Multi-dimensional Fokker-Planck equation analysis using the modified finite element method

0465305 - ÚTAM 2017 RIV GB eng J - Článek v odborném periodiku
Náprstek, Jiří - Král, Radomil
Multi-dimensional Fokker-Planck equation analysis using the modified finite element method.
Journal of Physics: Conference Series. Roč. 744, č. 1 (2016), č. článku 012177. ISSN 1742-6588. E-ISSN 1742-6596.
[International Conference on Motion and Vibration Control (MOVIC 2016) /13./ and International Conference on Recent Advances in Structural Dynamics (RASD 2016) /12./. Southampton, 04.07.2016-06.07.2016]
Grant CEP: GA ČR(CZ) GP14-34467P; GA ČR(CZ) GA15-01035S
Institucionální podpora: RVO:68378297
Klíčová slova: Fokker-Planck equation * finite element method * single degree of freedom systems (SDOF)
Kód oboru RIV: JM - Inženýrské stavitelství
http://iopscience.iop.org/article/10.1088/1742-6596/744/1/012177

The Fokker-Planck equation (FPE) is a frequently used tool for the solution of cross probability density function (PDF) of a dynamic system response excited by a vector of random processes. FEM represents a very effective solution possibility, particularly when transition processes are investigated or a more detailed solution is needed. Actual papers deal with single degree of freedom (SDOF) systems only.
So the respective FPE includes two independent space variables only. Stepping over this limit into MDOF systems a number of specific problems related to a true multi-dimensionality must be overcome. Unlike earlier studies, multi-dimensional simplex elements in any arbitrary dimension should be deployed and rectangular (multi-brick) elements abandoned. Simple closed formulae of integration in multi-dimension domain have been derived. Another specific problem represents the generation of multi-dimensional finite element mesh. Assembling of system global matrices should be subjected to newly composed algorithms due to multi-dimensionality. The system matrices are quite full and no advantages following from their sparse character can be profited from, as is commonly used in conventional FEM applications in 2D/3D problems. After verification of partial algorithms, an illustrative example dealing with a 2DOF non-linear aeroelastic system in combination with random and deterministic excitations is discussed.
Trvalý link: http://hdl.handle.net/11104/0263920