A Dynamic Programming Approach to the Design of Composite Aircraft Wings

Abstract

A light and reliable aircraft has been the major goal of aircraft designers. It is imperative to design the aircraft wing skins as efficiently as possible since the wing skins comprise more than fifty percent of the structural weight of the aircraft wing. The aircraft wing skin consists of many different types of material and thickness configurations at various locations. Selecting a thickness for each location is perhaps the most significant design task. In this paper, we formulate discrete mathematical programming models to determine the optimal thicknesses for three different criteria: maximize reliability, minimize weight, and achieve a trade-off between maximizing reliability and minimizing weight. These three model formulations are generalized discrete resource-allocation problems, which lend themselves well to the dynamic programming approach. Consequently, we use the dynamic programming method to solve these model formulations. To illustrate our approach, an example is solved in which dynamic programming yields a minimum weight design as well as a trade-off curve for weight versus reliability for an aircraft wing with thirty locations (or panels) and fourteen thickness choices for each location.

Decomposition of Mathematical Programming Models for Aircraft Wing Design Facilitating the Use of Dynamic Programming Approach

“…This paper presents an approach for designing aircraft wings, extending the research work presented by Tarun and Corley [1], who presented a discrete dynamic programming approach for obtaining optimal aircraft wing designs for the following possible design criteria: 1) minimizing an aircraft wing's weight while satisfying reliability requirements by selecting thicknesses for wing box components, 2) maximizing an aircraft wing's reliability within weight limitations by choosing thicknesses for various wing locations, or 3) determining trade-off designs between criteria (1) and (2). A numerical example was presented in [1] to illustrate their approach.…”

“…To solve Problems 1 and 2, we use the relationships among reliability, thickness, and weight developed in [1] from Lear Fan 2100 Jet data. For example, weight = area × thickness × density, while weight at a wing location increases linearly as thickness increases since the area and density of a wing are constant.…”

“…The discrete dynamic programming approach of [1], however, requires a large amount of computer RAM to carry out the computations associated with each stage and a large amount of storage capacity to store all information for each stage when the dynamic programming model involves a large number of stages and states. This paper addresses these issues by decomposing an optimization problem into subproblems prior to applying dynamic programming, thereby reducing computer RAM and storage capacity requirements.…”

“…This paper addresses these issues by decomposing an optimization problem into subproblems prior to applying dynamic programming, thereby reducing computer RAM and storage capacity requirements. As in [1], we focus only on the design of aircraft wings here.…”

“…In addition to [1], related research includes the following. Luo and Grandhi [3] present a methodology to reduce the failure probability in aircraft as a result of the uncertainty and randomness of the input information being used in structural optimization.…”