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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378297%3A_____%2F17%3A00478703" target="_blank" >RIV/68378297:_____/17:00478703 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S1877705817334471" target="_blank" >http://www.sciencedirect.com/science/article/pii/S1877705817334471</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/https://doi.org/10.1016/j.proeng.2017.09.033" target="_blank" >https://doi.org/10.1016/j.proeng.2017.09.033</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

20301 - Mechanical engineering

Projekt

<a href="/cs/project/GA15-01035S" target="_blank" >GA15-01035S: Dynamická stabilita a post-kritické procesy v nekonzervativních a neholonomních stochastických soustavách s interakcemi</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Procedia Engineering

ISBN

—

ISSN

1877-7058

e-ISSN

—

Počet stran výsledku

6

Strana od-do

735-740

Název nakladatele

Elsevier

Místo vydání

Amsterdam

Místo konání akce

Řím

Datum konání akce

10. 9. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000422868900116