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.

Modal testing and numerical modeling of the dynamic properties of layered sheet-steel structure

Recently, due to the increasing total construction and transportation cost and difficulties associated with handling massive structural components or assemblies, there has been increasing financial pressure to reduce structural weight. Furthermore, advances in material technology coupled with continuing advances in design tools and techniques have encouraged engineers to vary and combine materials, offering new opportunities to reduce the weight of mechanical structures. These new lower mass systems, however, are more susceptible to inherent imbalances, a weakness that can result in higher shock and harmonic resonances which leads to poor structural dynamic performances. The objective of this thesis is the modeling of layered sheet steel elements, to accurately predict dynamic performance. During the development of the layered sheet steel model, the numerical modeling approach, the Finite Element Analysis and the Experimental Modal Analysis are applied in building a modal model of the layered sheet steel elements. Furthermore, in view of getting a better understanding of the dynamic behavior of layered sheet steel, several binding methods have been studied to understand and demonstrate how a binding method affects the dynamic behavior of layered sheet steel elements when compared to single homogeneous steel plate. Based on the developed layered sheet steel model, the dynamic behavior of a lightweight wheel structure to be used as the structure for the stator of an outer rotor Direct-Drive Permanent Magnet Synchronous Generator designed for high-power wind turbines is studied.

Vibrations in Rotating Machinery Arising from Minor Imperfections in Component Geometries

Vibrations in machines can cause noise, decrease the performance, or even damage the machine. Vibrations appear if there is a source of vibration that excites the system. In the worst case scenario, the excitation frequency coincides with the natural frequency of the machine causing resonance. Rotating machines are a machine type, where the excitation arises from the machine itself. The excitation originates from the mass imbalance in the rotating shaft, which always exists in machines that are manufactured using conventional methods. The excitation has a frequency that is dependent on the rotational speed of the machine. The rotating machines in industrial use are usually designed to rotate at a constant rotational speed, the case where the resonances can be easily avoided. However, the machines that have a varying operational speed are more problematic due to a wider range of frequencies that have to be avoided. Vibrations, which frequencies equal to rotational speed frequency of the machine are widely studied and considered in the typical machine design process. This study concentrates on vibrations, which arise from the excitations having frequencies that are multiples of the rotational speed frequency. These vibrations take place when there are two or more excitation components in a revolution of a rotating shaft. The dissertation introduces four studies where three kinds of machines are experiencing vibrations caused by different excitations. The first studied case is a directly driven permanent magnet generator used in a wind power plant. The electromagnetic properties of the generator cause harmonic excitations in the system. The dynamic responses of the generator are studied using the multibody dynamics formulation. In another study, the finite element method is used to study the vibrations of a magnetic gear due to excitations, which frequencies equal to the rotational speed frequency. The objective is to study the effects of manufacturing and assembling inaccuracies. Particularly, the eccentricity of the rotating part with respect to non-rotating part is studied since the eccentric operation causes a force component in the direction of the shortest air gap. The third machine type is a tube roll of a paper machine, which is studied while the tube roll is supported using two different structures. These cases are studied using different formulations. In the first case, the tube roll is supported by spherical roller bearings, which have some wavinesses on the rolling surfaces. Wavinesses cause excitations to the tube roll, which starts to resonate at the frequency that is a half of the first natural frequency. The frequency is in the range where the machine normally operates. The tube roll is modeled using the finite element method and the bearings are modeled as nonlinear forces between the tube roll and the pedestals. In the second case studied, the tube roll is supported by freely rotating discs, which wavinesses are also measured. The above described phenomenon is captured as well in this case, but the simulation methodology is based on the flexible multibody dynamics formulation. The simulation models that are used in both of the last two cases studied are verified by measuring the actual devices and comparing the simulated and measured results. The results show good agreement.

Hygro-elasto-plastic behavior of planar orthotropic material

The mechanical and hygroscopic properties of paper and board are factors affecting the whole lifecycle of a product, including paper/board quality, production, converting, and material and energy savings. The progress of shrinkage profiles, loose edges of web, baggy web causing wrinkling and misregistration in printing are examples of factors affecting runnability and end product quality in the drying section and converting processes, where paper or board is treated as a moving web. The structural properties and internal stresses or plastic strain differences built up during production also cause the end-product defects related to distortion of the shape of the product such as sheet or box. The objective of this work was to construct a model capable of capturing the characteristic behavior of hygroscopic orthotropic material under moisture change, during different external in-plane stretch or stress conditions. Two independent experimental models were constructed: the elasto-plastic material model and the hygroexpansivity-shrinkage model. Both describe the structural properties of the sheet with a fiber orientation probability distribution, and both are functions of the dry solids content and fiber orientation anisotropy index. The anisotropy index, introduced in this work, simplifies the procedure of determining the constitutive parameters of the material model and the hygroexpansion coefficients in different in-plane directions of the orthotropic sheet. The mathematically consistent elasto-plastic material model and the dry solids content dependent hygroexpansivity have been constructed over the entire range from wet to dry. The presented elastoplastic and hygroexpansivity-shrinkage models can be used in an analytical approach to estimate the plastic strain and shrinkage in simple one-dimensional cases. For studies of the combined and more complicated effects of hygro-elasto-plastic behavior, both models were implemented in a finite element program for a numerical solution. The finite element approach also offered possibilities for studying different structural variations of orthotropic planar material, as well as local buckling behavior and internal stress situations of the sheet or web generated by local strain differences. A comparison of the simulation examples presented in this work to results published earlier confirms that the hygro-elasto-plastic model provides at least qualitatively reasonable estimates. The application potential of the hygro-elasto-plastic model is versatile, including several phenomena and defects appearing in the drying, converting and end-use conditions of the paper or board webs and products, or in other corresponding complex planar materials.

Distortion and internal warping torsion of a double symmetric hollow section

This thesis is made in cooperation with Laboratory of Steel Structures and the steel company SSAB. Maximization of the benefits of high-strength steel usually requires the usage of thin wall thicknesses. This means the failures related to buckling, distortion and warping stand out. One must be aware of these phenomena to design thin-walled structures stressed with forces such as torsional loading. It is also important to take into account small stress ranges when evaluating the accurate fatigue strength of structures. The objective of this thesis is to clarify the theory of the uniform and non-uniform torsion. This paper focuses on warping due to the non-uniform torsion in double symmetric box girder and structural hollow section. The arisen stress states are explained and researched using the finite element method. Another research target is the distortion in double symmetric box girder due to torsion, and the restraining effect of transverse diaphragms at the load end. Multiple transverse diaphragms are used to study more efficient restraining against warping and distortion than a common one end plate structure.

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.

Pyörivän keskiökärjen rakenteen kehittäminen työstövärähtelyjen välttämiseksi sorvauksessa

Tässä diplomityössä käsitellään sorvauksen työstövärähtelyjen ja sorvin keskiökärjen rakenteen yhteyttä. Työ on osa Lappeenrannan teknillisen yliopiston VMAX-projektia, ja sen taustalla on pyrkimys uudenlaisen, sorvin kärkipylkän puristusvoiman ajonaikaiseen säätämiseen perustuvan työstövärähtelyjen välttämismenetelmän kehittämiseen. Tämän menetelmän toiminnan todentaminen oli työn ensimmäinen tavoite. Menetelmän toteuttaminen asettaa kuitenkin käytetyn keskiökärjen rakenteelle tiettyjä vaatimuksia. Työn toisena tavoitteena oli nämä vaatimukset täyttävän keskiökärjen prototyypin kehittäminen. Tutkimus eteni seuraavasti. Ensimmäiseksi ongelma määriteltiin tutustumalla työn teoreettiseen taustaan ja aiheeseen liittyvään tutkimukseen Lappeenrannan teknillisestä yliopistosta ja muualta. Myös keskiökärkiä valmistavien yritysten tuotekatalogeja tarkasteltiin. Seuraavaksi siirryttiin alustavaan suunnitteluvaiheeseen, jossa verifioitiin menetelmän toiminta ja luotiin konsepteja keskiökärjen rakenteen kehittämistä varten. Tämän alustavan vaiheen jälkeen suoritettiin suunnitteluprosessi keskiökärjen prototyypille. Lopuksi, suunnitellun prototyypin rakenteen käyttäytymistä arvioitiin tietokonemallinnuksen avulla. Lisätuloksena tutkimuksen aikana johdettiin yksinkertaistettu elementtimenetelmään perustuva laskentamalli järjestelmän ominaistaajuuksien selvittämiseksi. Laskentamallin tarkkuutta arvoitiin. Suunnitteluprosessin tuloksena saatiin kaikki menetelmän toiminnan sekä normaalin käytön asettamat vaatimukset täyttävä rakenne keskiökärjen prototyypille. Myös johdetun laskentamallin tulokset ovat varsin lähellä 3D-elementtimallinnuksen antamia tuloksia. Tutkimuksen tavoitteiden voidaan siis sanoa toteutuneen. Koska prototyyppiä ja laskentamallia ei kuitenkaan ole vielä kokeellisesti verifioitu, tämä ei ole täysin varmaa.

Inventive design and product development of a mechanical element

The thesis is dedicated to enhancement and development of a Mechanism in Company X in order to increase its key parameters and approve its workability. Current Mechanism model is described in details. The basis of various analysis, models and theories that are reflecting the working process of the Mechanism are included in the thesis. According to these three directions of enhancements are chosen: from mechanical, tribological and conceptual points of view. As the result the list of improvements is presented. The new models of Mechanism are built. The efficiency and lifetime value are obtained in accordance with corresponding estimations. The comparative analysis confirms the necessity of conducted changes. Recommendations for the Company X specialists are represented in the thesis. Proposals for deeper research are also suggested.

The importance of package design to Japanese consumers: The role of visual and informational elements of package design in decision making

The importance of package design as a marketing tool is growing as the competition in retail environment increases. However, there is a lack of studies on how each element of package design affects consumer decisions in different countries. The objective of this thesis is to study the role of package design to Japanese consumers. The research was conducted through an experiment with a sample of 37 Japanese female participants. They were divided into two groups and were given different tasks: one group had to choose a chocolate for themselves, and the other for a group of friends. The participants were presented with 15 different Finnish chocolate boxes to choose from. The qualitative data was gathered through observation and semi-structured interviews. In addition, data from questionnaires was quantified and all the data was triangulated. The empirical results suggest that visual elements strongly affect the decision making of Japanese consumers. Image was the most important element which acted as both, a visual and an informational aspect in the experiment. Informational elements on the other hand have little effect, especially when the context is written in a foreign language. However, informational elements affected participants who were choosing chocolates for a group of friends. A unique finding was the importance of kawaii (cuteness) to Japanese consumers.

Influence of the polymorphisms of the α-major regulatory element HS-40 on in vitro gene expression

The α-MRE is the major regulatory element responsible for the expression of human α-like globin genes. It is genetically polymorphic, and six different haplotypes, named A to F, have been identified in some population groups from Europe, Africa and Asia and in native Indians from two Brazilian Indian tribes. Most of the mutations that constitute the α-MRE haplotypes are located in flanking sequences of binding sites for nuclear factors. To our knowledge, there are no experimental studies evaluating whether such variability may influence the α-MRE enhancer activity. We analyzed and compared the expression of luciferase of nine constructs containing different α-MRE elements as enhancers. Genomic DNA samples from controls with A (wild-type α-MRE) and B haplotypes were used to generate C-F haplotypes by site-directed mutagenesis. In addition, three other elements containing only the G→A polymorphism at positions +130, +199, and +209, separately, were also tested. The different α-MRE elements were amplified and cloned into a plasmid containing the luciferase reporter gene and the SV40 promoter and used to transiently transfect K562 cells. A noticeable reduction in luciferase expression was observed with all constructs compared with the A haplotype. The greatest reductions occurred with the F haplotype (+96, C→A) and the isolated polymorphism +209, both located near the SP1 protein-binding sites believed not to be active in vivo. These are the first analyses of α-MRE polymorphisms on gene expression and demonstrate that these single nucleotide polymorphisms, although outside the binding sites for nuclear factors, are able to influence in vitro gene expression.

Short-term levosimendan treatment protects rat testes against oxidative stress

The objective of this study was to evaluate the effect of short-term levosimendan exposure on oxidant/antioxidant status and trace element levels in the testes of rats under physiological conditions. Twenty male Wistar albino rats were randomly divided into two groups of 10 animals each. Group 1 was not exposed to levosimendan and served as control. Levosimendan (12 µg/kg) diluted in 10 mL 0.9% NaCl was administered intraperitoneally to group 2. Animals of both groups were sacrificed after 3 days and their testes were harvested for the determination of changes in tissue oxidant/antioxidant status and trace element levels. Tissue malondialdehyde (MDA) was significantly lower in the levosimendan group (P < 0.001) than in the untreated control group and superoxide dismutase and glutathione peroxidase (GSH-Px) levels were significantly higher in the levosimendan group (P < 0.001). Carbonic anhydrase, catalase and GSH levels were not significantly different from controls. Mg and Zn levels of testes were significantly higher (P < 0.001) and Co, Pb, Cd, Mn, and Cu were significantly lower (P < 0.001) in group 2 compared to group 1. Fe levels were similar for the two groups (P = 0.94). These results suggest that 3-day exposure to levosimendan induced a significant decrease in tissue MDA level, which is a lipid peroxidation product and an indicator of oxidative stress, and a significant increase in the activity of an important number of the enzymes that protect against oxidative stress in rat testes.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Development of the Food List for a Brazilian Total Diet Study

The objective of this paper is to establish a methodology for the Food List for the southeastern region of Brazil, according to the Total Diet Study (TDS) harmonized methodology at international level. The Food List can provide data for a further TDS with evaluation of essential and toxic element dietary intakes by food analysis in laboratories. The food consumption data source used was from 2008-2009 Household Budget Survey, by the Brazilian Institute of Geography and Statistics. The Food List was composed of 82 food items grouped into 19 food groups. It reflects 100% of the daily individual food consumption inside and outside Brazilian southeastern population households. According to the recommendation that each country should carry out their own TDS and the TDS methodology used, the Food List construction can contribute to the Food List of other Brazilian regions and other countries, besides allowing the TDS development. Additionally, the Food List showed the typical diet for the southeastern region of Brazil.

Survey of trace element and dietetic fiber composition of “Leblebi” which is a local snack food consumed in Turkey

Abstract In Turkey and several Middle East countries' people consume “leblebi” which is a traditional snack food made from chickpeas (Cicer arietinum L.). Chickpea products are highly nutritive and a cheap food for human consumption and have become an essential part of daily diets in the world. The present study aims to determine the chemical, nutritional and dietary composition of fifty leblebi samples marketed in Turkey. Protein values of the leblebi ranged from 19.4 to 23.9% dehulled and 20.3 to 20.8% for nondehulled leblebi while a value of 19.1% was recorded for chickpeas. Mineral results showed that Potassium (K) was the most abundant element in leblebi ranging from 6514 to 14431 mg/kg. The amount of dietary components neutral detergent fibre (NDF), acid detergent fibre (ADF), acid detergent lignin (ADL) and cellulose did not vary much between the samples analyzed.