Optimal representation of a varying temperature field for coupling with a structural reduced order model

This investigation focuses on determining how to optimally represent the temperature distribution of a structure to capture at best its effects on the nonlinear geometric response of the structure expressed in a given modal expansion format. More specifically, with the temperature assumed in an expansion form, it is desired to find thermal basis functions most adapted for the ensuing structural computations. Under the assumptions that the tensor of elasticity and coefficient of thermal expansion are independent of temperature, it is justified that these thermal basis functions 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. It is observed that the effects of the temperature on the structural response are indeed accurately captured without requiring a full modeling of the temperature field.