Thermal-structural reduced order models for unsteady/dynamic response of heated structures in large deformations

Abstract

This paper focuses on applications of recently developed thermoelastic reduced order models (ROMs) for the geometrically nonlinear response and temperature of heated structures. In these ROMs, both displacements and temperature fields with respect to the undeformed, unheated configuration are expressed in a reduced order modeling format, i.e., as modal-type expansions of the spatial and temporal variables with constant basis functions. Accordingly, the time varying generalized coordinates of the response and temperature expansions satisfy a generic set of coupled nonlinear differential equations derived from finite deformations thermoelasticity using a Galerkin approach. Finally, the coefficients of these governing equations, which characterize the structure considered and its loading conditions, are determined from structural and thermal finite element models non intrusively so that commercial finite element software can be used. This approach is considered here for the prediction of the displacements and stress fields in the presence of unsteady temperature distributions to enrich previous investigations limited to steady temperature distributions. Specifically considered here are: (i) a panel undergoing rapid heating and (ii) an oscillating flux on a panel. These problems not only demonstrate the extension of the thermal-structural reduced order framework to unsteady problems but also show the importance of the selection of the basis functions. It is also noted that the temperature dependence of the linear stiffness coefficients on temperature can induce in the unsteady situation the existence of a parametric-type excitation of the structure. This behavior is studied in the oscillating flux example and a strong sub-harmonic resonance is in particular found. The computational benefit of using ROMs is discussed and demonstrated.