Contact problems with respect to the formation and propagation of heat

Import 06/11/2014Hlavním cílem této diplomové práce je odvození matematického modelu termo-dynamického kontaktního problému, který by byl jednoduše aplikovatelný na numerický výpočet. Uvažujeme úlohu ve které je deformace těles ovlivněna vznikem tepla a jeho šířením, a opačně také vliv deformace těles na teplotu materiálu. K tomu dochází především v místě kontaktu, kde uvažujeme Coulombovský model tření závislý na tlaku na kontaktní hranici. Nejprve z fyzikálního modelu odvozujeme slabé formulace, které diskretizujeme v prostoru a čase. Tyto tvary převádíme na duální problém v Lagrangeovských multiplikátorech, které jsou vhodnější pro numerický výpočet. V poslední části popisujeme postup numerického řešení. Na závěr čtenář nalezne řešení úlohy pomocí postupu představeného v tomto textu.This thesis focuses mainly on the derivation of mathematical model of contact thermo-dynamics, which can be apply on numerical algorithm. We consider problem, where the thermal expansion affects displacement and vice versa where the displacement of solid influences temperature of the material. This happens especially on the contact boundary of each body, where we consider Coulomb friction, which depends on pressure on contact boundary. Firstly from physical equations we derive weak formulations and discretize them in space and time. We transform this equations into dual problem in Lagrange multipliers, which are more sutiable for numerical computation. In last part we describe the process of finding the numerical solution. At the end reader can see solution of problem based on process derived in this text.470 - Katedra aplikované matematikyvýborn

Předmět pedagogiky a pojetí sociální pedagogiky

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České pedagogické myšlení poslední doby a sociální pedagogika

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Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up

We investigate a particle system which is a discrete and deterministic approximation of the one-dimensional Keller-Segel equation with a logarithmic potential. The particle system is derived from the gradient flow of the homogeneous free energy written in Lagrangian coordinates. We focus on the description of the blow-up of the particle system, namely: the number of particles involved in the first aggregate, and the limiting profile of the rescaled system. We exhibit basins of stability for which the number of particles is critical, and we prove a weak rigidity result concerning the rescaled dynamics. This work is complemented with a detailed analysis of the case where only three particles interact

Homogenization of Composite Materials

Import 11/07/2012Import 03/08/2012Tato práce se zabývá kompozitními materiály a jejich matematickým převodem na materiál homogenní stejných vlastností. Je zde zkoumáno, jakým způsobem musí být kompozit složen, aby navenek jevil vlastnosti homogenního materiálu. Problém je převeden na okrajovou úlohu rovnice vedení tepla v 1D na intervalu \left<0,1\right>. Konkrétně je zde řešena periodická úloha, zadaná diferenciální rovnicí druhého řádu $-\big(a(x) \cdot u'(x)\big)'=f(x)$ s vhodnými okrajovými podmínkami. Řešení získáno pomocí metody konečných prvků a řešení pomocí asymptotické expanze je porovnáváno s limitním řešením. S různými funkcemi jsou hledány případy, kdy se materiál jeví jako homogenní.This thesis deals with composite materials and their mathematical transfer to homogenic material with same nature. Is exemined, how composite material is composed, to be seen as homogenic material. Problem is transform to boundary value problem of heat conduction equation in 1D on interval \left<0,1\right>. Specifically is solved periodical problem, specified with second order differential equation $-\big(a(x) \cdot u'(x)\big)'=f(x)$ with appropriate boundry value. Solution is obtained by finite element method and asymptotic expansion and is compared with limit solution. There are looked for instances, when composit is seen as homogenic matherial.470 - Katedra aplikované matematikydobř

Hloubkové kypřiče, jejich využití a význam při pěstování obilovin a řepky ozimé

This bachelor thesis comprehensively deals with depth soil cultivators. Their use in soil treatment and planting of stands is deeply discussed. Types of depth soil cultivators are described and demanding agrotechnical requirements are defined. This work also reveals minimization technologies for soil treatment and their influence on cultivation of individual plant species together with advantages and disadvantages of this soil treatment method. In the first part of this thesis, the history of soil treatment is briefly summarized from the very beginning of the agriculture development to the modern technologies. The types of soil treatment systems and development of the use of minimization technologies are discussed in this part together with explanation of their expansion and with reasons describing the development of their application in agriculture. Methodology of characteristics of agricultural enterprise and measured machinery is described in practical part. The data processed and evaluated by this methodology were measured on the fields owned by Zemědělské družstvo Bernartice and cultivated using Horsch Terrano 5FM and Strom Terraland TN 3000 H machinery. At the same time, the investment and operating costs and performance of the kits were assessed

Vliv složení směsi UF lepidla a disperzního PVAc lepidla na pevnost lepeného spoje

The thesis deals with the influence of mixture of the mixed adhesive and dispersion PVAc adhesive for bonding strength in shear strength. For the testing were selected two economically very important wood species (the spruce and beech wood) which are used in construction, furniture and building industry. All samples were grouped by the type of adhesive and by the temperature used for 28 days conditioning. All samples were bonded with coating 120 g/m2. After bonding, pressing and conditioning to required temperature were all samples subjected to a test, which examines the bonding strength in shear. The thesis deals with the comparison of the results and examines the effect of the adhesive mixture to bonding strength