Evolutionary analysis of Fokker-Planck equation using multi-dimensional Finite Element Method

0478703 - ÚTAM 2018 RIV GB eng C - Konferenční příspěvek (zahraniční konf.)
Náprstek, Jiří - Král, Radomil
Evolutionary analysis of Fokker-Planck equation using multi-dimensional Finite Element Method.
Procedia Engineering. Vol. 199. Amsterdam: Elsevier, 2017 - (Vestroni, F.; Romeo, F.; Gattulli, V.), s. 735-740. ISSN 1877-7058.
[EURODYN 2017, International Conference on Structural Dynamics /10./. Řím (IT), 10.09.2017-13.09.2017]
Grant CEP: GA ČR(CZ) GA15-01035S
Institucionální podpora: RVO:68378297
Klíčová slova: Fokker-Planck equation * Finite Element Method * simplex element * multi-dimensional problem * non-linear aero-elastic systems
Obor OECD: Mechanical engineering
http://www.sciencedirect.com/science/article/pii/S1877705817334471

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.
Trvalý link: http://hdl.handle.net/11104/0274771