Thermoelastic Reduced Order Models for Representative Hypersonic Structures

The construction of the reduced order model basis has usually been carried out by hand-picking specific linear and dual modes that are deemed to be important for the modeling of the nonlinear response. This process is fully appropriate in the simple geometries which have been considered in past investigations in which a good physical understanding of the response could indeed be expected and could provide the necessary basis selection guidance. In more complex structures, such as the representative hypersonic structure considered here, this process is far more complex and the physics of the nonlinear response cannot be expected to be sufficiently good as was demonstrated by obsereved local buckling of the panel induced by the deformation of the flange. What is desired then is an organized, consistent methodology for the selection of the key modes. It is proposed to base this methodology on the representation error uuuprojrep-=e (1) where u is the static displacement field computed by the finite element code and proju is its projection on the selected basis). Example plots of the representation error vs. the number of linear modes in the direction normal to the panel (i.e. normal to the top surface and the flanges) as well as in its tangential direction are shown in Fig. 1 for the displacement field induced by a uniform pressure leading to a peak displacement of 4 thicknesses downward. Clearly shown on these figures are localized drops in the error at specific linear mode numbers indicating that these modes are the ones contributing to the response modeling. This process suggests that modes 1, 3 (in case of fore-aft lack of symmetry expected with aerodynamics but not present here), 5, 6, 9, 12, 18 (significant at larger displacement levels), 21, 24, 27, 30 need to be selected. The focus of this supplemental effort is on the development of an automatic procedure for the selection of the basis function of the reduced order model which is based on the representation error of Eq. (1) as tentatively demonstrated in Fig. 1.