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NASA NTRS1986

Differential stiffness effects

Differential stiffness as developed in NASTRAN is a linear change in stiffness caused by applied loads. Examples of differential stiffness are the stiffening effects of gravity forces in a pendulum, centrifugal forces in rotor blades and pressure loading of shell structures. In cases wherein this stiffness caused by a load is destabilizing, the differential stiffness concept lends itself to nonlinear structural analysis. Rigid Formats 4 (static analysis with differential stiffness) and 13 (normal modes with differential stiffness) are specifically designed to account for such stiffness changes. How pressure loading may be treated in these rigid formats is clarified. This clarification results from modal correlation of Ground Vibration Test (GVT) results from the empty and pressurized Filament Wound Case (FWC) quarter-scale Space Shuttle solid rocket booster (QSSRB). A sketch of the QSSRB cantilevered to the floor by its external tank attachments is shown.

Ujihara, B. H.↗

NASA NTRS1988

The Flying Diamond: A joined aircraft configuration design project, volume 1

The results of the analysis conducted on the Joined Wing Configuration study are presented. The joined wing configuration employs a conventional fuselage and incorporates two wings joined together near their tips to form a diamond shape in both plan view and front view. The arrangement of the lifting surfaces uses the rear wing as a horizontal tail and as a forward wing strut. The rear wing has its root at the tip of the vertical stabilizer and is structurally attached to the trailing edge of the forward wing. This arrangement of the two wings forms a truss structure which is inherently resistant to the aerodynamic bending loads generated during flight. This allows for a considerable reduction in the weight of the lifting surfaces. With smaller internal wing structures needed, the Joined Wing may employ thinner wings which are more suitable for supersonic and hypersonic flight, having less induced drag than conventional cantilever winged aircraft. Inherent in the Joined Wing is the capability of the generation of direct lift and side force which enhance the performance parameters.

Ball, Chris↗

NASA NTRS1983

Flutter and steady/unsteady aerodynamic characteristics of supercritical and conventional transport wings

This paper presents the technical details and results of a high-speed wind-tunnel test program of an aeroelastic cantilevered transport type wing with two pylon-mounted engines. The tests were conducted in the NASA-Langley 16-foot Transonic Dynamic tunnel (TDT) during December 1981. Flutter of identical planforms, mass properties, and stiffness. The test parameters included different values of model stiffness and wing loading at various angles of attack. The models were instrumented at span-wise wing stations to determine bending and torsion deflections and vertical accelerations. At two model wing stations, pressure transducers were distributed along the chord to record static and unsteady oscillatory pressures during the approach to and onset of flutter. This paper presents the test program with results of the flutter characteristics and selected steady and unsteady aerodynamic data for both airfoils at different angles of attack for various Mach numbers and dynamic pressures.

Grosser, W. F.↗

NASA NTRS1960

Use of Subsonic Kernel Function in an Influence-Coefficient Method of Aeroelastic Analysis and some Comparisons with Experiment

This paper illustrates the development and application of an influence-coefficient method of analysis for calculating the response of a flexible wing in an airstream to an oscillating disturbing force and for treating such aeroelastic instabilities as flutter and divergence. Aerodynamic coefficients are derived on the basis of lifting - surface theory for subsonic compressible flow by use of the method presented in NASA Technical Report R-48. Application of the analysis is made to a uniform cantilever wing- tip tank configuration for which responses to a sinusoidal disturbing force and flutter speeds were measured over a range of subsonic Mach numbers and densities. Calculated responses and flutter speeds based on flexibility influence coefficients measured at nine stations are in good agreement with experiment, provided the aerodynamic load is distributed over the wing so that local centers of pressure very nearly coincide with these nine influence stations. The use of experimental values of bending and torsional structural damping coefficients in the analysis generally improved the agreement between calculated and experimental responses. Some calculations were made to study the effects on density on responses near the flutter conditions, and linear response trends were obtained over a wide range of densities.

Sewall, John L.↗

NASA NTRS1972

Study of the dynamics of orbital assemblies including interactions with geometrical appendages. Unified flexible spacecraft load program (LOAD): Final report and user's and operation manual

The addition of a dynamic loads computation capability to the Unified Flexible Spacecraft Simulation (UFSS) program is discussed. The added capability provides a means for determining the internal member loads due to the time-varying external loading conditions experienced by an orbiting spacecraft/cluster. The flexible bodies are modeled as a system of joints or nodes which are interconnected by weightless finite element members. All masses are lumped at the joints. The orthogonal functions used to describe the spatial deformation of the bodies are normally taken to be the orthonormal cantilever modes produced by a standard structural dynamics program.

Ness, D. J.↗

NASA NTRS1981

Vibration and local instability of thermally stressed plates

The vibration and buckling of a double wedge square cantilever plate has been investigated. It is shown that the free vibration modes, which occur at Delta T ref = 0, transition into the buckled modes which occur at Delta T ref = Delta T ref-cr for the respective mode. Delta T ref-cr for a particular mode is defined as the magnitude of thermal load at which the frequency of the particular mode vanishes. The analysis yields the same number of buckling eigenvalues and buckling modes as there are vibration eigenvalues and vibration modes. Gradual application of the load in the analysis permits the change in each vibration frequency of interest and its associated mode to be followed up to the load at which the frequency of the mode becomes zero. This constitutes the limit of linear theory. As the load is increased, the thin edges of the plate begin to deform during vibration. This local deformation, which begins in the vibration mode, is shown to transition into the phenomena of local edge buckling at Delta T ref-cr for the mode.

Bailey, C. D.↗

NASA NTRS1982

Finite element analysis for bearingless rotor blade aeroelasticity

A conventional articulated rotor blade has mechanical flap and lag hinges, a lag damper, and a pitch bearing. In connection with an interest in designs of greater mechanical simplicity and increased maintainability, hingeless and bearingless rotors have been developed. A hingeless blade lacks the hinges and is cantilevered at the hub. It does have a pitch bearing for pitch control. A bearingless design eliminates the hinges and the pitch bearing as well. In the present investigation of bearingless rotor blade characteristics, finite element analysis has been successfully applied to determine the solutions of the nonlinear trim equations and the linearized flutter equations of multiple-load-path blades. The employed formulation is based on Hamilton's principle. The spatial dependence of the equations of motion is discretized by dividing the flexbeams, the torque tube, and the outboard into a number of elements.

Sivaneri, N. T.↗

NASA NTRS1985

Definition of ground test for verification of large space structure control

Directions regarding the analytical models were received. A counter balance arm with weights was added at the top of the ASTROMAST to offset the arm with the gimbals. In addition to this model, three more models were requested from MSFC: structure as in the revised model with the addition of lumped masses at bays 46 and 91 of the ASTROMAST; cantilevered cruciform structure with lumped masses at bays 46 and 91, and an all up cruciform structure with lumped masses at bays 46 and 91. Figures for each model and their corresponding natural frequencies and general mode shapes associated with these frequencies are included. The drawbar in use in the cruciform models must be incorporated into the antenna and ASTROMAST models. The total tensile load carrying capability of the ASTROMAST is approximately 840 pounds.

Seltzer, S. M.↗

NASA NTRS2008

Preliminary Structural Design Considerations and Mass Efficiencies for Lunar Surface Manipulator Concepts

The mass and sizing characteristics of manipulators for Lunar and Mars planetary surface applications are investigated by analyzing three structural configurations: a simple cantilevered boom with a square tubular cross-section; a hybrid cable/boom configuration with a square tubular cross-section support structure; and a hybrid cable/boom configuration with a square truss cross-section support structure. Design procedures are developed for the three configurations and numerical examples are given. A new set of performance parameters are developed that relate the mass of manipulators and cranes to a loading parameter. These parameters enable the masses of different manipulator configurations to be compared over a wide range of design loads and reach envelopes (radii). The use of these parameters is demonstrated in the form of a structural efficiency chart using the newly considered manipulator configurations. To understand the performance of Lunar and Mars manipulators, the design procedures were exercised on the three manipulator configurations assuming graphite/epoxy materials for the tubes and trusses. It is also assumed that the actuators are electric motor, gear reduction systems. Numerical results for manipulator masses and sizes are presented for a variety of manipulator reach and payload mass capabilities. Results are presented that demonstrate the sensitivity of manipulator mass to operational radius, tip force, and actuator efficiency. The effect of the value of gravitational force on the ratio of manipulator-mass to payload-mass is also shown. Finally, results are presented to demonstrate the relative mass reduction for the use of graphite/epoxy compared to aluminum for the support structure.

Dorsey, John T.↗

NASA NTRS2023

Subsonic Ultra Green Aircraft Research: Phase IV Final Report – Volume I Mach 0.80 Transonic Truss-Braced Wing High-Speed Design Report

This design report summarizes work performed by the Boeing Subsonic Ultra-Green Aircraft Research (SUGAR) team from December 2016 through June 2018. In Phase IV of the SUGAR program, Boeing is working to improve the productivity of a TTBW configuration by updating the Mach 0.745 vehicle concept to operate efficiently at Mach 0.80. Due to the aerodynamic and structural design challenges associated with adapting the design to a higher speed, design tasks have been broken into several subtasks. The information in this report (Volume I) documents the development of a Mach 0.80 vehicle outer mold line, maturation of TTBW structural concepts, and presents a preliminary high-liftsystem assessment. Results from these studies were integrated into an aircraft-level performance code that estimates the benefits of TTBW technology, both on its own and as a part of the SUGAR integrated technology suite. The aerodynamic performance results presented herein detail the high cruise efficiency of the TTBW concept operating at M=0.80. Results from the RANS code OVERFLOW indicate that the TTBW is aerodynamically well suited for operation at the design M=0.80 transonic cruise Mach number. Aircraft-level performance predictions show that the TTBW offers a 7.2% improvement in fuel burn (per seat) for an economic mission of 900nm, and a 9.0% improvement in fuel burn (per seat) for a 3500nm mission with full passenger payload, relative to an aspect ratio 13 conventional tube and wing configuration of equivalent technology. Integration of the TTBW performance benefits into the SUGAR technology suite shows a 55.9% reduction in fuel burn (for the economic mission) relative to the reference (SUGAR Free) aircraft, which is a consistently sized traditional cantilever wing, single-aisle transport typical of the 2008 fleet. This benefit does not include the performance improvement potential of hybrid-electric systems studied in earlier phases of the SUGAR program Structural concept development work completed in Phase IV has identified several strut attachment concepts that are worth additional development activity – an inboard strut attachment swivel joint concept (which enables the strut to carry axial loads while avoiding strut bending induced by wing twist during flight) significantly simplifies the construction of the main strut. An outboard offset strut attachment concept holds significant potential for further reductions in wing-strut interference drag. Based on work performed to date on Phase IV and the previous phases of the SUGAR program, the TTBW concept continues to remain a viable concept for significantly improving the performance of future aircraft. High-fidelity aerodynamic analysis of the Mach 0.80 TTBW aircraft has shown fuel burn improvement that has exceeded initial expectations despite the increase in cruise Mach number. Structural concept maturation has continued to refine the TTBW structure, and has found no obvious ‘show-stoppers’ to date. Therefore, the potential benefit of improved performance through the use of a very high aspect ratio strut-braced wing continues to warrant additional study

SUGAR↗

NASA NTRS2007

A Procedure for Modeling Structural Component/Attachment Failure Using Transient Finite Element Analysis

Structures often comprise smaller substructures that are connected to each other or attached to the ground by a set of finite connections. Under static loading one or more of these connections may exceed allowable limits and be deemed to fail. Of particular interest is the structural response when a connection is severed (failed) while the structure is under static load. A transient failure analysis procedure was developed by which it is possible to examine the dynamic effects that result from introducing a discrete failure while a structure is under static load. The failure is introduced by replacing a connection load history by a time-dependent load set that removes the connection load at the time of failure. The subsequent transient response is examined to determine the importance of the dynamic effects by comparing the structural response with the appropriate allowables. Additionally, this procedure utilizes a standard finite element transient analysis that is readily available in most commercial software, permitting the study of dynamic failures without the need to purchase software specifically for this purpose. The procedure is developed and explained, demonstrated on a simple cantilever box example, and finally demonstrated on a real-world example, the American Airlines Flight 587 (AA587) vertical tail plane (VTP).

Lovejoy, Andrew E.↗

NASA NTRS1977

A NASTRAN DMAP alter for the coupling of modal and physical coordinate substructures

A method is described to derive a generalized coordinate model consisting of flexible cantilever modes and rigid body modes from a physical coordinate model using a direct matrix abstraction procedure alter to rigid format 3. This model can readily be coupled to other substructures using modal synthesis techniques. It allows the use of a reduced size model for structural analyses while maintaining the capability of recovering the accelerations, forces, stresses, etc., from the original, large, complex model. This output recovery is accomplished with the use of a loads transformation matrix which relates the output parameters to the modal coordinate accelerations. In addition, a method is described to synthesize structural models consisting of hybrid coordinates for use in dynamic response analyses where one structure is described using physical coordinates and the other using generalized modal coordinates.

Wilson, T. L.↗

NASA NTRS2001

Simulation of Aircraft Engine Blade-Out Structural Dynamics

A primary concern of aircraft structure designers is the accurate simulation of the blade-out event and the subsequent windmilling of the engine. Reliable simulations of the blade-out event are required to insure structural integrity during flight as well as to guarantee successful blade-out certification testing. The system simulation includes the lost blade loadings and the interactions between the rotating turbomachinery and the remaining aircraft structural components. General-purpose finite element structural analysis codes such as MSC NASTRAN are typically used and special provisions are made to include transient effects from the blade loss and rotational effects resulting from the engine's turbomachinery. The present study provides the equations of motion for rotordynamic response including the effect of spooldown speed and rotor unbalance and examines the effects of these terms on a cantilevered rotor. The effect of spooldown speed is found to be greater with increasing spooldown rate. The parametric term resulting from the mass unbalance has a more significant effect on the rotordynamic response than does the spooldown term. The parametric term affects both the peak amplitudes as well as the resonant frequencies of the rotor.

Lawrence, Charles↗

NASA NTRS2001

Simulation of Aircraft Engine Blade-Out Structural Dynamics

Lawrence, Charles↗

NASA NTRS1990

Experimental and numerical study of the British Experimental Rotor Programme blade

Wind-tunnel tests on the British Experimental Rotor Programme (BERP) tip are described, and the results are compared with computational fluid dynamics (CFD) results. The test model was molded using the Lynx-BERP blade tooling to provide a semispan, cantilever wing comprising the outboard 30 percent of the rotor blade. The tests included both surface-pressure measurements and flow visualization to obtain detailed information of the flow over the BERP tip for a range of angles of attack. It was observed that, outboard of the notch, favorable pressure gradients exist which ensure attached flow, and that the tip vortex also remains stable to large angles of attack. On the rotor, these features yield a very gradual break in control loads when the retreating-blade limit is eventually reached. Computational and experimental results were generally found to be in good agreement.

Brocklehurst, Alan↗

NASA NTRS1989

Shaft flexibility effects on aeroelastic stability of a rotating bladed disk

A comprehensive study of Coriolis forces and shaft flexibility effects on the structural dynamics and aeroelastic stability of a rotating bladed-disk assembly attached to a cantilever, massless, flexible shaft is presented. Analyses were performed for an actual bladed-disk assembly, used as the first stage in the fan of the 'E3' engine. In the structural model, both in-plane and out-of-plane elastic deformation of the bladed-disk assembly were considered relative to their hub, in addition to rigid disk translations and rotations introduced by shaft flexibility. Besides structural coupling between blades (through the flexible disk), additional coupling is introduced through quasisteady aerodynamic loads. Rotational effects are accounted for throughout the work, and some mode shapes for the whole structure are presented at a selected rpm.

Khader, Naim↗

NASA NTRS1953

Deflection and Stress Analysis of Thin Solid Wings of Arbitrary Plan Form with Particular Reference to Delta Wings

The structural analysis of arbitrary solid cantilever wings by small-deflection thin-plate theory is reduced to the solution of linear ordinary differential equations by the assumption that the chordwise deflections at any spanwise station may be expressed in the form of a power series in which the coefficients are functions of the spanwise coordinate. If the series is limited to the first two and three terms (that is, if linear and parabolic chordwise deflections, respectively, are assumed), the differential equations for the coefficients are solved exactly for uniformly loaded solid delta wings of constant thickness ratio. For cases for which exact solutions to the differential equations cannot be obtained, a numerical procedure is derived. Experimental deflection and stress data for constant-thickness delta-plate specimens of 45 degree and 60 degree sweep are presented and are found to compare favorably with the present theory.

Stein, Manuel↗

NASA NTRS1983

Residual strength assessment of low velocity impact damage of graphite-epoxy laminates

This report contains the study of Low Velocity Transverse Impact Damage of graphite-epoxy T300/5208 composite laminates. The specimen, 100 mm diameter clamped plates, were impact damaged by a cantilever-type instrumented 1-inch diameter steel ball. Study was limited to impact velocity 6 m/sec. Rectangular strips, 50 mm x 125 mm, were cut from the impact-damage specimens so that the impact damage zone was in the center of the strips. These strips were tested in tension to obtain their residual strength. An energy dissipation model was developed to predict the residual strength from fracture mechanics concepts. Net energy absorbed I(a) was evaluated from coefficient of restitution concepts based on shear dominated theory of fiber-reinforced materials, with the modification that during loading and unloading the shear deformation are respectively elastic-plastic and elastic. Delamination energy I(d) was predicted by assuming that the stiffness of the laminate dropped due to debonding. Fiber-breakage energy, assumed to be equal to the difference of I(a) and I(d), was used to determine the residual strength. Predictions were compared with test results.

Lal, K. M.↗