000015713 001__ 15713
000015713 005__ 20161115135327.0
000015713 04107 $$aeng
000015713 046__ $$k2013-06-12
000015713 100__ $$aCanor, T.
000015713 24500 $$aTransient Fokker-Planck Equation With Sph Method - Application in Seismic Design

000015713 24630 $$n34.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000015713 260__ $$bNational Technical University of Athens, 2013
000015713 506__ $$arestricted
000015713 520__ $$2eng$$aIn reliability theory, the knowledge of the time evolution of the probability density function (pdf) of the response of a diffusive random system may be required. The time evolution of this pdf is described by the transient Fokker-Planck-Kolmogorov (FPK) equation. This equation models the conservation of probability in the system state space. The transient FPK equation is an interesting tool for the study of reduced models of structures in the context of transient random excitations such as earthquakes. In this case, the deterministic approach can be competitive compared with classical Monte Carlo simulations, especially for extreme value problems. This paper presents a flexible method for the resolution of transient FPK equation using a Lagrangian method inspired by the mesh-free method: Smoothed Particle Hydrodynamics (SPH) method. Numerical implementation shows notable advantages of SPH method for solving FPK equation in an unbounded state-space compared with mesh-based method : (i) the conservation of total probability is explicitly written, (ii) no artefact is required in low density zones, (iii) the positivity of the pdf is ensured, (iv) the formalism offers straightforward extension to higher dimension systems, (v) the method is adapted for a large kind of initial conditions, even slightly dispersed distributions. In the paper, the method is illustrated with a particular interest for reliability problems in seismic applications. Probabilities of failure are calculated for strongly nonlinear systems (nonlinear viscous forces, hysteretic behaviour) subjected to transient excitations, for reasonable computation times compared with stochastic simulations.

000015713 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000015713 653__ $$aFokker-Planck equation, Smoothed Particle Hydrodynamics (SPH), Meshless method, Reliability problem

000015713 7112_ $$aCOMPDYN 2013 - 4th International Thematic Conference$$cIsland of Kos (GR)$$d2013-06-12 / 2013-06-14$$gCOMPDYN2013
000015713 720__ $$aCanor, T.$$iDenoel, V.
000015713 8560_ $$ffischerc@itam.cas.cz
000015713 8564_ $$s1072029$$uhttps://invenio.itam.cas.cz/record/15713/files/1311.pdf$$yOriginal version of the author's contribution as presented on CD, section: CD-RS 18 RELIABILITY OF DYNAMIC SYSTEMS
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000015713 962__ $$r15525
000015713 980__ $$aPAPER