The spectral expansion of the elasticity random field

Journal Article · Wed Dec 10 00:00:00 EST 2014 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4904635· OSTI ID:22390797

Malyarenko, Anatoliy ^[1]; Ostoja-Starzewski, Martin ^[2]

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1. Mälardalen University (Sweden)
2. University of Illinois at Urbana-Champaign (United States)

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.

• OSTI ID: 22390797
• Journal Information: AIP Conference Proceedings, Vol. 1637, 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); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRELATIONS
ELASTICITY
EXPANSION
INTEGRALS
O GROUPS
RANDOMNESS
SCATTERING
STOCHASTIC PROCESSES
TENSORS