UNSTEADY AEROELASTIC OPTIMIZATION IN THE TRANSONIC REGIME

A methodology. for including transonic flutter requirements in the pre liminary automated structural design environment is developed and test ed, The problem of minimizing structural weight while satisfying behav ioral constraints is stated in nonlinear mathematical programming form and is solved using a gradient-based optimizing technique, The struct ure is modeled by using finite elements, and the associated design var iables consist of the structural properties thicknesses of skins, spar s, and ribs; cross-sectional areas of posts and spar and rib raps; and concentrated masses, The method requires that the transonic unsteady aerodynamic forces be represented in the frequency or Laplace domain, In this work, the indicial response method is used fu transform time-d omain aerodynamic forces found by solving the transonic small disturba nce (TSD) equations into the Laplace domain, The indicial responses ar e calculated about static aeroelastic equilibriums round using file TS D equations for the steady aerodynamics. Once in the Laplace domain, t he unsteady aerodynamic forces are used to determine system dynamic st ability by the p-method and in semianalytic equations Tor tile flutter constraint sensitivities, With constraint values and the required gra dients, a Taylor series approximation is used to develop ant approxima te nonlinear mathematical programming problem for weight minimization. This approximate optimization problem is iteratively solved by the me thod of modified feasible directions until convergence of tile exact p roblem is obtained, Examples of the redesign methodology are given for the simultaneous consideration of constraints on transonic flutter st resses, and displacements. Results found using nonlinear aerodynamics show that designs can differ considerably from those obtained using li near unsteady aerodynamics when in the transonic flight regime.