### Abstract

This investigation focuses on determining how to optimally represent the temperature distribution of a structure to capture at best its effects on the nonlinear geometric response of the structure expressed in a given modal expansion format. More specifically, with the temperature assumed in an expansion form, it is desired to find thermal basis functions most adapted for the ensuing structural computations. Under the assumptions that the tensor of elasticity and coefficient of thermal expansion are independent of temperature, it is justified that these thermal basis functions should be proportional to linear and nonlinear stress distributions induced by each structural mode and linear combinations of two such modes in the absence of temperature. The implementation of this finding in the context of structural and thermal finite element models is described and validated on a hypersonic panel under strong coupling between structural, thermal, and aerodynamic analyses. It is observed that the effects of the temperature on the structural response are indeed accurately captured without requiring a full modeling of the temperature field.

Original language | English (US) |
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Title of host publication | Nonlinear Dynamics |

Editors | Gaetan Kerschen |

Publisher | Springer New York LLC |

Pages | 267-278 |

Number of pages | 12 |

ISBN (Print) | 9783319297385 |

DOIs | |

State | Published - Jan 1 2016 |

Event | 34th IMAC, A Conference and Exposition on Structural Dynamics, 2016 - Orlando, United States Duration: Jan 25 2016 → Jan 28 2016 |

### Publication series

Name | Conference Proceedings of the Society for Experimental Mechanics Series |
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Volume | 1 |

ISSN (Print) | 2191-5644 |

ISSN (Electronic) | 2191-5652 |

### Other

Other | 34th IMAC, A Conference and Exposition on Structural Dynamics, 2016 |
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Country | United States |

City | Orlando |

Period | 1/25/16 → 1/28/16 |

### Keywords

- Basis functions
- Cracked structure
- Generalized finite element modeling
- Local enrichment
- Nonlinear geometric response
- Reduced order modeling
- Structural model
- Thermal model

### ASJC Scopus subject areas

- Engineering(all)
- Computational Mechanics
- Mechanical Engineering

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## Cite this

*Nonlinear Dynamics*(pp. 267-278). (Conference Proceedings of the Society for Experimental Mechanics Series; Vol. 1). Springer New York LLC. https://doi.org/10.1007/978-3-319-29739-2_25