Unsteady Aeroelastic Optimization in the Transonic Regime

Abstract

A methodology for including transonic e utter requirements in the preliminary automated structural design environment is developed and tested. The problem of minimizing structural weight while satisfying behavioral constraints is stated in nonlinear mathematical programming form and is solved using a gradient-based optimizing technique. The structure is modeled by using e nite elements, and the associated design variables consist of the structural properties: thicknesses of skins, spars, and ribs; cross-sectional areas of posts and spar and rib caps; 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 to transform time-domain aerodynamic forces found by solving the transonic small disturbance (TSD) equations into the Laplace domain. The indicial responses are calculated about static aeroelastic equilibriums found using the TSD equations for the steady aerodynamics. Once in the Laplace domain, the unsteady aerodynamic forces are used to determine system dynamic stability by the p-method and in semianalytic equations for the e utter constraint sensitivities. With constraint values and the required gradients, a Taylor series approximation is used to develop an approximate nonlinear mathematical programming problem for weight minimization. This approximate optimization problem is iteratively solved by the method of modie ed feasible directions until convergence of the exact problem is obtained. Examples of the redesign methodology are given for the simultaneous consideration of constraints on transonic e utter, stresses, and displacements. Results found using nonlinear aerodynamics show that designs can differ considerably from those obtained using linear unsteady aerodynamics when in the transonic e ight regime.