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Title: The spectral expansion of the elasticity random field

We consider a deformable body that occupies a region D in the plane. In our model, the body’s elasticity tensor H(x) is the restriction to D of a second-order mean-square continuous random field. Under translation, the expected value and the correlation tensor of the field H(x) do not change. Under action of an arbitrary element k of the orthogonal group O(2), they transform according to the reducible orthogonal representation k ⟼ S{sup 2}(S{sup 2}(k)) of the above group. We find the spectral expansion of the correlation tensor R(x) of the elasticity field as well as the expansion of the field itself in terms of stochastic integrals with respect to a family of orthogonal scattered random measures.
Authors:
 [1] ;  [2]
  1. Mälardalen University (Sweden)
  2. University of Illinois at Urbana-Champaign (United States)
Publication Date:
OSTI Identifier:
22390797
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1637; Journal Issue: 1; Conference: ICNPAA 2014: 10. International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, Narvik (Norway), 15-18 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; ELASTICITY; EXPANSION; INTEGRALS; O GROUPS; RANDOMNESS; SCATTERING; STOCHASTIC PROCESSES; TENSORS