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Elastostatics of a Half-Plane under Random Boundary Excitations

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Abstract

A stochastic analysis of an elastostatics problem for a half-plane under random white noise excitations of the displacement vector prescribed on the boundary is given. Solutions of the problem are inhomogeneous random fields governed by the Lamé equation with random boundary conditions. This is used to model the displacements, strain tensor, vorticity, and the deformation energy, and to give exact representations for their correlation tensors, as well as the corresponding Karhunen-Loève (K-L) expansions. Numerical calculations illustrating the rate of convergence of the spectral and K-L expansions are also given. An interesting behaviour of the strain correlation tensor for the increasing value of the elasticity constant is found theoretically and confirmed by calculations. The paper presents the second part of our study, the first being published recently in Sabelfeld and Shalimova (J. Stat. Phys. 132(6):1071–1095, 2008) where only the displacement correlation tensor was derived and analyzed.

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Authors and Affiliations

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

    Karl Sabelfeld & Irina Shalimova

Authors
  1. Karl Sabelfeld
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  2. Irina Shalimova
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Correspondence to Karl Sabelfeld.

Additional information

Support of the RFBR under Grants 09-01-00152-a, 09-01-12028-ofi-m, and 09-01-00639-a is kindly acknowledged.

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Sabelfeld, K., Shalimova, I. Elastostatics of a Half-Plane under Random Boundary Excitations. J Stat Phys 137, 521–537 (2009). https://doi.org/10.1007/s10955-009-9857-3

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  • DOI: https://doi.org/10.1007/s10955-009-9857-3

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