Doubly spectral stochastic finite element method (DSSFEM) for random field problems
Adhikari, S. and Roy Mahapatra, D.
IISc Centenary International Conference on Aerospace Engineering and Exhibition (ICEAE 2009),
Bangalore, India, May 2009.
Uncertainties in complex dynamical systems play an important role in the prediction of dynamic response in the mid and high frequency ranges. For distributed parameter systems, parametric uncertainties can be represented by random fields leading to stochastic partial differential equations. Over the past two decades spectral stochastic finite element method has been developed to discretise the random fields and solve such problems. On the other hand, for deterministic distributed parameter linear dynamical systems, spectral finite element method has been developed to efficiently solve the problem in the frequency domain.
In spite of the fact that both approaches use spectral decomposition (one for the random fields and while the other for the dynamic displacement fields), there has been very little overlap between them in literature. In this paper these two spectral techniques have been unified with the aim that the unified approach would outperform any of the spectral methods considered on its own. Considering exponential and triangular autocorrelation functions for the random fields, frequency depended element stiffness, mass and damping matrices are derived for axial and bending vibration of rods. Closed-form exact expressions are derived using Karhunen-Loeve expansion. Numerical examples are given to illustrate the unified spectral approach.
BiBTeX Entry
@INPROCEEDINGS{cp75,
AUTHOR={S. Adhikari and D. \protect{Roy Mahapatra}},
TITLE={Doubly spectral stochastic finite element method (DSSFEM) for random field problems},
BOOKTITLE={IISc Centenary International Conference on Aerospace Engineering and Exhibition (ICEAE 2009)},
YEAR={2009},
Address={Bangalore, India},
Month={May}
}
by Sondipon Adhikari