The spectral expansion of the elasticity random field

Anatoliy Malyarenko, Martin Ostoja Starzewski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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 2 (S 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.

Original languageEnglish (US)
Title of host publication10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014
EditorsSeenith Sivasundaram
PublisherAmerican Institute of Physics Inc.
Pages647-655
Number of pages9
ISBN (Electronic)9780735412767
DOIs
StatePublished - Dec 10 2014
Event10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014 - Narvik, Norway
Duration: Jul 15 2014Jul 18 2014

Publication series

NameAIP Conference Proceedings
Volume1637
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014
CountryNorway
CityNarvik
Period7/15/147/18/14

Fingerprint

elastic properties
tensors
expansion
constrictions

Keywords

  • elasticity
  • random field
  • spectral expansion

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Malyarenko, A., & Starzewski, M. O. (2014). The spectral expansion of the elasticity random field. In S. Sivasundaram (Ed.), 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014 (pp. 647-655). (AIP Conference Proceedings; Vol. 1637). American Institute of Physics Inc.. https://doi.org/10.1063/1.4904635

The spectral expansion of the elasticity random field. / Malyarenko, Anatoliy; Starzewski, Martin Ostoja.

10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014. ed. / Seenith Sivasundaram. American Institute of Physics Inc., 2014. p. 647-655 (AIP Conference Proceedings; Vol. 1637).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Malyarenko, A & Starzewski, MO 2014, The spectral expansion of the elasticity random field. in S Sivasundaram (ed.), 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014. AIP Conference Proceedings, vol. 1637, American Institute of Physics Inc., pp. 647-655, 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014, Narvik, Norway, 7/15/14. https://doi.org/10.1063/1.4904635
Malyarenko A, Starzewski MO. The spectral expansion of the elasticity random field. In Sivasundaram S, editor, 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014. American Institute of Physics Inc. 2014. p. 647-655. (AIP Conference Proceedings). https://doi.org/10.1063/1.4904635
Malyarenko, Anatoliy ; Starzewski, Martin Ostoja. / The spectral expansion of the elasticity random field. 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014. editor / Seenith Sivasundaram. American Institute of Physics Inc., 2014. pp. 647-655 (AIP Conference Proceedings).
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