A computational procedure to estimate the stochastic dynamic response of large non-linear FE-models

An algorithm for the computation of the stochastic non-stationary non-linear response of large FE-models is presented. In stochastic analysis, the response is described by the mean and covariance function and possibly by the probability distribution of the non-linear response. To estimate the covari...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2003-02, Vol.192 (7), p.777-801
Main Authors: Pradlwarter, H.J., Schuëller, G.I., Schenk, C.A.
Format: Article
Language:English
Subjects:
Computational techniques
Covariance matrix
Exact sciences and technology
Filtered white noise excitation
Finite-element and galerkin methods
Fundamental areas of phenomenology (including applications)
Karhunen–Loéve expansion
Large FE-models
Mathematical methods in physics
Physics
Solid mechanics
Statistical equivalent linearization
Stochastic non-linear response
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Vibrations and mechanical waves
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Summary:An algorithm for the computation of the stochastic non-stationary non-linear response of large FE-models is presented. In stochastic analysis, the response is described by the mean and covariance function and possibly by the probability distribution of the non-linear response. To estimate the covariance matrix, the method of equivalent statistical linearization is applied for linearizing all non-linear elements. The large fully populated and symmetric covariance matrix of dimension ⩾2 n is described by the so called Karhunen–Loéve expansion representation, which allows one to employ a feasible description. In this context, an efficient procedure is suggested to determine the minimal number of Karhunen–Loéve vectors necessary to assure a sufficiently accurate representation. This method in fact allows one to employ any available deterministic integration scheme to compute the Karhunen–Loéve vectors. To increase the computational efficiency, modal coordinates are used to represent the linear sub-system. Special attention is given to the effects of mode truncation which are generally not negligible for large FE-systems. Moreover, the suggested approach has no limitation w.r.t. the size of the model in terms of degrees of freedom (DOFs) or the number of non-linear elements. The feasibility of the proposed procedure is demonstrated in the numerical examples where the methodology is applied to an office building with approximately 25, 50 and 100 thousand DOFs containing hysteretic damping elements.
ISSN:0045-7825
1879-2138
DOI:10.1016/S0045-7825(02)00595-9