WIAS Preprint No. 1217, (2007)

Stochastic simulation method for a 2D elasticity problem with random loads


  • Sabelfeld, Karl
  • Shalimova, Irina
  • Levykin, Alexander I.

2010 Mathematics Subject Classification

  • 65C05 65C20 65Z05


  • Isotropic Random Fields, Spectral Tensor, Poisson integral formula, Random Walk on Fixed Spheres, Lamé equation, Successive Over Relaxation Method, Transverse and Longitudinal Correlations


We develop a stochastic simulation method for a numerical solution of the Lamé equation with random loads. To treat the general case of large intensity of random loads, we use the Random Walk on Fixed Spheres (RWFS) method described in our paper citesab-lev-shal-2006. The vector random field of loads which stands in the right-hand-side of the system of elasticity equations is simulated by the Randomization Spectral method presented in citesab-1991 and recently revised and generalized in citekurb-sab-2006. Comparative analysis of RWFS method and an alternative direct evaluation of the correlation tensor of the solution is made. We derive also a closed boundary value problem for the correlation tensor of the solution which is applicable in the case of inhomogeneous random loads. Calculations of the longitudinal and transverse correlations are presented for a domain which is a union of two arbitrarily overlapped discs. We also discuss a possibility to solve an inverse problem of determination of the elastic constants from the known longitudinal and transverse correlations of the loads.

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