Steady and unsteady nonlinear thermoelastodynamic response of panels by reduced order models

This paper focuses on the continued development and validation of thermoelastic reduced order models for the geometrically nonlinear response and temperature of heated structures. Following a recent investigation, both displacements and temperature fields in the undeformed, unheated configuration are expressed in a reduced order modeling format, i.e. as modal-type expansions of the spatial and temporal variables. Then, a set of coupled nonlinear differential equations governing the time varying generalized coordinates of the response and temperature expansion were derived from finite thermoelasticity using a Galerkin approach. This approach is considered again here for the prediction of the displacement and stresses fields in the presence of both steady and unsteady temperature distributions. To complement the previous validation efforts, three new situations are considered here, i.e. (1) a beam modeled with 8-node brick elements subjected to a steady temperature field (2) a freely expanding plate also subjected to a steady temperature distribution, and (3) a beam of case 1 subjected to a rapid unsteady heating. The first example focuses on the validation of the thermo-mechanical stresses while the second one confirms the validity of reduced order models to an unusual, but practical, boundary conditions with peculiar properties. Finally, the last validation case provides a final, positive assessment of reduced order models in unsteady heating situations, in particular in the presence of rapid heating.