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Stochastic Analysis of an Elastic 3D Half-Space Respond to Random Boundary Displacements: Exact Results and Karhunen-Loéve Expansion

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Abstract

A stochastic response of an elastic 3D half-space to random displacement excitations on the boundary plane is studied. We derive exact results for the case of white noise excitations which are then used to give convolution representations for the case of general finite correlation length fluctuations of displacements prescribed on the boundary. Solutions to these elasticity problem are random fields which appear to be horizontally homogeneous but inhomogeneous in the vertical direction. This enables us to construct explicitly the Karhunen-Loève (K-L) series expansion by solving the eigen-value problem for the correlation operator. Simulation results are presented and compared with the exact representations derived for the displacement correlation tensor. This paper is a complete 3D generalization of the 2D case study we presented in Sabelfeld and Shalimova (J. Stat. Phys. 132(6):1071–1095, 2008).

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Russian Acad. Sci., Lavrentieva str., 6, 630090, Novosibirsk, Russia

    I. A. Shalimova & K. K. Sabelfeld

Authors
  1. I. A. Shalimova
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  2. K. K. Sabelfeld
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Correspondence to K. K. Sabelfeld.

Additional information

This work is supported partly by the RFBR Grants N 06-01-00498, N 09-01-00152, the WIAS Institute, Berlin, and DFG, Germany, under Grant SA 861/6-1 of 2008.

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Shalimova, I.A., Sabelfeld, K.K. Stochastic Analysis of an Elastic 3D Half-Space Respond to Random Boundary Displacements: Exact Results and Karhunen-Loéve Expansion. J Stat Phys 135, 547–569 (2009). https://doi.org/10.1007/s10955-009-9737-x

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