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NASA NTRS1997

Static Aeroelastic Analysis of Transonic Wind Tunnel Models Using Finite Element Methods

A computational method for accurately predicting the static aeroelastic deformations of typical transonic transport wind tunnel models is described. The method utilizes a finite element method (FEM) for predicting the deformations. Extensive calibration/validation of this method was carried out using a novel wind-off wind tunnel model static loading experiment and wind-on optical wing twist measurements obtained during a recent wind tunnel test in the National Transonic Facility (NTF) at NASA LaRC. Further validations were carried out using a Navier-Stokes computational fluid dynamics (CFD) flow solver to calculate wing pressure distributions about several aeroelastically deformed wings and comparing these predictions with NTF experimental data. Results from this aeroelastic deformation method are in good overall agreement with experimentally measured values. Including the predicted deformations significantly improves the correlation between CFD predicted and experimentally measured wing & pressures.

Hooker, John R.↗

NASA NTRS1998

Model Deformation Measurements at NASA Langley Research Center

Only recently have large amounts of model deformation data been acquired in NASA wind tunnels. This acquisition of model deformation data was made possible by the development of an automated video photogrammetric system to measure the changes in wing twist and bending under aerodynamic load. The measurement technique is based upon a single view photogrammetric determination of two dimensional coordinates of wing targets with a fixed third dimensional coordinate, namely the spanwise location. A major consideration in the development of the measurement system was that use of the technique must not appreciably reduce wind tunnel productivity. The measurement technique has been used successfully for a number of tests at four large production wind tunnels at NASA and a dedicated system is nearing completion for a fifth facility. These facilities are the National Transonic Facility, the Transonic Dynamics Tunnel, and the Unitary Plan Wind Tunnel at NASA Langley, and the 12-FT Pressure Tunnel at NASA Ames. A dedicated system for the Langley 16-Foot Transonic Tunnel is scheduled to be used for the first time for a test in September. The advantages, limitations, and strategy of the technique as currently used in NASA wind tunnels are presented. Model deformation data are presented which illustrate the value of these measurements. Plans for further enhancements to the technique are presented.

Burner, A. W.↗

NASA NTRS1996

Method and system for measurement of mechanical properties of molecules and cells

Mechanical stresses and deformations are applied directly to cell surface receptors or molecules and measured using a system including a magnetic twisting device in combination with ferromagnetic microbeads coated with ligands for integrins or any other surface receptors. The system can be used diagnostically to characterize cells and molecules and to determine the effect of transformation and compounds, including drugs, on the cells and molecules. The system can also be used to induce cells to grow or alter production of molecules by the cells.

Butler, James P.↗

NASA NTRS1949

Investigation of the Effect of Tip Tanks on the Wing Loading of a Republic F-84 Airplane in the Ames 40- by 80-foot Wind Tunnel

Wind-tunnel tests at low Mach number of a Republic F-84C airplane were conducted to determine by pressure-distribution measurements the air loads on wing-tip tanks and the change in wing load distribution due to the presence of tip tanks. Measurements of the aeroelastic twist of the wing were also obtained. Results are presented in the form of loading coefficient, center-of- pressure location, pitching-moment coefficient, aerodynamic-center location, and aeroelastic twist. The investigation revealed that the redistributions in loading brought about by either the tip tanks or elastic deformation of the wing were relatively small when compared with the chnnges in loading normally associated with the deflection of an aileron.

Hunton, Lynn W.↗

NASA NTRS2018

Study of Skin-Stringer Separation in Postbuckled Composite Aeronautical Structures

Aeronautical composite stiffened structures have the capability to carry loads deep into postbuckling, yet they are typically designed to operate below the buckling load to avoid potential issues with durability and structural integrity. Large out-of-plane postbuckling deformation of the skin can result in the opening of the skin-stringer interfaces, especially in the presence of defects, such as impact damage. To ensure that skin-stringer separation does not propagate in an unstable mode that can cause a complete collapse of the structure, a deeper understanding of the interaction between the postbuckling deformation and the development of damage is required. The present study represents a first step towards a methodology based on analysis and experiments to assess and improve the strength, life, and damage tolerance of stiffened composite structures subjected to postbuckling deformations. Two regions were identified in a four-stringer panel in which skin-stringer separation can occur, namely the region of maximum deflection and the region of maximum twisting. Both regions have been studied using a finite element model of a representative single-stringer specimen. For the region of maximum deflection, a seven-point bending configuration was used, in which five supports and two loading points induce buckling waves to the specimen. The region of maximum twisting was studied using an edge crack torsion configuration, with two supports and two loading points. These two configurations were studied by changing the positions of the supports and the loading points. An optimization procedure was carried out to minimize the error between the out-of-plane deformation of the representative single-stringer specimen and the corresponding region of the four-stringer panel.

Kootte, Lucas J.↗

NASA NTRS1991

Extension-bend-twist coupling behavior of thin-walled advanced composite beams with initial twist

An analytical model is developed for assessing the extension-bend-twist coupling behavior of nonhomogeneous anisotropic beams with initial twist. The model is formulated as a coupled two-dimensional boundary value problem, where the displacement solutions are defined with pretwist-dependent functions that represent the extension, bending, and torsion, and unknown functions that represent local in-plane deformations and out-of-plane cross-section warping. The unknown deformation functions are determined by applying the principle of minimum potential energy to a discretized representation of the cross section. Numerical results are presented that fully verify this approach and illustrate the strong extension-twist coupling behavior present in pretwisted beams with thin-wall laminated composite cross sections as a function of ply angle, initial twist level, and initial twist axis location. Cross-sections analyzed include; thin laminated rectangles with either asymmetric or symmetric ply stacking sequences and a thin-wall single cell D-section composed of a graphite/epoxy woven cloth.

Kosmatka, J. B.↗

NASA NTRS1993

Flexure-torsion behavior of prismatic beams. I - Section properties via power series

The behavior of a tip-loaded cantilever beam with an arbitrary cross section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross sections, the calculated coefficients represented a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-sectional properties (torsion constant, shear correction factors, shear deformation coefficients, and shear center location). A new linear relation is developed for locating the shear center, where the twist rate is zero about the line of shear centers. Moreover, the kinematic relations for a new fully compatible one-dimensional beam theory are developed. Numerical results are presented first to verify the approach and second to provide section data on NACA four-series airfoils not currently found in the literature.

Kosmatka, J. B.↗

NASA NTRS1999

Drop Breakup in Fixed Bed Flows as Model Stochastic Flow Fields

We examine drop breakup in a class of stochastic flow fields as a model for the flow through fixed fiber beds and to elucidate the general mechanisms whereby drops breakup in disordered, Lagrangian unsteady flows. Our study consists of two parallel streams of investigation. First, large scale numerical simulations of drop breakup in a class of anisotropic Gaussian fields will be presented. These fields are generated spectrally and have been shown in a previous publication to be exact representations of the flow in a dilute disordered bed of fibers if close interactions between the fibers and the drops are dynamically unimportant. In these simulations the drop shape is represented by second and third order small deformation theories which have been shown to be excellent for the prediction of drop breakup in steady strong flows. We show via these simulations that the mechanisms of drop breakup in these flows are quite different than in steady flows. The predominant mechanism of breakup appears to be very short lived twist breakups. Moreover, the occurrence of breakup events is poorly predicted by either the strength of the local flow in which the drop finds itself at breakup, or the degree of deformation that the drop achieves prior to breakup. It is suggested that a correlation function of both is necessary to be predictive of breakup events. In the second part of our research experiments are presented where the drop deformation and breakup in PDMS/polyisobutylene emulsions is considered. We consider very dilute emulsions such that coalescence is unimportant. The flows considered are simple shear and the flow through fixed fiber beds. Turbidity, small angle light scattering, dichroism and microscopy are used to interrogate the drop deformation process in both flows. It is demonstrated that breakup at very low capillary numbers occurs in both flows but larger drop deformation occurs in the fixed bed flow. Moreover, it is witnessed that breakup in the bed occurs continuously during flow and apparently with uniform probability through the bed length. The drop deformations witnessed in our experiments are larger than those predicted by the numerical simulations, and future plans to investigate these differences are discussed.

Shaqfeh, Eric S. G.↗

NASA NTRS2013

Experimental Investigation of Aeroelastic Deformation of Slender Wings at Supersonic Speeds Using a Video Model Deformation Measurement Technique

A video-based photogrammetric model deformation system was established as a dedicated optical measurement technique at supersonic speeds in the NASA Langley Research Center Unitary Plan Wind Tunnel. This system was used to measure the wing twist due to aerodynamic loads of two supersonic commercial transport airplane models with identical outer mold lines but different aeroelastic properties. One model featured wings with deflectable leading- and trailing-edge flaps and internal channels to accommodate static pressure tube instrumentation. The wings of the second model were of single-piece construction without flaps or internal channels. The testing was performed at Mach numbers from 1.6 to 2.7, unit Reynolds numbers of 1.0 million to 5.0 million, and angles of attack from -4 degrees to +10 degrees. The video model deformation system quantified the wing aeroelastic response to changes in the Mach number, Reynolds number concurrent with dynamic pressure, and angle of attack and effectively captured the differences in the wing twist characteristics between the two test articles.

Erickson, Gary E.↗

NASA NTRS1974

The design, analysis and experimental evaluation of an elastic model wing

An elastic orbiter model was developed to evaluate the effectiveness of aeroelasticity computer programs. The elasticity properties were introduced by constructing beam-like straight wings for the wind tunnel model. A standard influence coefficient mathematical model was used to estimate aeroelastic effects analytically. In general good agreement was obtained between the empirical and analytical estimates of the deformed shape. However, in the static aeroelasticity case, it was found that the physical wing exhibited less bending and more twist than was predicted by theory.

Cavin, R. K., III↗

NASA NTRS1967

Integrating Matrix Method for Determining the Natural Vibrations of a Rotating, Unsymmetrical Beam with Application to Twisted Propeller Blades

A numerical method is Presented for determining the natural vibration frequencies, and the corresponding mode shapes, of a rotating cantilever beam which has a nonuniform, unsymmetrical cross section. Two coupled fourth-order differential equations of motion with variable coefficients are derived which govern the motion of such a beam having deformations in two directions. Through the development and utilization of the integrating matrix, the solution of the differential equations is obtained in the form of an eigenvalue problem. The solutions to the eigenvalue problem are determined by an iteration method based upon a special orthogonality relationship which is derived. Numerical examples, including an application to a twisted propeller blade, are presented with the results of the integrating matrix solutions being compared to exact solutions and experimental data.

Hunter, William F.↗

NASA NTRS2005

Torsion of Noncircular Composite Cylinders

The paper presents a brief overview of the predicted deformation and failure characteristics of noncircular composite cylinders subjected to torsion. Using a numerical analysis, elliptical cylinders with a minor-to-major diameter ratio of 0.7 are considered. Counterpart circular cylinders with the same circumference as the elliptical cylinders are included for comparison. The cylinders are constructed of a medium-modulus graphite-epoxy material in a quasi-isotropic lay-up. Imperfections generated from the buckling mode shapes are included in the initial cross-sectional geometry of the cylinders. Deformations until first fiber failure, as predicted using the maximum stress failure criterion and a material degradation scheme, are presented. For increasing levels of torsion, the deformations of the elliptical cylinders, in the form of wrinkling of the cylinder wall, occur primarily in the flatter regions of the cross section. By comparison the wrinkling deformations of the circular cylinders are more uniformly distributed around the circumference. Differences in the initial failure and damage progression and the overall torque vs. twist relationship between the elliptical and circular cylinders are presented. Despite differences in the response as the cylinders are being loaded, at first fiber failure the torque and twist for the elliptical and circular cylinders nearly coincide.

Rouse, Marshall↗

NASA NTRSDate not supplied

Structural Design and Aeromechanical Analysis of Unconventional Blades for Future Mars Rotorcraft

The structural design for rotor blades with thin, unconventional airfoils for Earth-based testing is obtained using three-Dimensional (3D) aeromechanical analysis. This analysis is in support of the NASA ROAMX project. The outer mold was provided by NASA, but the internal structural design was developed at the University of Maryland and is presented here, along with a thorough aeromechanical analysis. The main objectives are to verify the structural integrity of the design and understand the unique aeroelastic behavior of the non-conventional airfoils designed for low-Reynolds number and high-Mach number flow. Six different blade models are considered, with the pitch axis varied from quarter-chord to mid-chord to determine the effect of C.G. offset on natural frequencies, blade deformations, root loads, and 3D stresses. All six blade designs are first studied under rotation in pure vacuum, and significant reductions in root loads and 3D stresses are achieved by moving the pitch axis closer to mid-chord to reduce the C.G. offset. Based on the vacuum analysis, the blade design with the pitch axis at 40% chord is selected for aerodynamic analysis. The blade control load, airloads, deformations, and 3D stresses are studied for steady hover. Dynamic control load and dynamic 3D stresses are studied for unsteady hover achieved using cyclic. Significant elastic twist is observed due to the trapeze effect and propeller moment, affecting the spanwise distribution of aerodynamic loads on the blades. However, the effect of aerodynamic loads on 3D stresses and the blade control load is found to be minimum. The dynamic control load is found to increase significantly due to inertial coupling from the C.G. offset. The dynamic stresses also increase, although still have factors of safety greater than two for both tensile and compressive stress.

Structural Design↗

NASA NTRS2023

Structural Design and Aeromechanical Analysis of Unconventional Blades for Future Mars Rotorcraft

The structural design for rotor blades with thin, unconventional airfoils for Earth-based testing is obtained using three-Dimensional (3D) aeromechanical analysis in support of the NASA ROAMX project. The outer mold line was provided by NASA, but the internal structural design was developed at the University of Maryland and is presented here along with a thorough aeromechanical analysis. The main objectives are to verify the structural integrity of the design and understand the unique aeroelastic behavior of the non-conventional airfoils designed for low-Reynolds number and high subsonic Mach number. Four different blade models are considered, with the pitch axis varied from quarter-chord to mid-chord to determine the effect of C.G. offset on natural frequencies, blade deformations, root loads, and 3D stresses. First, torsional stability is calculated for each of the designs – especially important due to the low Lock number on Mars. All four blade designs are studied under rotation in vacuum, and significant reductions in root loads and 3D stresses are achieved by moving the pitch axis closer to mid-chord to reduce the C.G. offset. Based on the vacuum analysis, the blade design with the pitch axis at 40% chord is selected for aeromechanical analysis. The blade control load, airloads, deformations, and 3D stresses are studied for steady hover. Dynamic control load and dynamic 3D stresses are studied for unsteady hover achieved using cyclic. Significant elastic twist is observed due to the trapeze effect and propeller moment, affecting the spanwise distribution of aerodynamic loads on the blades. The dynamic control load is found to increase significantly due to inertial coupling from the C.G. offset. The dynamic stresses also increase, although still have factors of safety greater than two for both tensile and compressive stress.

Structural Design↗

NASA NTRS1998

Test of a flexible spacecraft dynamics simulator

There are a number of approaches one can take to modeling the dynamics of a flexible body. While one can attempt to capture the full dynamical behavior subject to disturbances from actuators and environmental torques, such a detailed description often is unnecessary. Simplification is possible either by limiting the amplitude of motion to permit linearization of the dynamics equations or by restricting the types of allowed motion. In this work, we study the nonlinear dynamics of bending deformations of wire booms on spinning spacecraft. The theory allows for large amplitude excursions from equilibrium while enforcing constraints on the dynamics to prohibit those modes that are physically less relevant or are expected to damp out fast. These constraints explicitly remove the acoustic modes (i.e., longitudinal sound waves and shear waves) while allowing for arbitrary bending and twisting, motions which typically are of lower frequency. As a test case, a spin axis reorientation maneuver by the Polar Plasma Laboratory (POLAR) spacecraft has been simulated. POLAR was chosen as a representative spacecraft because it has flexible wire antennas that extend to a length of 65 meters. Bending deformations in these antennas could be quite large and have a significant effect on the attitude dynamics of the spacecraft body. Summary results from the simulation are presented along, with a comparison with POLAR flight data.

Dichmann, Donald↗

NASA NTRS2019

Structure Deformation Calculation Program Based on Displacement Theory for Shape Predictions

Separated programs were written in C/C++ to validate the Displacement Transfer Functions. The Structure Deformation Calculation Program was written to combine all of the programs to calculate deformed shapes of a structure using surface strain data and structural geometrical parameters. Users do not need to know the material properties, nor the complex internal structures geometry because the Displacement Theory is purely geometrical in nature. Users only need to know the structure types as defined in this report and information such as the structure length, depth factors, number of strain sensors, and the surface strains measured at the strain-sensing stations installed on the structures. Depending on the structure type, an applicable Displacement Transfer Function will be used. This program requires two input files created by users; the recorded strain data file in comma-separated values format and the structure geometry data file in text format. The program will output the out-of-plane deflections, slopes, cross-sectional twist angles, and depth factors if applicable. All output files are created in comma-separated values format. A section in this report describes step-by-step procedures on how to use the Structure Deformation Calculation Program for structure deformed shape calculations.

Displacement theory↗

NASA NTRSDate not supplied

Effect of Composite Stiffened Panel Design on Skin-Stringer Separation in Postbuckling

To design aeronautical composite multi-stringer panels that can safely operate in a postbuckled state, it is important to identify the parameters that can influence the different modes in which skin-stringer separation might occur. A methodology is under development to study the interaction between the skin-stringer separation and the postbuckling deformation using the building block approach and single-stringer specimens. In particular, the methodology can identify whether the skin-stringer separation occurs due to bending or twisting, so that these two possible modes can be studied separately. For bending, a simple criterion that can predict the location of initiation is presented. This procedure has the potential to reduce the overall development cost and allows the investigation of the design parameters that influence the skin-stringer separation.

Lucas J. Koote↗

NASA NTRS1939

Experimental Study of Deformation and of Effective Width in Axially Loaded Sheet-stringer Panels

The deformation of two sheet-stringer panels subjected to end compression under carefully controlled end conditions was measured at a number of points and at a number of loads, most of which were above the load at which the sheet had begun to buckle. The two panels were identical except for the sheet, which was 0.70-inch 24st alclad for specimen 1 and 0.025-inch 24st aluminum alloy for specimen 6. A technique was developed for attaching Tuckerman optical strain gauges to the sheet without disturbing the strain distribution in the sheet by the method of attachment. This technique was used to explore the strain distribution in the sheet at various loads. The twisting and the bending of the stringers was measured by means of pointers attached to the stringers. The shape of the buckles in the sheet of specimen 6 was recorded at two loads by means of plaster casts. The sheet and the stringer loads at failure are compared with the corresponding loads for five similar panels tested at the Navy Model Basin. A detailed comparison is made between the measured deformation of the buckled sheet and the deformation calculated from approximate theories for the deformation in a rectangular sheet with freely supported edges buckling under end compression advanced by Timoshenko, Frankland, and Marguerre. The measured effective width for the specimens is compared with the effective width given by nine different relations for effective width as a function of the edge stress divided by the buckling stress of the sheet. The analysis of the measured stringer deformation is confined to an application of Southwell's method of plotting deformation against deformation over load. It was concluded that the stringer failure in both specimens were due to an instability in which the stringer was simultaneously twisted and bent as a column.

FORMULAS - BUCKLING - KARMAN↗