TY - GEN
T1 - The spectral expansion of the elasticity random field
AU - Malyarenko, Anatoliy
AU - Ostoja-Starzewski, Martin
N1 - Publisher Copyright:
© 2014 AIP Publishing LLC.
PY - 2014/12/10
Y1 - 2014/12/10
N2 - 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 → S2(S2(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.
AB - 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 → S2(S2(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.
KW - elasticity
KW - random field
KW - spectral expansion
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U2 - 10.1063/1.4904635
DO - 10.1063/1.4904635
M3 - Conference contribution
AN - SCOPUS:85015266204
T3 - AIP Conference Proceedings
SP - 647
EP - 655
BT - 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014
A2 - Sivasundaram, Seenith
PB - American Institute of Physics Inc.
T2 - 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014
Y2 - 15 July 2014 through 18 July 2014
ER -