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Reliability of deterministic non‐linear systems subjected to stochastic dynamic excitation
Author(s) -
Pradlwarter H. J.,
Schuëller G. I.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3017
Subject(s) - monte carlo method , estimator , excitation , subspace topology , linear subspace , dissipation , curse of dimensionality , reliability (semiconductor) , sampling (signal processing) , finite element method , stochastic process , computer science , mathematics , statistical physics , power (physics) , physics , mathematical analysis , structural engineering , engineering , geometry , statistics , filter (signal processing) , quantum mechanics , machine learning , computer vision , thermodynamics
Engineering structures react to exceptionally high forces caused by, for example, extreme winds, sea waves, earthquakes, avalanches, etc. in a non‐linear way, before they finally collapse. Mostly these environmental loadings cause dynamic excitations which are adequately modeled by the so‐called stochastic processes. To identify subsets of the excitation, which may trigger failure, methods based on power inputs of the stochastic excitation will be exploited. This procedure is based on the simple consideration that any excitation that maximizes the energy input into the system has the potential to adversely affect the integrity of the structure. This method considers the velocity of the displacement field of the structure and the energy dissipation induced by viscous damping, friction and hysteresis. For an efficient reliability estimation, the n ‐dimensional standard normal space S [0] ∈ℜ n , in which the stochastic excitation is modeled, is split into two disjunct subspaces S [1] ∈ℜ m and S [2] ∈ℜ n − m . The subset S [1] ∈ℜ m represents the space of important directions, which is identified by a procedure based on an approximation of the gradient of the energy input. Directional sampling in the subspace S [1] and direct Monte Carlo sampling in the subspace S [2] are combined to established an efficient estimator for the structural reliability. The proposed methodology is generally applicable to finite element models with strong non‐conservative non‐linearities. Copyright © 2010 John Wiley & Sons, Ltd.