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Evolutionary analysis of Fokker-Planck equation using multi-dimensional Finite Element Method
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SYSNO ASEP 0478703 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Evolutionary analysis of Fokker-Planck equation using multi-dimensional Finite Element Method Author(s) Náprstek, Jiří (UTAM-F) RID, ORCID, SAI
Král, Radomil (UTAM-F) RID, SAINumber of authors 2 Source Title Procedia Engineering, X International Conference on Structural Dynamics, EURODYN 2017, 199. - Amsterdam : Elsevier, 2017 / Vestroni F. ; Romeo F. ; Gattulli V. - ISSN 1877-7058 Pages s. 735-740 Number of pages 6 s. Publication form Print - P Action EURODYN 2017, International Conference on Structural Dynamics /10./ Event date 10.09.2017 - 13.09.2017 VEvent location Řím Country IT - Italy Event type WRD Language eng - English Country GB - United Kingdom Keywords Fokker-Planck equation ; Finite Element Method ; simplex element ; multi-dimensional problem ; non-linear aero-elastic systems Subject RIV JM - Building Engineering OECD category Mechanical engineering R&D Projects GA15-01035S GA ČR - Czech Science Foundation (CSF) Institutional support UTAM-F - RVO:68378297 UT WOS 000422868900116 EID SCOPUS 85029908986 DOI https://doi.org/10.1016/j.proeng.2017.09.033 Annotation Response characteristics, stability and other problems of non-linear dynamic systems under randomly variable loading are mostly analyzed by means of Fokker-Planck equation. However, possibilities of its analytical investigation are very limited and rather restricted to steady state problems only. Thus a number of non-conventional problems are out of effect of this popular tool. So the Finite Element Method reveals to be a powerful or sometimes the only applicable approach for analysis of non-stationary problems, as for instance quasi-periodic response, post-critical states, unstable states in time limited period, special configuration of boundary conditions, etc. However, a number of specific problems must be overcome. They follow predominantly from the large multi-dimensionality of the Fokker-Planck equation, shape of the definition domain and special requirements on the nature of the solution form, which is out of a common practice of Finite Element employment. In particular: (i) selection of the element type, (ii) development of new original algorithms for multi-dimensional element mesh generation and (iii) working out the original procedures for governing differential and algebraic systems assembling and their subsequent solution. A couple of illustrative examples dealing with SDOF and TDOF systems under random excitation of additive and multiplicative types are presented. Workplace Institute of Theoretical and Applied Mechanics Contact Kulawiecová Kateřina, kulawiecova@itam.cas.cz, Tel.: 225 443 285 Year of Publishing 2018 Electronic address http://www.sciencedirect.com/science/article/pii/S1877705817334471
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