INTRINSICALLY-SMART COUPLED BOX BEAMS


Moishe Garfinkle                     Christopher Pastore

garfinkm@mail.drexel.edu     pastorec@philau.edu


CONTENTS

1.    Nomenclature
2.    Fabrication of Coupled Box-Beams
3.    Performance of Quasi-Unbalanced Box-Beams
4.    Configurational Considerations
5.    Application Considerations
5.    Specific Applications
7.    Combined Techniques
8.    Summary


A smart textile composite is a structure tailored to exhibit a desirable elastic deformation behavior not necessarily proportional to the imposed load. An example of such a structure would be a box-beam so tailored that an imposed cantilever load results in twisting as well as bending, although no torsional load was imposed. Reversible behavior would be exhibited if in addition an imposed torsional load results in bending as well as twisting, although no cantilever load was imposed. Such a structure is said to exhibit twist-bend coupling. The composite fabrication technique required to produce such a complex response can be either intrinsically-smart (passive) or extrinsically-smart (active):

Intrinsically-Smart (Passive)
The symmetry and balance of the composite filament plies controls the elastic deformation response to loading of the composite structure.
 
Extrinsically-Smart (Active)
The sequence of actuation of piezoelectric or magnetostrictive actuators embedded between the composite plies controls the elastic deformation response to loading of the composite structure.
 

The effect of combining these diverse techniques is discussed.


1.    Nomenclature

The winding sequence of continuous-wound intrinsically-smart box-beams is denoted by balance and symmetry. A winding is denoted symmetric  when the fiber orientation does not change with a 180° rotation of the beam and denoted balanced  when the sum of the plies oriented at any angle from the longitudinal axis of the beam is equal to the number of plies oriented at an equal angle but in the opposite direction, taking into account the windings on both the top and bottom surfaces. Balance is required for fabrication by continuous-filament winding.

Figure 1A illustrates a conventionally-wound box-beam, which is both symmetric and balanced. Because the windings have opposite angles on opposite sides of the beam, the preferential bending axis is normal to the longitudinal axis of the beam.

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Figure 1. Balanced and Unbalanced Winding Architecture

Figure 1B illustrates a non-symmetrical, unbalanced box-beam. Because the winding angles are the same on opposite sides of the beam, the preferential bending axis is essentially the winding angle. Hence on bending this beam will exhibit twist-bend coupling. Non-symmetry is required for coupling. The flexural behavior of the balanced (uncoupled) and unbalanced (coupled) architecture are shown in Figures 2U and 2C, respectively.
 

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Figure 2. Elastic behavior of Uncoupled (U) and Coupled (C) Box-Beams

Coupling is measured analytically as the incremental change in twist angle with bend angle, as shown in Figure 3. The beam is shown twisting upwards with upwards bending, indicating divergent coupling.

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Figure 3. Coupling Convention


2.    Fabrication of Coupled Box-Beams

Unfortunately, an unbalanced box-beam cannot be fabricated by continuous winding as is evident from Figure 1B. Rather it must be fabricated from L-shaped or U-shaped patches of unidirectional fabric, the former shown in Figure 4A. These patches are then positioned on a mandrel, as shown in Figure 4B.

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Figure 4. Fabrication of Coupled Box-Beam by Patch Layup

This construction was utilized by Atonasoff & Vizzini to study the coupling behavior of the non-symmetrical unbalanced architecture. This fabricating technique is also being studied by Corso, Popelka & Nixon for engineering application purposes. Because individual patches must be manually laid-up process uniformity is difficult to maintain and mechanical properties can be inconsistant. The greatest concern involving the application of such discontinuous fabric construction in life-critical applications however is the presence of longitudinal seams all along the corners of the resultant box-beam. These are zones of weakness and can constitute potential delamination-initiation regions.

In response to the crucial concerns associated with manual-layup of critical load-bearing box-beam members an alternative continuous-winding technique has been developed denote the non-symmetric quasi-unbalanced architecture.    This construction has been described in detail by Garfinkle; Greenhalgh, Pastore & Garfinkle; and analysed by Bogdanovich, Pastore, Greenhalgh & Birger. Box-beams fabricated using this proprietary technique exhibit pronounced twist-bend coupling.
 
 

Figure 5. Fabrication of Quasi-Unbalanced Box Beam

Two balanced symmetrical box-beams as shown in Figure 1A are wound in opposite directions and stacked as shown in Figure 5A. The combination is obviously non-symmetrical as the upper and lower winding angles are identical as seen in Figure 5B, yet the beam is ostensibly balanced.


3.    Performance of Quasi-Unbalanced Box-Beams

Five prototype box-beams were fabricated from Uniweave fabric comprising 12K AS-4 carbon yarn in the warp direction and 200 denier E-Glass yarn in the weft direction. The warp yarn comprised 98% of the fabric weight. For each demonstration beam the uniweave was wound around two foam cores without laps, producing two oppositely wound helices. The two cores were then stacked and saturated with Shell 8132 resin with U40 hardener. Consolidation occurred in a closed mold at ambient temperature under a pressure of 100 kPa. The beams were then post-cured at 120 C for at least four hours. The measured winding angles of the five beams tested were 17, 29, 43 and 65 degrees as described in detail by Greenhalgh, Pastore & Garfinkle. The cross-sectional dimensions of the beams were nominally 50 mm x 50 mm.
 
 

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Figure 6. Elastic Behavior of a Quasi-Unbalanced Box-Beam

It is evident from Figure 6 that the observed twist-bend coupling Z is highly dependent on the fiber-placement angle. The coupling exhibited at the optimum placement angle was far greater than would be expected, with Z exceeding unity. Accordingly the twist angle exhibited significantly exceeded the bending angle directly imposed by the bending load. The curve shown was derived by Bogdanovich, Pastore, Greenhalgh & Birger using meso-volume representations of the box-beam, with the numerical data converging with finer meso-volume meshes.


4.    Configurational Considerations

For load-bearing purposes of course longitudinal fibers would be required in the fabrication of the quasi-unbalanced wing spar as in usual practice as shown in Figure 7. The spar would be covered with a balanced wound or braided overwrap.

Figure 7. Load-Supporting Smart Box-Beam

Bending of a box-beam is accompanied by warping of the sidewalls, as shown in Figures 8A and 8B. If the loading is excessive the sidewalls will fail by buckling.

Figure 8. Warping of Box-Beam Sidewalls Under Load

As shown in Figure 8C however, the internal web of the quasi-unbalanced box-beam constrains the sidewalls, both increasing the resistance of the box-beam to bending deformation and to buckling failure. Because the smart windings are only a portion of the total composite structure the internal web will account for an almost insignificant proportion of the weight of the structure.


5.    Application Considerations

The first full-scale application of bend-twist coupling in wing construction involved the X-29 experimental aircraft with swept-forward wings. Although such wings delay compressibility effects and exhibits relatively benigh stalling characteristics they do exhibit divergent twist-bend coupling (Z>0) wherein upward wing bending results in upward wing pitching, destabilizing the aircraft in roll. For the X-29 the solution was to fabricate the entire wing skin using the patch-layup technique shown in Figure 4, with the fabric patches overlaping around the leading and trailing edges of the wing as described by Allburn, Retelle, Krone & Lamar. The resulting wing, shown in Figure 9A, exhibited convergent twist-bend coupling (Z<0).

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Figure 9. X-29 Wing with Unbalanced Fiber Layup

The manual fabric layup of the X-29 wing, with its accompanying fabrication inconsistancies, mitigates against the practical application of this labor-intensive tailoring technique. As might be expected evidence of delamination of the wing layups was found as a result of aerodynamic loading under flight conditions. In contrast, utilization of a quasi-unbalanced box-beam shown in Figure 7 as the wing spar, had the spar existed at that time, would have resulted in the wing shown in Figure 9B: exhibiting convergent twist-bend coupling (Z<0) but amenable to conventional wing construction.

Accordingly, the conventional wing construction, which does not induce convergent twist-bend coupling as shown in Figure 10U, can be retained, with the quasi-unbalanced smart wing spar shown in Figure 10C inducing the desired convergent twist-bend coupling (Z<0).

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Figure 10. Behavior of Coupled Airfoil

 
 
The conventional wing structure (Z=0) shown in Figure 10A, when subject to abnormal aerodynamic loading must rely on the elastic constraint of the wing structure alone to effect damping. Such limited damping can prove inadequate under severe loading associated with abrupt maneuvers or can lead to oscillations when wings with substantial tip loads are involved, as described by Goorjian, Tu & Guruswamy. When sufficiently severe such adverse loading can lead to structural failure. Accordingly conventional wing structures must be constructed significantly more rigidly than abnormal aerodynamic loading would dictate, and consequently heavier.

In contrast, the convergently coupled wing structure (Z<0) shown in Figure 6B, when subject to abnormal aerodynamic loading, can rely on significant aeroelastic restoring forces to effect damping of the wing structure, as described by Shirk, Hertz & Weissharr. Accordingly cost-effective convergently-coupled (Z<0) wing structures can be constructed less rigidly than required by conventional wings, and consequently can be both lighter and cheaper.


6.    Specific Application
a.   Resistance of wing spars to torque loading is all as important as the resistance to deflection loading.  In fact tip oscillations induced by adverse air forces on wings with heavy tip loads can be strong enough at resonance frequencies to cause wing failure.  The BA 609 tilt-rotor aircraft designed for general-aviation applications is a prime example of an aircraft with heavily tip-loaded wings.

The components of a short section of the complex built-up wing-support structure of the BA 609 is illustrated by Clements in Figure 11A.   Fabrication of the components requires extensive hand-layup, as does fabrication of the finished wing shown in Figure 11B.

 

Figure 11. BA 609 Wing Support Structure

 

Consider now the configuration of the BA 609 wing supported by a proposed bend-twist coupled spar.  The principal load-supporting structure comprises wound box-beams as shown in Figure 12A, essentially eliminating manual fabrication of not only the beams but the overwrapping.  Moreover box-beam construction will permit a lighter structure than the present built-up structure because load-bearing seams are eliminated along the wing shown in Figure 12B.

Figure 12. BA 609 Projected Wing Utilizing a Coupled Wing Spar

The coupled-spar wing will not only resist torque loads imposed on the wing but will actively compensate for wing twisting moments arising from lift-engine twisting about its support structure.

b. Larger aircraft, either military or commercial, require fuel cells in the wing structure. These can take many forms, but to be compatible with the coupled spar probably tubular cells, such as illustrated in Figure 13 would be the most practical.

 

Figure 13. Fuel Cell Arrangement in a Coupled Wing

The coupled spars themselves would serve as fuel cells without diminishing their effectiveness.


7.    Combined Techniques

Perhaps the greatest benefit of smart structures will ultimately be attained by combining the architecture of the intrinsically-smart passive structure with the control of the extrinsically-smart active structure. Coupling would be attained using fiber architecture while fine control would be achieved using actuators. In this manner large elastic deformations with fine control could be realized without causing any structural delaminations.


8.    Summary

Figure 14. Potential Applications of Quasi-Unbalanced Wing Spar

The convergently coupled wing structure with the quasi-unbalanced architecture is particularly advantageous for aircraft with very high aspect-ratio wings designed for loitering flights, highly maneuverable aircraft with tip stores such as ordinance, and VTOL aircraft with tip-mounted lift engines, as shown in Figure 14. Aeroelastic tailoring will permit such aircraft to be significantly more effective in conducting their missions. 


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