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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-c5ae31f7-a0bb-42b0-82a0-108a74857435

Czasopismo

Control and Cybernetics

Tytuł artykułu

Optimal reliability for components under thermomechanical cyclic loading

Autorzy Bittner, L.  Gottschalk, H. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN We consider the existence of optimal shapes in a context of the thermo-mechanical system of partial differential equations (PDE) using the recent approach based on elliptic regularity theory (Gottschalk and Schmitz, 2015; Agmon, Douglis and Nirenberg, 1959,1964; Gilbarg and Trudinger, 1977). We give an extended and improved definition of the set of admissible shapes based on a class of sufficiently differentiable deformation maps applied to a baseline shape. The obtained set of admissible shapes again allows to prove a uniform Schauder estimate for the elasticity PDE. In order to deal with thermal stress, a related uniform Schauder estimate will be derived for the heat equation. Special emphasis is put on Robin boundary conditions, which are motivated by the convective heat transfer processes. It is shown that these thermal Schauder estimates can serve as an input to the Schauder estimates for the elasticity equation (Gottschalk and Schmitz, 2015). This is needed to prove the compactness of the (suitably extended) solutions of the entire PDE system in some state space that carries a C2-Hölder topology for the temperature field and a C3-Hölder topology for the displacement. From this, one obtains the property of graph compactness, which is the essential tool to prove the existence of optimal shapes. Due to the topologies employed, the method works for objective functionals that depend on the displacement and its derivatives up to third order, as well as on the temperature field and its derivatives up to second order. This general result in shape optimization is then applied to the problem of optimal reliability, i.e. the problem of finding shapes that have minimal failure probability under cyclic thermomechanical loading.
Słowa kluczowe
EN shape optimization   probabilistic failure times   optimal reliability  
Wydawca Systems Research Institute, Polish Academy of Sciences
Czasopismo Control and Cybernetics
Rocznik 2016
Tom Vol. 45, no. 4
Strony 421--455
Opis fizyczny Bibliogr. 26 poz., rys.
Twórcy
autor Bittner, L.
autor Gottschalk, H.
Bibliografia
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[5] Bolten, M., Gottschalk, H., and Schmitz, S. (2015) Minimal failure probability for ceramic design via shape control. Journal of Optimization Theory and Applications, 166:983–1001.
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[8] Ciarlet, P. (1988) Mathematical Elasticity - Volume I: Three-Dimensional Elasticity. Studies in Mathematics and its Applications, 20. NorthHolland.
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[12] Gilbarg, D. and Trudinger, N. S. (1977) Elliptic Partial Differential Equations of Second Order. Springer, Berlin–Heidelberg-New York.
[13] Gottschalk, H. and Schmitz, S. (2015) Optimal reliability in design for fatigue life. Journal of Control and Optimization, 52 (5): 2727–2752.
[14] Haslinger, J. and Mäkinen, R. A. E. (2003) Introduction to Shape Optimization. SIAM.
[15] Hetnarski, R. B. and Eslami, M. R. (2009) Thermal Stresses - Advanced Theory and Applications. Springer, Berlin–Heidelberg–New York.
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[19] McGraw–Hill. Mäde, L., Schmitz, S., Rollmann, G., Gottschalk, H., and Beck, T. (2017) Probabilistic lcf risk evaluation of a turbine vane by combined size effect and notch support modeling. ASME-Turbo Expo, GT2017–64408.
[20] Pflug, G. C. and Römisch, W. (2007) Modeling, Measuring and Managing Risk. World Scientific.
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[22] Schmitz, S. (2014) A Local and Probabilistic Model for Low-Cycle Fatigue: New Aspects of Structural Analysis. Hartung–Gorre.
[23] Schmitz, S., Beck, T., Krause, R., Rollmann, G., Seibel, T., and Gottschalk, H. (2013a) A probabilistic model for lcf. Computational Materials Science, 79:584–590.
[24] Schmitz, S., Seibel, T., Gottschalk, H., Beck, T., Rollmann, G., and Krause, R. (2013b) Probabilistic analysis of the lcf crack initiation life for a turbine blade under thermo–mechanical loading. Proc. Int. Conf LCF 7. Deutscher Verband für Materialforschung und Prüfung, Berlin.
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Uwagi
PL Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
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