### 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 language | English (US) |
---|---|

Title of host publication | 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014 |

Editors | Seenith Sivasundaram |

Publisher | American Institute of Physics Inc. |

Pages | 647-655 |

Number of pages | 9 |

ISBN (Electronic) | 9780735412767 |

DOIs | |

State | Published - Dec 10 2014 |

Event | 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014 - Narvik, Norway Duration: Jul 15 2014 → Jul 18 2014 |

### Publication series

Name | AIP Conference Proceedings |
---|---|

Volume | 1637 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Other

Other | 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2014 |
---|---|

Country | Norway |

City | Narvik |

Period | 7/15/14 → 7/18/14 |

### Fingerprint

### Keywords

- elasticity
- random field
- spectral expansion

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - The spectral expansion of the elasticity random field

AU - Malyarenko, Anatoliy

AU - Starzewski, Martin Ostoja

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 → 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.

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 → 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.

KW - elasticity

KW - random field

KW - spectral expansion

UR - http://www.scopus.com/inward/record.url?scp=85015266204&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015266204&partnerID=8YFLogxK

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.

ER -