Stochastic small perturbation based simulation technique for solving isotropic elastostatics equations

Kolyukhin Dmitriy () and Sabelfeld Karl K. ()
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Kolyukhin Dmitriy: Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, Akademika Koptyuga Prosp. 3, 630090 Novosibirsk, Russia
Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentieve str. 6, 630090 Novosibirsk, Russia

Monte Carlo Methods and Applications, 2015, vol. 21, issue 2, 153-161

Abstract: The paper deals with a stochastic analysis of random displacements governed by isotropic elasticity equations. The elasticity constants are assumed to be random fields with gaussian distribution. Under the assumption of small fluctuations of elasticity constants but not ignoring their distribution and correlation structure, we derive the spectral tensor of the random displacement field. A randomized spectral representation is then used to simulate this random field numerically. The same approach was applied to the case of random loading. In this case, the intensity of fluctuations may be arbitrarily large. A series of test calculations confirm the high accuracy and computational efficiency of the method.

Keywords: Lamé equation; stochastic small perturbations; random fields; random loads; randomization simulation technique; correlation functions (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/mcma-2014-0016

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