• Overview
• FSW Airplane in Level Flight (Example HA144A)
• Jet Transport Wing in Roll (Example HA144B)
• A 15-Degree Sweptback Wing in a Wind Tunnel (Example HA144C)
• FSW Airplane in Antisymmetric Maneuvers (Example HA144D)
• FSW Airplane in Unsymmetric Quasi-Steady Maneuvers (Example HA144E)
• FSW Airplane with Bodies (Example HA144F)
• Unit Solutions for Loadings of the FSW Airplane (Examples HA144GA and HA144GB)
6.1
Overview
Static aeroelastic problems consider the application of steady-state aerodynamic forces to a flexible vehicle, which deflects under the applied loads resulting in perturbed aerodynamic forces. The solution of these problems assumes that the system comes to a state of static (or quasi-static) equilibrium. The aerodynamic load redistribution and consequent internal structural load and stress redistributions can be used for design purposes by structural analysts.
The possibility of a static aeroelastic instability, i.e., divergence, is also of concern to structural analysts. Static aeroelastic effects are of concern to other analysts as well. For example, aerodynamicists are concerned with the effects on induced drag, and control systems analysts are concerned with the effects on control effectiveness and static stability. The needs of these analysts from several related disciplines have been considered in the static aeroelastic capability of NX Nastran.
Seven quasi-static examples are included in this chapter. These examples produce the symmetric and antisymmetric static stability derivatives as well as loads and stresses due to a variety of potential design conditions:
• Examples HA144A and HA144DFSW Airplane in Antisymmetric Maneuvers (Example HA144D) are symmetric and antisymmetric models of an idealized forward swept wing (hereafter referred to as FSW) configuration.
• Example HA144F adds a fuselage and two underwing stores to the HA144E example. • Examples HA144GA and HA144GB use the FSW configuration to provide unit solutions for
the loadings for the initial incidence and each of the trim variables.
• Example HA144B produces static aeroelastic results for the BAH wing [the jet transport wing analyzed throughout Bisplinghoff, Asheley, and Halfman(1955)].
• Example HA144C considers a 15-deg swept untapered wing when mounted on a wind-tunnel wall at a prescribed angle of attack.
6.2
FSW Airplane in Level Flight (Example HA144A)
The first example is the FSW airplane considered by Rodden and Love (1985) in trimmed level flight. The model is extremely idealized as shown inFigure 6-1. The wing has an aspect ratio of 4.0, no taper, twist, or camber, but an incidence of 0.1 deg relative to the fuselage, and a forward sweep angle of 30 deg. The canard has an aspect ratio of 1.0, no taper, twist, camber, incidence, or sweep, and is hinged about its quarter-chord. The chords of both the wing and canard are 10.0 ft, the reference chord is chosen as = 10 ft, and the reference area is S = 200 sq ft for the half-span model. Both subsonic (m = 0.9) and supersonic (m = 1.3) speeds are considered.
Figure 6-1. Idealization of FSW Configuration
The half-span model of the wing is divided into 32 equal aerodynamic boxes, as shown on the left wing inFigure 6-1, for both the Doublet-Lattice and ZONA51 methods of aerodynamic analysis, and the canard is divided into eight equal boxes, as also shown inFigure 6-1. Aerodynamic forces on the fuselage are neglected. (Note that the right-hand side is modeled; the aerodynamic boxes are shown on the left side for convenience.) The right wing and fuselage inFigure 6-1show the structural idealization. Four weights are located at the one-quarter and three-quarter span and
chord positions of the wing, and are assumed to be connected to the 50% chord elastic axis by rigid streamwise bars. The weights are 600 lb forward and 400 lb aft, giving a wing centroid at 45% of the wing chord. The wing is assumed to be uniform with equal bending (ELy) and torsion (GJ) stiffnesses of 25 × 107lb-ft2and is connected to the fuselage at its root. The right-side
fuselage is assumed to have the same bending stiffness as the wing and is shown with four equal and equidistant weights (1500 lb each per side). The fuselage length is 30.0 ft. The total weight per side is 8000 lb, the center of gravity is 12.82 ft forward of the intersection of the fuselage and wing elastic axis, and the centroidal moment of inertia in pitch per side is Iy= 892,900 lb-ft2. For
the subsonic case, the airplane is assumed to be flying at a Mach number m = 0.9 at sea level ( = 1200 psf). The low speed characteristics (but at m = 0.9) are obtained by assuming a low value of dynamic pressure, = 40 psf, to illustrate the behavior of the quasi-rigid vehicle. In the supersonic case, the airplane is assumed to be flying at m = 1.3 at 20,000 ft ( = 1151 psf).
Structural Model
The input of structural data is considered first. The fuselage model is illustrated inFigure 6-1. The fuselage length from GRID 97 to GRID 100 is 30.0 ft. BAR elements are used between grid points, and a CONM2 weight of 1500 lb is at each fuselage grid point except GRID 90. The wing input is also illustrated inFigure 6-1. Grid points 111, 112, 121, and 122 are connected to the elastic axis by rigid bars. The wing stiffnesses were assumed to be equal in bending and torsion, ELy= GJ = 25.0 + 07; thus, assuming E = 1.44 + 0.9 psf and G = 5.40 + 08 psf, leads to
Iy= 0.173611 ft4 and J = 0.462963 ft4, respectively. Values of cross-sectional area, A = 1.5 ft2,
and chordwise inertia, Iz= 20 ft4, are chosen arbitrarily. A nominal symmetrical rectangular
cross section with a 6.0 ft chord and 1.0 ft depth is also assumed for the wing structural box for stress recovery purposes at the four corners. The wing forward CONM2 weights are 600 lb, and the aft weights are 400 lb. The half-fuselage material properties are assumed to be the same as in the wing with the same vertical cross-sectional moment of inertia, Iy= 0.173611 ft4. The
remaining fuselage cross-sectional area properties are selected arbitrarily for stiffness and stress recovery, specifically, A = 2.0 ft2, I
z= 0.15 ft4, J = 0.5 ft4, and the points selected for stress recovery are at y,z = ±1.0, ±1.0. There are two rigid body motions in this model: vertical translation and rotation in pitch. A SUPORT Bulk Data entry defines a reference point for these rigid body modes on GRID 90, DOFs 3 and 5. Component 4 (roll) of wing grid points 110 and 120 is omitted from the calculation in order to illustrate this means of reducing the problem size and thus has no effect on the results. GRID 90 is constrained longitudinally, and all of the fuselage grid points are constrained for symmetry using SPC1 entries. PARAM entries select GRID 90 as the inertial property reference point and convert the input weights to masses in slugs. [Note that PARAM,WTMASS,1/G provides the conversion of weight to mass; PARAM,AUNITS,1/G allows for the input of the accelerations using load factors (Gs).] CORD2R 100 provides the NACA reference axes for the stability derivatives. The trim angle of attack is the angle of attack of the structural axis at the SUPORT point.