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    Wyświetlanie 1-7 z 7
    Tytuł:
    Crack detection by the topological gradient method
    Autorzy:
    Amstutz, S.
    Horchani, I.
    Masmoudi, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970147.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    wykrywanie pęknięć
    wrażliwość topologiczna
    gradient topologiczny
    równanie Poissona
    crack detection
    topological sensitivity
    topological gradient
    Poisson equation
    Opis:
    The topological sensitivity analysis consists in studying the behavior of a shape functional when modifying the topology of the domain. In general, the perturbation under consideration is the creation of a small hole. In this paper, the topological asymptotic expansion is obtained for the Laplace equation with respect to the insertion of a short crack inside a plane domain. This result is illustrated by some numerical experiments in the context of crack detection.
    Źródło:
    Control and Cybernetics; 2005, 34, 1; 81-101
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Algorithm of rebuilding a boundary of domain during creation of an optimal shape
    Autorzy:
    Freus, K.
    Freus, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/122780.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Laplace equation
    boundary element method
    heat transfer
    topological-shape sensitivity method
    równanie Laplace'a
    metoda elementów brzegowych
    wymiana ciepła
    Opis:
    In order to achieve the desired topology we often have to remove material of the area considered. This work presents the author's algorithm which can be used in the reconstruction of the boundary of domain after elimination of a certain amount of material. The paper introduces some details about the procedure that allows one to achieve the expected shape of a domain. The topological-shape sensitivity method for the Laplace equation is used to obtain an optimal topology, whereas numerical methodology utilizes the boundary element method. In the conclusion of the paper the example of computation is shown.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 1; 17-24
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Applying the topological derivative and the boundary element method to design of shape of the heat exchanger
    Autorzy:
    Freus, K.
    Freus, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/122334.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    topological derivative
    topological sensitivity
    Laplace equation
    boundary element method
    heat transfer
    Opis:
    In this work, the topological derivative for the Laplace equation is used to solve a design problem. This derivative describes the sensitivity of the problem when a small hole is formed at an arbitrary point of the domain. The goal of this work is to design topology of the domain when the Robin condition is imposed on the holes. Physically, the holes can be construed as cooling channels. For finding the solution of the governing equation the boundary element method is applied. The final part of the paper presents the design of the heat exchanger and results of computations.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 2; 5-12
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Determination of an optimal shape of domain using the topological derivative and the Boundary Element Method
    Autorzy:
    Freus, K.
    Freus, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/122328.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    topological derivative
    topological sensitivity
    topology optimization
    heat transfer
    Laplace equation
    boundary element method
    pochodna topologiczna
    wrażliwość topologiczna
    optymalizacja topologiczna
    wymiana ciepła
    równanie Laplace'a
    metoda elementów brzegowych
    Opis:
    In the paper, the topological derivative for the Laplace equation is taken into account. The governing equation is solved by means of the Boundary Element Method. The topological-shape sensitivity method is used to determine the points showing the lowest sensitivities. On the selected points, material is eliminated by opening a hole, using the appropriate iterative process. This one is halted when a given amount of material is removed. The objective of this work is to obtain an optimal topology of the domain considered. In the final part of the paper, the example of computations is shown.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 4; 41-48
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Adaptive finite elements based on sensitivities fortopological mesh changes
    Autorzy:
    Friederich, J.
    Leugering, G.
    Steinmann, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/205694.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    adaptive mesh refinement
    sensitivity-based refinement
    topological sensitivity
    asymptotic expansion
    Opis:
    We propose a novel approach to adaptive refinement in FEM based on local sensitivities for node insertion. To this end, we consider refinement as a continuous graph operation, for instance by splitting nodes along edges. Thereby, we introduce the concept of the topological mesh derivative for a given objective function. For its calculation, we rely on the first-order asymptotic expansion of the Galerkin solution of a symmetric linear second-order elliptic PDE. In this work, we apply this concept to the total potential energy, which is related to the approximation error in the energy norm. In fact, our approach yields local sensitivities for minimization of the energy error by refinement. Moreover, we prove that our indicator is equivalent to the classical explicit a posteriori error estimator in a certain sense. Numerical results suggest that our method leads to efficient and competitive adaptive refinement.
    Źródło:
    Control and Cybernetics; 2014, 43, 2; 279-306
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Chaos theory from the mathematical point of view
    Autorzy:
    Kwietniak, Dominik
    Oprocha, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/748392.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    topological dynamics, chaos, topological entropy, topological transitivity, topological horseshoe, Li-Yorke chaos, Auslander-Yorke chaos, Devaney chaos, distributional chaos, Li-Yorke pair, sensitivity.
    Opis:
    Niniejsza praca stanowi próbę przedstawienia istniejących definicji chaosu dla dyskretnych układów dynamicznych. Dyskusję zawężono do zagadnień związanych z dynamiką topologiczną. Przedstawiono i umotywowano definicje: wrażliwości na warunki początkowe, chaosu w sensie Li i Yorke’a, Auslandera i Yorke’a, Devaneya, chaosu dystrybucyjnego, entropii topologicznej i podkowy topologicznej. Podzielono się pewnymi uwagami historycznymi. Omówiono znane związki między różnymi definicjami chaosu i przypomniano związane z nimi problemy otwarte.
    This work is intended as an attempt to survey existingde finitions of chaos for discrete dynamical systems. Discussion is restricted to the settingof topological dynamics, while the measure-theoretic (ergodic theory) and smooth (differentiable dynamical systems) aspects are omitted as exceedingt he scope of this paper. Chaos theory is understood here as a part of topological dynamics, so aforementioned definitions of chaos are just examples of particular dynamical system properties, and are considered inside the framework of the mathematical theory of discrete dynamical systems. It is not the purpose of this article to study chaos theory understood as a new kind of interdisciplinary branch of science devoted to nonlinear phenomena. As for prerequisites, the reader is expected to possess some mathematical maturity, and to be familiar with basic topology of (compact) metric spaces. No preliminary knowledge of the dynamical systems theory is required, however some is recommended. The first two section are devoted to general discussion of the term „chaos” and contains authors opinion on this subject. To facilitate access to the rest of the article some relevant material from the dynamical system theory is briefly repeated in the third section. The next section (Section 4) introduces the notion of topological transitivity along with some stronger variants, namely topological mixing and weak mixing. Section 5 gives a detailed account of the famous Sharkovskii’s Theorem in its full generality. This is required for characterization of chaotic interval maps. Sections 6-13 are devoted to various notions of chaos or related to chaos in dynamical systems. Each section contains an attempt to motivate the notion, historical background and formal definition followed with a review of known properties, relations between various notions of chaos, and some relevant open problems. Section 6 is devoted to a sensitivity to initial conditions – a notion which is accepted as a basic indicator of chaotic behavior. Section 7 introduces a definition of chaos accordingt o Auslander and Yorke. Section 8 examines the notion of Li-Yorke pair and Li-Yorke chaos. Section 9 deals with the definition of chaos introduced in Devaney’s book (Devaney chaos). Section 10 recalls some facts connected with symbolic dynamics, which provides a rich source of examples for various interestingb ehavior, and it is an indispensable tool for exploration of many systems. Section 11 describes the so-called “topological horseshoes”, which are generalizations of the famous example due to Smale. The existence of a horseshoe in a given dynamical system proves the existence of a subsystem with a dynamics similar to some symbolic dynamical system, hence with a very complicated behavior. Section 12 gives a brief exposition of the topological entropy and its relation to chaos. The review of various notions of chaos ends with section 13, containingd escription of distributional chaos.
    Źródło:
    Mathematica Applicanda; 2008, 36, 50/09
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topological derivative for linear elastic plate bending problems
    Autorzy:
    Novotny, A. A.
    Feijoo, R. A.
    Padra, C.
    Taroco, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/970132.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    pochodna topologiczna
    analiza wrażliwości kształtu
    sformułowanie wariacyjne
    zginanie płyty
    topological derivative
    shape sensitivity analysis
    variational formulation
    plate bending
    Opis:
    This study concerns the application of the Topological-Shape Sensitivity Method as a systematic procedure to determine the Topological Derivative for linear elastic plate bending problems within the framework of Kirchhoff's kinematic approach. This method, based on classical Shape Sensitivity Analysis, leads to a constructive procedure to obtain the Topological Derivative. Utilising the well known terminology of structural optimization, we adopt, the total potential strain energy as the cost function and the equilibrium equation as the constraint. Variational formulation as well as the direct differentiation method are used to perform the shape derivative of the cost function. Finally, in order to obtain a uniform distribution of bending moments in several plate problems, the Topological Derivative was approximated, by the Finite Element Method, and used to find the best place to insert holes. A simple hard-kill like topology algorithm, which furnishes satisfactory qualitative results in agreement with those reported in the literature, is also shown.
    Źródło:
    Control and Cybernetics; 2005, 34, 1; 339-361
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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