Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Calculation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Computer program for calculation of complex chemical equilibrium compositions and applications. Part 1: Analysis

This report presents the latest in a number of versions of chemical equilibrium and applications programs developed at the NASA Lewis Research Center over more than 40 years. These programs have changed over the years to include additional features and improved calculation techniques and to take advantage of constantly improving computer capabilities. The minimization-of-free-energy approach to chemical equilibrium calculations has been used in all versions of the program since 1967. The two principal purposes of this report are presented in two parts. The first purpose, which is accomplished here in part 1, is to present in detail a number of topics of general interest in complex equilibrium calculations. These topics include mathematical analyses and techniques for obtaining chemical equilibrium; formulas for obtaining thermodynamic and transport mixture properties and thermodynamic derivatives; criteria for inclusion of condensed phases; calculations at a triple point; inclusion of ionized species; and various applications, such as constant-pressure or constant-volume combustion, rocket performance based on either a finite- or infinite-chamber-area model, shock wave calculations, and Chapman-Jouguet detonations. The second purpose of this report, to facilitate the use of the computer code, is accomplished in part 2, entitled 'Users Manual and Program Description'. Various aspects of the computer code are discussed, and a number of examples are given to illustrate its versatility.

Gordon, Sanford↗
NASA NTRS1995

Calculated Coupling Efficiency Between an Elliptical-Core Optical Fiber and a Silicon Oxynitride Rib Waveguide [Corrected Copy]

The effective-index method and Marcatili's technique were utilized independently to calculate the electric field profile of a rib channel waveguide. Using the electric field profile calculated from each method, the theoretical coupling efficiency between a single-mode optical fiber and a rib waveguide was calculated using the overlap integral. Perfect alignment was assumed and the coupling efficiency calculated. The coupling efficiency calculation was then repeated for a range of transverse offsets.

Tuma, Margaret L.↗
NASA NTRS1998

The Calculation of Theoretical Chromospheric Models and the Interpretation of the Solar Spectrum

Since the early 1970s we have been developing the extensive computer programs needed to construct models of the solar atmosphere and to calculate detailed spectra for use in the interpretation of solar observations. This research involves two major related efforts: work by Avrett and Loeser on the Pandora computer program for non-LTE modeling of the solar atmosphere including a wide range of physical processes, and work by Rurucz on the detailed synthesis of the solar spectrum based on opacity data or over 58 million atomic and molecular lines. our goals are: to determine models of the various features observed on the Sun (sunspots, different components of quiet and active regions, and flares) by means of physically realistic models, and to calculate detailed spectra at all wavelengths that match observations of those features. These two goals are interrelated: discrepancies between calculated and observed spectra are used to determine improvements in the structure of the models, and in the detailed physical processes used in both the model calculations and the spectrum calculations. The atmospheric models obtained in this way provide not only the depth variation of various atmospheric parameters, but also a description of the internal physical processes that are responsible for non-radiative heating, and for solar activity in general.

Avrett, Eugene H.↗
NASA NTRS1959

Supersonic and Moment-of-Area Rules Combined for Rapid Zero-Lift Wave-Drag Calculations

The concepts of the supersonic area rule and the moment-of-area rule are combined to develop a new method for calculating zero-lift wave drag which is amenable to the use of ordinary desk calculators. The total zero-lift wave drag of a configuration is calculated by the new method as the sum of the wave drag of each component alone plus the interference between components. In calculating the separate contributions each component or pair of components is analyzed over the smallest allowable length in order to improve the convergence of the series expression for the wave drag. The accuracy of the present method is evaluated by comparing the total zero-lift wave-drag solutions for several simplified configurations obtained by the present method with solutions given by slender-body and linearized theory. The accuracy and computational time required by the present method are also evaluated relative to the supersonic area rule and the moment-of-area rule. The results of the evaluation indicate that total zero-lift wave-drag solutions for simplified configurations can be obtained by the present method which differ from solutions given by slender-body and linearized theory by less than 6 percent. This accuracy for simplified configurations was obtained from only nine terms of the series expression for the wave drag as a result of calculating the total zero-lift wave drag by parts. For the same number of terms these results represent an accuracy greater than that for solutions obtained by either of the two methods upon which the present method is based, except in a few isolated cases. For the excepted cases, solutions by the present method and the supersonic area rule are identical. Solutions by the present method are obtained in one fifth the computing time required by the supersonic area rule. This difference in computing time of course would be substantially reduced if the complete procedures for both methods were programmed on electronic computing machines.

Levy, Lionel L., Jr.↗
NASA NTRS1979

Finite-field Calculations of Molecular Polarizabilities Using Field-Induced Polarization Functions: Second- and Third-order Perturbation Correlation Corrections to the Coupled Hartree-Fock Polarizability of H2O

Ordinary Rayleigh-Schroudinger perturbation theory with Moller-Plesset (RSMP) partitioning is used to calculate second- and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule by a finite-field procedure. Pade approximants are found to be useful in accelerating the convergence of the property perturbation expansions. Field-induced polarization functions suitable for polarizability calculations are determined. The average polarizability calculated, neglecting vibrational averaging, with Dunning's (9s5p/4s-4s2p/2s) contracted GTO basis set augmented by field-induced lslp2d/lp polarization functions is within 3 per cent of the experimental result. Correlation corrections to the dipole moment and polarizability of the water molecule calculated by the finite-field RSMP and single + double excitation CI(SDCI) methods for the same basis set are found to be in close agreement. The RSMP approach has the advantages of being size-consistent and of being capable of greater efficiency than the SCDI method. Comparative calculations carried out using Epstein-Nesbet partitioning show that through third order RSEN correlation perturbation expansions for the dipole moment and polarizability are less rapidly convergent than RSMP expansions. However, reasonable accord with RSMP results can be achieved by using Pade approximants to accelerate the convergence of RSEN energy perturbation expansions. The convergence of RSMP property correlation expansions based on the zeroth-order uncoupled-Hartree-Fock (UCHF) and coupled-Hartree-Fock (CHF) approximations are compared through third order. Whereas the CHF + RSMP expansions are for practical purposes fully converged, the UCHF + RSMP expansions are not adequately converged.

Langhoff, S. R.↗
NASA NTRS1999

Detailed Comparison of Observed Dose-Time Profile of October 19-20, 1989 SPE on Mir with Model Calculations

The dose rate dynamics of the October 19-20,1989 solar energetic particle (SPE) event as observed by the Liulin instrument onboard the Mir orbital station was analyzed in light of new calculations of the geomagnetic cutoff and improved estimates of the less than 100 MeV energy spectra from the GOES satellite instrument. The new calculations were performed using the as-flown Mir orbital trajectory and includes time variations of the cutoff rigidity due to changes in the kappa (sub p) index. Although the agreement of total event integrated calculated dose to the measured dose is good, it results from some measured dose-time profile been higher and some lower than model calculations. They point to the need to include the diurnal variation of the geomagnetic cutoff and modifications of the cutoffs to variations in kappa (sub p) in model calculations. Understanding of such events in light of the upcoming construction of the International Space Station during the period of maximum solar activity needs to be vigorously pursued.

Badhwar, Gautam D.↗
NASA NTRS2000

Sensitivity of Age-of-Air Calculations to the Choice of Advection Scheme

The age of air has recently emerged as a diagnostic of atmospheric transport unaffected by chemical parameterizations, and the features in the age distributions computed in models have been interpreted in terms of the models' large-scale circulation field. This study shows, however, that in addition to the simulated large-scale circulation, three-dimensional age calculations can also be affected by the choice of advection scheme employed in solving the tracer continuity equation, Specifically, using the 3.0deg latitude X 3.6deg longitude and 40 vertical level version of the Geophysical Fluid Dynamics Laboratory SKYHI GCM and six online transport schemes ranging from Eulerian through semi-Lagrangian to fully Lagrangian, it will be demonstrated that the oldest ages are obtained using the nondiffusive centered-difference schemes while the youngest ages are computed with a semi-Lagrangian transport (SLT) scheme. The centered- difference schemes are capable of producing ages older than 10 years in the mesosphere, thus eliminating the "young bias" found in previous age-of-air calculations. At this stage, only limited intuitive explanations can be advanced for this sensitivity of age-of-air calculations to the choice of advection scheme, In particular, age distributions computed online with the National Center for Atmospheric Research Community Climate Model (MACCM3) using different varieties of the SLT scheme are substantially older than the SKYHI SLT distribution. The different varieties, including a noninterpolating-in-the-vertical version (which is essentially centered-difference in the vertical), also produce a narrower range of age distributions than the suite of advection schemes employed in the SKYHI model. While additional MACCM3 experiments with a wider range of schemes would be necessary to provide more definitive insights, the older and less variable MACCM3 age distributions can plausibly be interpreted as being due to the semi-implicit semi-Lagrangian dynamics employed in the MACCM3. This type of dynamical core (employed with a 60-min time step) is likely to reduce SLT's interpolation errors that are compounded by the short-term variability characteristic of the explicit centered-difference dynamics employed in the SKYHI model (time step of 3 min). In the extreme case of a very slowly varying circulation, the choice of advection scheme has no effect on two-dimensional (latitude-height) age-of-air calculations, owing to the smooth nature of the transport circulation in 2D models. These results suggest that nondiffusive schemes may be the preferred choice for multiyear simulations of tracers not overly sensitive to the requirement of monotonicity (this category includes many greenhouse gases). At the same time, age-of-air calculations offer a simple quantitative diagnostic of a scheme's long-term diffusive properties and may help in the evaluation of dynamical cores in multiyear integrations. On the other hand, the sensitivity of the computed ages to the model numerics calls for caution in using age of air as a diagnostic of a GCM's large-scale circulation field.

Eluszkiewicz, Janusz↗
NASA NTRS1996

Stress Calculations for Carbon Nanotubes

Atomic stresses were calculated for carbon nanotubes under strain conditions. Graphitic tubules with radii ranging from approximately 2 to 11 Angstroms and two different tubule structures with varying atomic orientations were included in the calculations. Elongations and contractions were applied in the axial direction and atomic stress values were calculated for infinitely long tubules. The calculations were carried out using Brenner's function which was developed for carbon species. Results indicate that the stress is tensile in the radial direction while it is compressive in the tangential direction. Variations in stress values in the direction of the cylindrical aids were investigated as a function of applied strain. Furthermore, using the stress-strain curve (calculated based on atomic considerations), the values of Young's modulus and Poisson's ratio for nanotubules were also estimated.

Halicioglu, Timur↗
NASA NTRS2003

Calculations of Aerosol Radiative Forcing in the SAFARI Region from MODIS Data

SAFARI 2000 provided the opportunity to validate MODIS aerosol retrievals and to correct any assumptions in the retrieval process. By comparing MODIS retrievals with ground-based sunphotometer data, we quantified the degree to which the MODIS algorithm underestimated the aerosol optical thickness. This discrepancy was attributed to underestimating the degree of light absorption by the southern African smoke aerosol. Correcting for this underestimation of absorption, produces more realistic aerosol retrievals that allow various applications of the MODIS aerosol products. One such application is the calculation of the aerosol radiative forcing at the top and bottom of the atmosphere. The combination of MODIS accuracy, coverage, resolution and the ability to separate fine and coarse mode make this calculation substantially advanced over previous attempts with other satellites. We focus on the oceans adjacent to southern Africa and use a solar radiative transfer model to perform the flux calculations. The forcing at the top of atmosphere is calculated to be 10 W/sq m, while the forcing at the surface is -26 W/sq m. These results resemble those calculated from INDOEX data, and are most sensitive to assumptions of aerosol absorption, the same parameter that initially interfered with our retrievals.

Remer, L. A.↗
NASA NTRS1996

The calculation of radial dose from heavy ions: predictions of biological action cross sections

The track structure model of heavy ion cross sections was developed by Katz and co-workers in the 1960s. In this model the action cross section is evaluated by mapping the dose-response of a detector to gamma rays (modeled from biological target theory) onto the radial dose distribution from delta rays about the path of the ion. This is taken to yield the radial distribution of probability for a "hit" (an interaction leading to an observable end-point). Radial integration of the probability yields the cross section. When different response from ions of different Z having the same stopping power is observed this model may be indicated. Since the 1960s there have been several developments in the computation of the radial dose distribution, in the measurement of these distributions, and in new radiobiological data against which to test the model. The earliest model, by Butts and Katz made use of simplified delta ray distribution functions, of simplified electron range-energy relations, and neglected angular distributions. Nevertheless it made possible the calculation of cross sections for the inactivation of enzymes and viruses, and allowed extension to tracks in nuclear emulsions and other detectors and to biological cells. It set the pattern for models of observable effects in the matter through which the ion passed. Here we outline subsequent calculations of radial dose which make use of improved knowledge of the electron emission spectrum, the electron range-energy relation, the angular distribution, and some considerations of molecular excitation, of particular interest both close to the path of the ion and the outer limits of electron penetration. These are applied to the modeling of action cross sections for the inactivation of several strains of E-coli and B. subtilis spores where extensive measurements in the "thin-down" region have been made with heavy ion beams. Such calculations serve to test the radial dose calculations at the outer limit of electron penetration. We lack data from which to test these calculations in regions close to the path of the ion aside from our earliest work on latent tracks in plastics, though it appears that the criterion then suggested for the threshold of track formation, of a minimal dose at a minimal distance (of about 20 angstroms, in plastics), remains valid.

NASA Discipline Radiation Health↗
NASA NTRS2004

Role of shielding in modulating the effects of solar particle events: Monte Carlo calculation of absorbed dose and DNA complex lesions in different organs

Distributions of absorbed dose and DNA clustered damage yields in various organs and tissues following the October 1989 solar particle event (SPE) were calculated by coupling the FLUKA Monte Carlo transport code with two anthropomorphic phantoms (a mathematical model and a voxel model), with the main aim of quantifying the role of the shielding features in modulating organ doses. The phantoms, which were assumed to be in deep space, were inserted into a shielding box of variable thickness and material and were irradiated with the proton spectra of the October 1989 event. Average numbers of DNA lesions per cell in different organs were calculated by adopting a technique already tested in previous works, consisting of integrating into "condensed-history" Monte Carlo transport codes--such as FLUKA--yields of radiobiological damage, either calculated with "event-by-event" track structure simulations, or taken from experimental works available in the literature. More specifically, the yields of "Complex Lesions" (or "CL", defined and calculated as a clustered DNA damage in a previous work) per unit dose and DNA mass (CL Gy-1 Da-1) due to the various beam components, including those derived from nuclear interactions with the shielding and the human body, were integrated in FLUKA. This provided spatial distributions of CL/cell yields in different organs, as well as distributions of absorbed doses. The contributions of primary protons and secondary hadrons were calculated separately, and the simulations were repeated for values of Al shielding thickness ranging between 1 and 20 g/cm2. Slight differences were found between the two phantom types. Skin and eye lenses were found to receive larger doses with respect to internal organs; however, shielding was more effective for skin and lenses. Secondary particles arising from nuclear interactions were found to have a minor role, although their relative contribution was found to be larger for the Complex Lesions than for the absorbed dose, due to their higher LET and thus higher biological effectiveness. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

Non-NASA Center↗
NASA NTRS2004

Flutter Stability of the Efficient Low Noise Fan Calculated

The TURBO-AE aeroelastic code has been used to verify the flutter stability of the Efficient Low Noise Fan (ELNF), which is also referred to as the trailing-edge blowing fan. The ELNF is a unique technology demonstrator being designed and fabricated at the NASA Glenn Research Center for testing in Glenn's 9-by-15-Foot Low-Speed Wind Tunnel. In the ELNF, air can be blown out of slots near the trailing edges of the fan blades to fill in the wakes downstream of the rotating blades. This filling of the wakes leads to a reduction of the rotor-stator interaction (tone) noise that results from the interaction of wakes with the downstream stators. The ELNF will demonstrate a 1.6-EPNdB1 reduction in tone noise through wake filling, without increasing the broadband noise. Furthermore, the reduced blade row interaction will decrease the possibility of forced response and enable closer spacing of blade rows, thus reducing engine length and weight. During the design of the ELNF, the rotor blades were checked for flutter stability using the detailed aeroelastic analysis capability of the three-dimensional Navier-Stokes TURBOAE code. The aeroelastic calculations were preceded by steady calculations in which the blades were not allowed to vibrate. For each rotational speed, as the back-pressure was increased, the mass flow rate decreased, and the operating point moved along the constant speed characteristic (speed-line) from choke to stall as shown on the fan map. The TURBO-AE aeroelastic analyses were performed separately for the first two vibration modes (bending and torsion) and covered the complete range of interblade phase angles or nodal diameters at which flutter can occur. The results indicated that the ELNF blades would not encounter flutter at takeoff conditions. The calculations were then repeated for a part-speed condition (70-percent rotational speed), and the results again showed no flutter in the operating region. On the fan map (shown), the predicted flutter point at part speed condition was located beyond the stall line, which means that the ELNF will not encounter flutter since it will never operate beyond the stall line. All the calculations done so far have been for the nonblowing case, and selected calculations will be repeated with air blowing from the trailing edge of the fan.

Bakhle, Milind A.↗
NASA NTRS2007

Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition: Inclusion of Correlation Effects - III

In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.

Shertzer, Janine↗
NASA NTRS2006

Comparison of Measured Leakage Current Distributions with Calculated Damage Energy Distributions in HgCdTe

This paper presents a combined Monte Carlo and analytic approach to the calculation of the pixel-to-pixel distribution of proton-induced damage in a HgCdTe sensor array and compares the results to measured dark current distributions after damage by 63 MeV protons. The moments of the Coulombic, nuclear elastic and nuclear inelastic damage distribution were extracted from Monte Carlo simulations and combined to form a damage distribution using the analytic techniques first described in [I]. The calculations show that the high energy recoils from the nuclear inelastic reactions (calculated using the Monte Car10 code MCNPX [2]) produce a pronounced skewing of the damage energy distribution. The nuclear elastic component (also calculated using the MCNPX) has a negligible effect on the shape of the damage distribution. The Coulombic contribution was calculated using MRED [3,4], a Geant4 [4,5] application. The comparison with the dark current distribution strongly suggests that mechanisms which are not linearly correlated with nonionizing damage produced according to collision kinematics are responsible for the observed dark current increases. This has important implications for the process of predicting the on-orbit dark current response of the HgCdTe sensor array.

Marshall, C. J.↗
NASA NTRS2007

Comparison of Measured Dark Current Distributions with Calculated Damage Energy Distributions in HgCdTe

This paper presents a combined Monte Carlo and analytic approach to the calculation of the pixel-to-pixel distribution of proton-induced damage in a HgCdTe sensor array and compares the results to measured dark current distributions after damage by 63 MeV protons. The moments of the Coulombic, nuclear elastic and nuclear inelastic damage distributions were extracted from Monte Carlo simulations and combined to form a damage distribution using the analytic techniques first described in [1]. The calculations show that the high energy recoils from the nuclear inelastic reactions (calculated using the Monte Carlo code MCNPX [2]) produce a pronounced skewing of the damage energy distribution. While the nuclear elastic component (also calculated using the MCNPX) contributes only a small fraction of the total nonionizing damage energy, its inclusion in the shape of the damage across the array is significant. The Coulombic contribution was calculated using MRED [3-5], a Geant4 [4,6] application. The comparison with the dark current distribution strongly suggests that mechanisms which are not linearly correlated with nonionizing damage produced according to collision kinematics are responsible for the observed dark current increases. This has important implications for the process of predicting the on-orbit dark current response of the HgCdTe sensor array.

Marshall, C. J.↗
NASA NTRS2006

Room-temperature Broadening and Pressure-shift Coefficients in the nu(exp 2) Band of CH3D-O2: Measurements and Semi-classical Calculations

We report measured Lorentz O2-broadening and O2-induced pressure-shift coefficients of CH3D in the nu(exp 2) fundamental band. Using a multispectrum fitting technique we have analyzed 11 laboratory absorption spectra recorded at 0.011 cm(exp 1) resolution using the McMath-Pierce Fourier transform spectrometer, Kitt Peak, Arizona. Two absorption cells with path lengths of 10.2 and 25 cm were used to record the spectra. The total sample pressures ranged from 0.98 to 339.85 Torr with CH3D volume mixing ratios of 0.012 in oxygen. We report measurements for O2 pressure-broadening coefficients of 320 nu(exp 2) transitions with quantum numbers as high as J0(sup w) = 17 and K = 14, where K(sup w) = K' is equivalent to K (for a parallel band). The measured O2-broadening coefficients range from 0.0153 to 0.0645 cm(exp -1) atm(exp -1) at 296 K. All the measured pressure-shifts are negative. The reported O2-induced pressure-shift coefficients vary from about -0.0017 to -0.0068 cm(exp -1) atm(exp -1). We have examined the dependence of the measured broadening and shift parameters on the J(sup W), and K quantum numbers and also developed empirical expressions to describe the broadening coefficients in terms of m (m = -J(sup W), J(sup W), and J(sup w) + 1 in the QP-, QQ-, and QR-branch, respectively) and K. On average, the empirical expressions reproduce the measured broadening coefficients to within 4.4%. The O2-broadening and pressure shift coefficients were calculated on the basis of a semiclassical model of interacting linear molecules performed by considering in addition to the electrostatic contributions the atom-atom Lennard-Jones potential. The theoretical results of the broadening coefficients are generally larger than the experimental data. Using for the trajectory model an isotropic Lennard-Jones potential derived from molecular parameters instead of the spherical average of the atom-atom model, a better agreement is obtained with these data, especially for |m| <= 12 values (11.3% for the first calculation and 8.1% for the second calculation). The O2-pressure shifts whose vibrational contribution are either derived from parameters fitted in the QQ-branch of selfinduced shifts of CH3D or those obtained from pressure shifts induced by Xe in the nu(sup 3) band of CH3D are in reasonable agreement with the scattered experimental data (17.0% for the first calculation and 18.7% for the second calculation).

Predoi-Cross, Adriana↗
NASA NTRS2011

Axisymmetric Calculations of a Low-Boom Inlet in a Supersonic Wind Tunnel

This paper describes axisymmetric CFD predictions made of a supersonic low-boom inlet with a facility diffuser, cold pipe, and mass flow plug within wind tunnel walls, and compares the CFD calculations with the experimental data. The inlet was designed for use on a small supersonic aircraft that would cruise at Mach 1.6, with a Mach number over the wing of 1.7. The inlet was tested in the 8-ft by 6-ft Supersonic Wind Tunnel at NASA Glenn Research Center in the fall of 2010 to demonstrate the performance and stability of a practical flight design that included a novel bypass duct. The inlet design is discussed here briefly. Prior to the test, CFD calculations were made to predict the performance of the inlet and its associated wind tunnel hardware, and to estimate flow areas needed to throttle the inlet. The calculations were done with the Wind-US CFD code and are described in detail. After the test, comparisons were made between computed and measured shock patterns, total pressure recoveries, and centerline pressures. The results showed that the dual-stream inlet had excellent performance, with capture ratios near one, a peak core total pressure recovery of 96 percent, and a large stable operating range. Predicted core recovery agreed well with the experiment but predicted bypass recovery and maximum capture ratio were high. Calculations of offdesign performance of the inlet along a flight profile agreed well with measurements and previous calculations.

Chima, Rodrick V.↗
NASA NTRS2012

First-and Second-Order Displacement Transfer Functions for Structural Shape Calculations Using Analytically Predicted Surface Strains

New first- and second-order displacement transfer functions have been developed for deformed shape calculations of nonuniform cross-sectional beam structures such as aircraft wings. The displacement transfer functions are expressed explicitly in terms of beam geometrical parameters and surface strains (uniaxial bending strains) obtained at equally spaced strain stations along the surface of the beam structure. By inputting the measured or analytically calculated surface strains into the displacement transfer functions, one could calculate local slopes, deflections, and cross-sectional twist angles of the nonuniform beam structure for mapping the overall structural deformed shapes for visual display. The accuracy of deformed shape calculations by the first- and second-order displacement transfer functions are determined by comparing these values to the analytically predicted values obtained from finite element analyses. This comparison shows that the new displacement transfer functions could quite accurately calculate the deformed shapes of tapered cantilever tubular beams with different tapered angles. The accuracy of the present displacement transfer functions also are compared to those of the previously developed displacement transfer functions.

Ko, William L.↗