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4. matematický workshop 20. října 2005

On the optimization of microstructurally motivated calculations in engineering mechanics O optimalizaci mikrostrukturálně motivovaných výpočtů v inženýrské mechanice. 4. matematický workshop 20. října 2005. Jiří Vala ( vala.j@fce.vutbr.cz ).

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4. matematický workshop 20. října 2005

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  1. On the optimization of microstructurally motivated calculations in engineering mechanicsO optimalizaci mikrostrukturálně motivovaných výpočtů v inženýrské mechanice 4. matematický workshop20. října 2005 Jiří Vala (vala.j@fce.vutbr.cz) Ústav matematiky a deskriptivní geometrie Fakulty stavební VUT v Brně

  2. Topics • Macro- and microanalysis in computational mechanics • Makro- a mikroanalýza ve výpočetní mechanice • Iterative algorithm for a model problem • Iterační algoritmus pro modelový problém • Generalizations and examples of technical applications • Zobecnění a příklady technických aplikací Keywords computations “from nano-scale particles to terrestrial bodies” homogenization techniques two-scale grids  two-scale convergence classical FEM mesh-free methods

  3. Structure of some building materials gas concrete fire-clay brick foam polyethylen 2 types of polyurethan-based insulation straw pannel Stramit Laboratory of Building Physics, Faculty of Civil Engineering,Brno University of Technology

  4. Example:temperature field in the rubber-based insulation in certain part of the window construction 0.1 mm local thermal fluxes ANSYS-supported calculations

  5. Microstructure of some advanced alloys Ni-Al-Cr-Ta alloy superaustenitic iron NICROFER Ni superalloy CMSX4 Bi-Sn-Zn alloy Institute of Physics of Materials, Academy of Sciences of the Czech Republic inBrno

  6. Two basic approaches to two-scale problems: • some multiple levels of not necessarily nested grids considered (and some successive corrections needed) without deeper analysis of microstructural phenomena (Rech et al. 2003, Glowinski et al. 2005, …) • mathematical two-scale convergence (homogenization) theory (as generalization ofG-, H-, Γ-, … convergence)applied • (Nguetseng 1989, Allaire 1992, Holmbom 1997, ...)

  7. Notation

  8. Model elliptic problem

  9. Two-scale convergence

  10. Construction of homogenized characteristics

  11. Iterative algorithm

  12. Projection onto micro- and macroscopic scales

  13. Convergence analysis

  14. Finite element interpolation theory (cf. Zlámal 1968)

  15. Several concluding references to recent author’s papers • heat propagation in buildings: thermal insulation and accumulation J.V. & S.Šťastník, Modelling, July 2005 in Pilsen • diffusivephase transformation in substitutional alloys J.V. & J.Svoboda, Algoritmy, March 2005 in Podbanské J. Svoboda & J. V., Defect & Diffusion Forum 240 (2005), 647-653 J.V., Equadiff, July 2005 in Bratislava • convergence analysis for an iterative algorithm in case of classical FEM J. V., Numerical Methods in Computational Mechanics, August 2005 in Žilina J. V., Journal of Mechanical Engineering, to appear

  16. Thank you for your attention. Questions and remarks are welcome. Supported by GA ČR, Reg. No. 103/05/0292 Better results are being prepared for the 5-th workshop (probably) in Brno in October 2006….

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