Discrete Variable Approximation to Minimum Weight Panels with Fixed Flutter Speed

Abstract

T paper presents a numerical technique for determining the minimumweight design of a one-dimensional panel for which an aeroelastic eigenvalue characterizing the flutter speed is held constant. The governing differential equations are approximated by sets of difference equations adjoined to the weight function via a penalty function. A conjugate gradient method is applied to the resulting sequence of unconstrained minimization problems. Numerical results are obtained for solid simplysupported panels with constant inplane stresses. These results supplement those of Armand and Vitte who posed a solid panel problem without inplane stresses and Weisshaar who obtained numerical solutions for a sandwich panel without inplane stresses using a minimum thickness constraint. The discrete variable technique has been applied previously to flight path optimization and is thought to have several advantages, including 1) ease of implementation, 2) exact satisfaction of boundary conditions, 3) ability to treat the frequency parameter a as an additional problem variable, 4) ability to avoid the differential equation end point singularities without imposing a minimum thickness constraint, and 5) ease in obtaining adequate initial solution estimates.