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NASA NTRS2009

Further Development of Ko Displacement Theory for Deformed Shape Predictions of Nonuniform Aerospace Structures

The Ko displacement theory previously formulated for deformed shape predictions of nonuniform beam structures is further developed mathematically. The further-developed displacement equations are expressed explicitly in terms of geometrical parameters of the beam and bending strains at equally spaced strain-sensing stations along the multiplexed fiber-optic sensor line installed on the bottom surface of the beam. The bending strain data can then be input into the displacement equations for calculations of local slopes, deflections, and cross-sectional twist angles for generating the overall deformed shapes of the nonuniform beam. The further-developed displacement theory can also be applied to the deformed shape predictions of nonuniform two-point supported beams, nonuniform panels, nonuniform aircraft wings and fuselages, and so forth. The high degree of accuracy of the further-developed displacement theory for nonuniform beams is validated by finite-element analysis of various nonuniform beam structures. Such structures include tapered tubular beams, depth-tapered unswept and swept wing boxes, width-tapered wing boxes, and double-tapered wing boxes, all under combined bending and torsional loads. The Ko displacement theory, combined with the fiber-optic strain-sensing system, provide a powerful tool for in-flight deformed shape monitoring of unmanned aerospace vehicles by ground-based pilots to maintain safe flights.

Ko, William L.↗

NASA NTRS2007

Displacement Theories for In-Flight Deformed Shape Predictions of Aerospace Structures

Displacement theories are developed for a variety of structures with the goal of providing real-time shape predictions for aerospace vehicles during flight. These theories are initially developed for a cantilever beam to predict the deformed shapes of the Helios flying wing. The main structural configuration of the Helios wing is a cantilever wing tubular spar subjected to bending, torsion, and combined bending and torsion loading. The displacement equations that are formulated are expressed in terms of strains measured at multiple sensing stations equally spaced on the surface of the wing spar. Displacement theories for other structures, such as tapered cantilever beams, two-point supported beams, wing boxes, and plates also are developed. The accuracy of the displacement theories is successfully validated by finite-element analysis and classical beam theory using input-strains generated by finite-element analysis. The displacement equations and associated strain-sensing system (such as fiber optic sensors) create a powerful means for in-flight deformation monitoring of aerospace structures. This method serves multiple purposes for structural shape sensing, loads monitoring, and structural health monitoring. Ultimately, the calculated displacement data can be visually displayed to the ground-based pilot or used as input to the control system to actively control the shape of structures during flight.

Ko, William L.↗

NASA NTRS1993

Aeroelastic character of a National Aerospace Plane demonstrator concept

The paper provides an analytical assessment of the flutter character of an unclassified National Aerospace Plane configuration known as the demonstrator. Linear subsonic, supersonic, and hypersonic analysis indicate that the vehicle is prone to body-freedom flutter resulting from the decrease in vibration frequency of the all-moveable wing at high flight dynamic pressures. As the wing-pivot frequency decreases, it couples with the vehicle short-period mode resulting in dynamic instability. A similar instability sometimes occurs when the pivot mode couples with the fuselage-bending mode. Also assessed, for supersonic flight conditions, are configuration variations that include relocation of the wing further aft on the lifting-body fuselage, and the addition of body flaps to the rear of the vehicle. These changes are destabilizing because they result in severe wing-pivot/fuselage-bending instabilities at dynamic pressures lower than the instabilities indicated for the original demonstrator. Finally, a two-point wing support and actuation system concept is proposed for the National Aerospace Plane, which if developed may (according to cursory analysis) enhance overall stability.

Spain, Charles V.↗