Optimum thermal modes for coupled structural-thermal reduced order models

This investigation focuses on the existence and determination of temperature distributions on a structure that most strongly affect its linear/nonlinear geometric response assumed expressed in a given finite modal expansion format. The knowledge of these distributions would support the construction of thermal reduced order models adapted for the determination of the response of hot structures. Under the assumptions that the tensor of elasticity and coefficient of thermal expansion are independent of temperature, it is shown that the desired temperature distributions 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. A reduction process is further proposed to synthesize from the ensemble of linear and nonlinear stress modes a small set of orthogonal functions, referred to as the optimum thermal modes, that accurately capture the effects of temperature on the structure.