Wing Structural Mass Optimization of the Second-Generation Supersonic Aircraft under the Strength and Buckling Constraints


Аuthors

Pogosyan M. A.*, Shirokov M. V.**, Strelets D. Y.***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: kaf101@mai.ru
**e-mail: Gittwell@outlook.com
***e-mail: maksmai33@gmail.com

Abstract

In recent years, a resurgence of interest in the passenger supersonic air travel developing and implementing is being observed. Special attention is being paid to the small supersonic business jets designing accommodating from 20 to 48 passengers with a cruising speed within the range of 1.2–2.2 Mach number. The task of mass minimizing while the strength characteristics pertaining is a key one for the competitive aircraft creation. The article considers the wing structure optimization of the Second-Generation Supersonic Passenger Aircraft (SPA-2) under the strength and buckling constraints under various operational flight modes.
A model with smeared stiffeners, in which stiffeners are treated as T-profile beams arranged at uniform intervals, is being employed. The model utilizes the first order shear deformation theory and Timoshenko beam theory. The skin and stiffeners are considered as structures made of different composite materials, characterized by a set of ply angles and their proportions.
The article analyzes several failure modes of the wing structural elements. The inverse reserve factor (IRF) is used to the failure modes assessing. The Tsai-Wu criterion is applied to evaluate the load-bearing capacity loss of the VKU-18tr composite material, while the von Mises energy criterion is used for aluminum alloys. The following buckling modes are being considered for the panels stability analysis: global buckling of the entire panel, local buckling of the skin between stiffeners, and buckling of the stiffeners.
The Kreisselmeier–Steinhauser (KS) aggregation function is applied. To account for all constraints, multiple levels of KS aggregation are used, which allows reducing the number of costly coupled conjugated solutions.
A gradient-based optimization algorithm is presented. The object of optimization is the SPA-2wing. The wing structure comprises 15 ribs and 12 spars. For parameterization, the model is divided into 190 sections: 24 correspond to ribs, 68 to spars, and 49 each to the upper and lower panels.
Two characteristic wing loading modes are being analyzed in the framework of this optimization problem. These are Case A and Case D. Case A corresponds to the high-angle-of-attack flight, where the maximum lift coefficient is being achieved, with a design loading factor of 2.5g. Case D involves curvilinear maneuvering with a negative lift coefficient and a loading factor of 1g.
To ensure smooth variation in geometric parameters of the adjacent panels, corresponding constraints are introduced. Additional constraints are imposed on the dimensions of structural elements for all panels. Thus, the total number of constraints is 1,293. The design variables include skin and stiffener thicknesses, stiffener height, and stiffener spacing. The total number of design variables in the problem is 609. The objective function is the wing structure mass minimization.
The optimization is performed with the TACS (Toolkit for the Analysis of Composite Structures) software package using Python. As the result, an optimal wing configuration is obtained. The article presents the convergence histories of the objective and constraint functions, and analyzes the IRF distribution fields across the wing structure. Additionally, it presents the equivalent thicknesses of the wing structural elements.

Keywords:

optimal design, supersonic passenger aircraft, mass minimization, composite wing, Kreisselmeyer–Steinhauser aggregation, gradient optimization methods, static strength, buckling, finite element method

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