Nonlinear Reduced Order Modeling of Heated Structures with Temperature-Dependent Properties

Abstract

This paper focuses on extending coupled structural–thermal reduced order modeling approaches for the prediction of the nonlinear geometric response of heated structures to efficiently account for temperature-dependent structural and thermal properties. Structurally, a linear dependence of the elasticity tensor and thermal expansion coefficient is assumed consistently with typical material behavior. The resulting structural reduced order model (ROM) equations exhibit polynomials of the temperature generalized coordinates, the coefficients of which are readily identified. A different strategy is proposed for conductance and capacitance properties which typically depend nonlinearly on temperature. It relies on splitting the temperature generalized coordinates into a small set of dominant ones having a nonlinear effect on the ROM conductances and capacitances and a much larger set affecting them linearly. The inclusion of uncertainty in the structural ROM is also addressed extending earlier work limited to temperature independent properties. These strategies are exemplified on a representative hypersonic vehicle panel undergoing a full mission profile and with aero-thermal–structural coupling. The ROM predictions are observed to be very close to the full finite element ones for the mean model. Moreover, an uncertainty analysis demonstrates the strong sensitivity of the response to the structural model in the strongly nonlinear regions of the trajectory.