Optimization of Wing Structures for Flutter: An Interval Approach

Abstract

This paper presents an uncertainty based automated optimum design of airplane wing structures with multiple design constraints. The maximization of flutter velocity of supersonic aircraft wing structures is considered as the objective. The wing is assumed to fly through a specific flight condition and the restrictions imposed upon the behavior of the structure involve limitations on taxiing stress, gust stress, landing stress and the range in which the natural frequencies are allowed to fall along with strength requirements. The design parameters of the aircraft wing are assumed to be uncertain and are described by a range of values. Second order piston theory is used to predict the aerodynamic load distribution and the dynamic aeroelastic characteristics of the wing. The procedure is illustrated with two examples. One is a symmetric double wedge airfoil, based on a beam type of analysis, and the other is a supersonic airplane wing, based on a finite element analysis. An interval analysis - based nonlinear programming techniques (penalty function approach and sequential quadratic programming), is used for the optimum solution of two aircraft wings. 1. Design Criteria The optimum design methods with deterministic parameters have been very well developed. In the present work, the problem of designing a supersonic wing structure with uncertain data is considered. The probability-based structural optimization method can be applied to problems in which design parameters are of a random nature. In design problems there exists a vast amount of uncertain data which can not be modeled using probability principles. Such problems can be solved using a fuzzy approach assuming fuzzy information for the geometry, strength (resistances) as well as applied loads. In this paper the problem of optimum structural design in a fuzzy environment is considered. The fuzzy set is divided into finite subsets by using discrete values of membership function. Each fuzzy subset represents the range of imprecision corresponding to a specified α value. Thus, an interval can be used to describe a fuzzy subset. In this work, the flutter velocity of an aircraft wing is maximized subject to constraints. The maximum stress, wing tip deflection, root angle of attack, the natural frequencies of the wing structure, the stresses induced in the wing structure due to taxiing, gust and landing loads are suitably constrained. The design criteria to be satisfied, in the specified flight condition, are the following: 1. The first p natural frequencies of the structure i ω are to be excluded from certain bands