Süpersonik uçak kanadının optimizasyonu

Abstract

Statik aeroelastik teorinin uygulanmasıyla süpersonik hızda seyreden bir uçak kanadının incelenmesi I-DEAS paket programının yardımıyla yapılmaktadır. Kanat üzerindeki yük dağılımı statik aeroelastik teoriden elde edilmekte ve I-DEAS programına giriş verisi olarak kullanılmaktadır. Daha sonra program yardımı ile lineer statik analiz ve optimizasyon yapılmaktadır. Optimizasyon işlemi sırasında kanat kaplama kalınlığının ve kiriş eleman kesitlerin optimum hale getirilmesi ile, verilen yük koşullarım sağlayan minimum ağırlıklı yapının eldesi hedeflenmektedir.

Impressive developments have seen in the power and applicability of structural optimization programs over the past 15 years. These programs which have been developed by research centers and universities can perform complex sizing exercises minimizing structural weight subject to the satisfaction of behavioral constraints. These codes are not only an integral part of a commercial finite element program, but also can stand outside of a specific system. Examples of these are MSC optimizer in NASTRAN, OPTI in the SAMCEF, OPTISEN in SDRC's I-DEAS, RAE/SGICON STARS and USAF's ASTROS. In addition to these commercially available codes there are a variety of in-house programs with equal power to those supplied by vendors. There is a wide availability of structural optimization programs and this has resulted in the extensive use of this capability in the aerospace industry. Today none of the airplanes is designed without performing structural optimization. Optimization has got a growing popularity as a major design tool has been matched by an ever increasing breadth of applicability. A decade ago structural optimization was only performed subject to static strength and stiffness constraints for isotropic structures. Today the scope has reached to the point where aeroelastic factors relating to efficiency, flutter speed limitations, active control aspects etc. are routinely included together with composite material properties. Current developments are focused on increasing the problem scope still further to include performance, avionics aspects and in certain cases shape parameters. An example is shown in Fig. 1 for the current developments. Static aeroelastic phenomena such as load distribution, divergence and loss of control involves interaction of aerodynamic and elastic forces. The phenomena of load distribution particularly plays an important role in the structural design of thin, low aspect ratio wings at supersonic speeds. VI The classical theory of elasticity deals with the stresses and deformation of an elastic body under prescribed external forces or displcements. The external loading acting on the body is, in general, independent of the deformation of the body. It is usually assumed that the deformation is small and does not affect the action of external forces. In such a case, the changes in dimensions of the body are neclected and the calculations are based on the initial shape. The situation is different, however, in most significant problems of aeroelasticity. The dynamic forces depend critically on the attitude of the body relative to the flow. The elastic deformation plays an important role in determining the external loading itself. The magnitude of the aerodynamic force is not known until the elastic deformation is determined. In general, therefore, the external load is not known until the problem is solved. The determination of the loads acting on a supersonic wing in any specified flight condition, and the resulting distribution is considered. The loads encountered during a pull-up maneuver are taken as the design loads in the present thesis. In the actual case, landing loads, gust loads, or loads from another type of maneuver may be critical condition for some portion of the structure, but they are not incorporated in the present thesis. Aerodynamic load on a deformed wing is shown in Fig. 2. The overall loading is specified by the gross weight or lift required and the ultimate load factor. The detailed pressure distribution corresponding to this overall load depends upon the flight Mach number, altitude and the elastic deformation of the wing. Since the pressure distribution as well as the deflection pattern of the wing are unknown, an iterative process is to be used to find the correct pressure distribution. Once the pressure distribution was determined utilizing classical static aeroelastic theory optimization analysis can be performed. SDRC's I-DEAS package program is used to find the optimum structure of the wing by means of resizing of the skin thickness and cross-sections of beam elements. Quadrilateral thin shell elements are used to model skins, spars and ribs of the wing while rod elements are used to model the spar caps, the rib caps and the stringers. vn Shock Fuselage "" skin thickness t Thrust Engine Change t Structural deformations Weight &C.G. £ Shock wave position on inlet Propulsion efficiency Performance Angle of attack 3. Vehicle res zing Figure 1. Optimization of supersonic aircraft wing cross-section +- x Airplane reference axis Figure 2. Aerodynamic load on a deformed wing vni Optimization will find the combination of design changes that satisfy the performance criteria while minimizing the redesign objective. The allowable design changes and the performance criteria must be defined. The alowable design changes are called optimization variables. Optimization variables can be virtually any physical property, beam property, material property, or shape parameter. Examples of optimization variables are shell thickness, beam cross-section dimension, Young's modulus, hole diameter, anf beam length. The performance criteria are called optimization constraints. Optimization constraints can be applied to strength (stress), stiffness (displacement), and dynamic behavior (frequency). The corresponding values of stress, displacement, and frequency are called constrained values as they are constrained to lie between given limits. The optimization module of I-DEAS package program has got three solution procedures: 1-) Fully stressing theory 2-) Size redesign theory 3-) Shape redesign theory In the present thesis "Fully stressing theory" is used to resize the wing structure. Fully stressing seeks to satisfy stress optimization constraints as equalities. This is done by resizing the optimization variables based on the stress values in the associated optimization element groups. Fully stressing can be understood as achieving an optimum design by using material to carry the maximum allowable load. Six parameters are used as optimization variables to minimize the weight of wing structure: 1-) Skin thickness 2-) Spar thickness 3-) Rib thickness 4-) Cross-section of spar caps 5-) Cross-section of rib caps 6-) Cross-section of stringers IX A delta wing is considered for the optimization. It has a 45° sweep angle at the leading edge with a planform area of 414 m. The material of the wing is taken as Titanium. The wing is assumed to fly at altitude of 7600 m with Mach number 2.5 and pull-up acceleration of 3.5 g. The initial values of optimization variables are choosen as follows: 1-) Skin thickness 2-) Spar thickness 3-) Rib thickness 4-) Cross-section of spar caps 5-) Cross-section of rib caps 6-) Cross-section of stringers 100 mm 50 mm 5 mm 2827 mm2 314 mm2 707 mm2