Simultaneous Design and Control of Stiffened Laminated Composite Structures

Abstract

The problem investigated here concerns the simultaneous design and control of structures. The structure considered is a laminated stiffened composite plate for which an optimum control system is designed by the minimization of an appropriate performance index with respect to both the control forces and structural design variables consisting of stiffener areas and the number of plies of a given orientation. To ensure a physically realistic structure appropriate constraints on the stiffener sizes, total weight, and structural frequencies are imposed. Nonlinear mixed‐integer programming is used to force the number of plies to take on integral values. The entire problem is posed as a three‐level optimization problem. Using the well‐known independent modal space control method, effects of plate geometry, initial disturbance conditions, and control effort penalty parameters on the optimal design are considered. The minimization process requires derivatives of eigenvalues and eigenvectors with respect to the design variables. These derivatives can be computed by an involved analytical procedure or a relatively simple finite‐difference procedure. This paper also examines the computer cost‐effectiveness of these two procedures for the sensitivity‐derivative calculations.