Structural optimization with static aeroelastic and stress constraints using expandable modal basis

Abstract

Recent developments of the modal-based aeroelastic optimization approach facilitated efficient treatment of static-aeroelastic and stress constraints. The reduced-size models use low-frequency normal modes of the baseline structure as fixed generalized coordinates throughout the optimization process. The modal approach is extended to allow the expansion of the modal basis by the addition of static modes generated in previous design steps. Being based on modal perturbations stored in the modal data base before the optimization process starts, the basis expansion accelerates the convergences to the optimal design. Numerical examples with realistic fighter- aircraft models demonstrate practical applications with CPU speed-up factors of ~10, compared with the regular discrete-coordinate approach, with negligible loss of accuracy. HE desire for efficient procedures for optimal design of com- plex structures motivated the development of reduced-size op- timization schemes in which calculations of stability and response parameters and their sensitivity to changes in the design variables are based on a set of low-frequency vibration modes of a base- line structure. The modal approach is especially attractive in multi- disciplinary cases in which the excitation loads are affected by the structural response, such as in aeroelastic and control-augmented systems. The ASTROS code1 was developed to provide a multidisciplinary analysis and design capability for aerospace structures. The con- sidered disciplines include structural analysis, aeroelastic analysis, and some features of the interaction with the control system. As in other commonly used analysis and optimization schemes,24 the dynamic response and the stability features are treated by the modal approach, but the static-aeroelastic and stress disciplines are treated by the discrete approach. The use of modal coordinates in static-aeroelastic analysis was shown in Ref. 5 to be extremely efficient and of good accuracy in application to realistic aircraft models. Structural optimization with static-aeroelastic constraints was later performed with the base- line normal modes serving as a fixed set of generalized coordinates throughout the entire optimization run.6 The fixed-modal-basis ap- proach was shown in Ref. 6 to be of good accuracy with design variable changes of less than ~20%. Larger changes required the update of the full finite-element model such that the optimization process could be resumed with new modal coordinates. Even when the modal approach was successfully applied in multidisciplinary optimization with static- and dynamic-aeroelastic constraints,7 it was not ready yet for application to stress constraints. The main reason for not using the modal approach for stresses was that it might yield erroneous results in cases of concentrated loads and in cases of local structural changes. Recent developments of the