Nonlinear Reduced-Order Models for Thermoelastodynamic Response of Isotropic and Functionally Graded Panels
The focus of this investigation is on the development and validation of thermoelastic reduced-order models for the geometrically nonlinear response and temperature of heated structures. The reduced-order modeling approach is based on a modal-type expansion of both displacements and temperatures in the undeformed, unheated configuration. A set of coupled nonlinear differential equations governing the time-varying generalized coordinates of the response and temperature expansion are derived from finite thermoelasticity using a Galerkin approach. Furthermore, the selection of the basis functions to be used in these reduced-order models is discussed, and the numerical evaluation of the model coefficients is addressed. This approach is first validated on an isotropic beam subjected to both thermal effects and external loads. The thermal effects are large enough to induce a significant buckling of the panel, while the time-varying loads lead to snap-throughs ranging in frequency from infrequent to continuous. Validation to a functionally graded material panel in similar conditions is then performed. In both cases, the reduced-order modeling predicted temperatures and responses are found to very closely match their full finite element counterparts.