the sets of directions that can be the set of non-expansive directions of a 2D SFT. Finally, we prove that for every computable sequence of 2D SFTs with an expansive direction, there exists a universal object that simulates all of the elements of the sequence. We use the so called hierarchical, self-simulating or fixed-point method for constructing 2D SFTs which has been previously used by Ga´cs, Durand, Romashchenko and Shen.