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NASA NTRS1981

An improved transverse shear deformation theory for laminated antisotropic plates

An improved transverse shear deformation theory for laminated anisotropic plates under bending is presented. The theory eliminates the need for an arbitrarily chosen shear correction factor. For a general laminate with coupled bending and stretching, the constitutive equations connecting resultants with average displacements and rotations are derived. Simplified forms of these relations are also obtained for the special case of a symmetric laminate with uncoupled bending. The governing equation for this special case is obtained as a sixth-order equation for the normal displacement requiring prescription of the three physically natural bounday conditions along each edge. For the limiting case of isotropy, the present theory reduces to an improved version of Mindlin's theory. Numerical results are obtained from the present theory for an example of a laminated plate under cylindrical bending. Comparison with results from exact three-dimensional analysis shows that the present theory is more accurate than other theories of equivalent order.

Murthy, M. V. V.↗

NASA NTRS1983

Propagation of flexural and membrane waves with fluid loaded NASTRAN plate and shell elements

Modeling of flexural and membrane type waves existing in various submerged (or in vacuo) plate and/or shell finite element models that are excited with steady state type harmonic loadings proportioned to e(i omega t) is discussed. Only thin walled plates and shells are treated wherein rotary inertia and shear correction factors are not included. More specifically, the issue of determining the shell or plate mesh size needed to represent the spatial distribution of the plate or shell response is of prime importance towards successfully representing the solution to the problem at hand. To this end, a procedure is presented for establishing guide lines for determining the mesh size based on a simple test model that can be used for a variety of plate and shell configurations such as, cylindrical shells with water loading, cylindrical shells in vacuo, plates with water loading, and plates in vacuo. The procedure for doing these four cases is given, with specific numerical examples present only for the cylindrical shell case.

Kalinowski, A. J.↗

NASA NTRS1984

Dynamic analysis of laminated plates using a higher-order theory

This paper deals with the dynamic analog of the higher-order shear deformation plate theory developed by the senior author. The theory is based on a displacement field in which the inplane displacements are expanded as cubic functions of the thicknes coordinate and the transverse deflection is assumed to be constant through the thickness. The additional dependent unkowns introduced with the quadratic and cubic terms of the thickness coordinate are eliminated by requiring the transverse shear stresses to vanish on the bounding planes of the plate. The theory accounts for the parabolic distribution of the transverse shear stresses, and hence no shear correction coefficients are required.

Reddy, J. N.↗

NASA NTRS1985

Analysis of laminated composite plates using a higher-order shear deformation theory

A higher-order deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, and requires no shear correction coefficients. A displacement finite element model of the theory is developed, and applications of the element to bending, vibration and stability of laminated plates are discussed. The present solutions are compared with those obtained using the classical plate theory and the three-dimensional elasticity theory.

Phan, N. D.↗

NASA NTRS1986

Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory

A mixed shear flexible finite element, with relaxed continuity, is developed for the geometrically linear and nonlinear analysis of layered anisotropic plates. The element formulation is based on a refined higher order theory which satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate and requires no shear correction coefficients. The mixed finite element developed herein consists of eleven degrees of freedom per node which include three displacements, two rotations and six moment resultants. The element is evaluated for its accuracy in the analysis of the stability and vibration of anisotropic rectangular plates with different lamination schemes and boundary conditions. The mixed finite element described here for the higher order theory gives very accurate results for buckling loads and natural frequencies.

Putcha, N. S.↗

NASA NTRS1986

A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates

The present study is concerned with the development of a mixed shear flexible finite element with relaxed continuity for the geometrically linear and nonlinear analysis of laminated anisotropic plates. The formulation of the element is based on a refined higher-order theory. This theory satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate. Shear correction coefficients are not needed. The developed element consists of 11 degrees-of-freedom per node, taking into account three displacements, two rotations, and six moment resultants. An evaluation of the element is conducted with respect to the accuracy obtained in the bending of laminated anistropic rectangular plates with different lamination schemes, loadings, and boundary conditions.

Putcha, N. S.↗

NASA NTRS1987

Computational fluid dynamics near the continuum limit

Two dimensional Navier-Stokes equations for a perfect gas are solved for hypersonic flow over a flat plate at Reynolds numbers ranging from continuum to the free molecule flow. In the transition flow regime, new slip boundary conditions are introduced, which reduce to the well-known slip conditions of Maxwell at small Knudsen numbers and yield the correct shear stress and heat transfer in the limiting case of free molecule flow. Comparison of the computed results with the existing experimental data and Monte Carlo calculations indicates that the continuum Navier-Stokes equations give surprisingly realistic results throughout the transition flow regime, when the new slip boundary conditions are used.

Maccormack, Robert W.↗

NASA NTRS1989

Analysis of multilayered anisotropic plates - A new look at an old problem

The paper is concerned with the effects of variation in the lamination and geometric parameters of multilayered anisotropic plates on the accuracy of the static and vibrational responses predicted by six modeling approaches based on two-dimensional shear deformation theories. Extensive numerical results are presented for antisymmetrically laminated anisotropic rectangular plates. It is shown that, for most practical problems, the transverse shear deformation has a much more pronounced effect on the response of multilayered composite plates than that of transverse normal strain and stress. It is also shown that the accuracy of the predictions of the first-order deformation theory is strongly dependent on the values of the composite shear correction factors used.

Noor, Ahmed K.↗

NASA NTRS1991

Formulation of an elastodynamic theory of laminated shear-deformable flat panels

A higher order shear deformation theory (HSDT) is developed, designed to preserve all the characteristics of the first-order shear deformation theory (FSDT) with regard to the number of the unknowns and to the order of the associated governing equations. In contrast to the FSDT theory, the HSDT theory is characterized by a parabolic distribution of transverse shear stress and strain components throughout the laminate thickness thus eliminating the need of a shear correction factor, and by the elimination of the contradictory assumption of the FSDT concerning the simultaneous consideration of zero transverse normal stress and zero transverse normal strain. The governing equations of the HSDT are presented, and several special applications are discussed.

Librescu, L.↗

NASA NTRS1991

Analysis and testing of a space crane articulating joint testbed

The topics are presented in viewgraph form and include: space crane concept with mobile base; mechanical versus structural articulating joint; articulating joint test bed and reference truss; static and dynamic characterization completed for space crane reference truss configuration; improved linear actuators reduce articulating joint test bed backlash; 1-DOF space crane slew maneuver; boom 2 tip transient response finite element dynamic model; boom 2 tip transient response shear-corrected component modes torque driver profile; peak root member force vs. slew time torque driver profile; and open loop control of space crane motion.

Thomas R Sutter↗

NASA NTRS1959

Use of a Stanton Tube for Skin-Friction Measurements

A small total-pressure tube resting against a flat-plate surface was used as a Stanton tube and calibrated as a skin-friction meter at various subsonic and supersonic speeds. Laminar flow was maintained for the supersonic runs at a Mach number M(sub infinity) of 2. At speeds between M(sub infinity) = 1.33 and M(sub infinity) = 1.87, the calibrations were carried-out in a turbulent boundary layer. The subsonic flows were found to be in transition. The skin-friction readings of a floating-element type of balance served as the reference values against which the Stanton tube was calibrated. A theoretical model was developed which, for moderate values of the shear parameter tau, accurately predicts the performance of the Stanton tube in subsonic and supersonic flows. A "shear correction factor" was found to explain the deviations from the basic model when T became too large. Compressibility effects were important only in the case of turbulent supersonic flows, and they did not alter the form of the calibration curve. The test Reynolds numbers, based on the distance from the leading edge and free-stream conditions, ranged from 70,000 to 875,000. The turbulent-boundary-layer Reynolds numbers, based on momentum thickness, varied between 650 and 2,300. Both laminar and turbulent velocity profiles were taken and the effect of pressure gradient on the calibration was investigated.

Abarbanel, S. S.↗

NASA NTRS2002

Dynamic Stability of Uncertain Laminated Beams Under Subtangential Loads

Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. In this research, we focus on the deterministic and probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. Thus a shear-deformable laminated beam element, including warping effects, is derived to study the deterministic and probabilistic response of laminated beams. This twenty-one degrees of freedom element can be used for solving both static and dynamic problems. In the first-order shear deformable model used here we have employed a more accurate method to obtain the transverse shear correction factor. The dynamic version of the principle of virtual work for laminated composites is expressed in its nondimensional form and the element tangent stiffness and mass matrices are obtained using analytical integration The stability is studied by giving the structure a small disturbance about an equilibrium configuration, and observing if the resulting response remains small. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: Exact Monte Carlo Simulation, Sensitivity Based Monte Carlo Simulation, and Probabilistic FEA. These methods were integrated into the developed finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems, as well as to study the stability analysis, using the dynamic criterion.

Goyal, Vijay K.↗

NASA NTRS2005

Effect of Free Jet on Refraction and Noise

This article investigates the role of a free jet on the sound radiated from a jet. In particular, the role of an infinite wind tunnel, which simulates the forward flight condition, is compared to that of a finite wind tunnel. The second configuration is usually used in experiments, where the microphones are located in a static ambient medium far outside the free jet. To study the effect of the free jet on noise, both propagation and source strength need to be addressed. In this work, the exact Green's function in a locally parallel flow is derived for a simulated flight case. Numerical examples are presented that show a reduction in the magnitude of the Green's function in the aft arc and an increase in the forward arc for the simulated flight condition. The effect of finite wind tunnel on refraction is sensitive to the source location and is most pronounced in the aft arc. A Reynolds-averaged Navier-Stokes solution (RANS) yields the required mean flow and turbulence scales that are used in the jet mixing noise spectrum calculations. In addition to the sound/flow interaction, the separate effect of source strength and elongation of the noise-generating region of the jet in a forward flight is studied. Comparisons are made with experiments for the static and finite tunnel cases. Finally, the standard free-jet shear corrections that convert the finite wind tunnel measurements to an ideal wind tunnel arrangement are evaluated.

Khavaran, Abbas↗

NASA NTRS2002

The StarLight interferometer architecture and operational concepts

The StarLight flight project was designed to demonstrate the key technologies of spacebome long-baseline stellar interferometry and precision formation flying for potential use on the Terrestrial Planet Finder (TPF) and other future astrophysics missions. Interferometer performance validation could be achieved over a 6-12 month period by obtaining several hundred fringe visibility amplitude measurements for stars in the band 600-1000 nm for a variety of stellar visibilities (0.2-1.0), magnitudes (Mv = 2-5), and baselines (B = 30-125 meters). Interferometry could be performed both in a 1 meter fixed-baseline combiner-only mode and in a two-spacecraft formation mode. In formation mode, the combiner spacecraft would remain at the focus of a virtual parabola, while the collector spacecraft assumed various positions along the parabola such that the two arms of the interferometer remained equal over a variety of separations and bearing angles. Challenges to be encountered in flight include high-bandwidth inter-spacecraft stellar and metrology pointing control, alignment and shear correction, delay and delay-rate estimation, visibility calibration, and robust fringe tracking in the presence of local and inter-spacecraft dynamics. This paper is based on the StarLight project design-capture of March 2002 and will describe the StarLight Interferometer System architecture and selected operational concepts (both of which have relevance to the on-going TPF Technology Program).

stellar↗

DOE OSTI2023

A differentiable perturbation-based weak lensing shear estimator

Upcoming imaging surveys will use weak gravitational lensing to study the large-scale structure of the Universe, demanding sub-per cent accuracy for precise cosmic shear measurements. We present a new differentiable implementation of our perturbation-based shear estimator (fpfs), using jax, which is publicly available as part of a new suite of analytic shear algorithms called anacal. This code can analytically calibrate the shear response of any non-linear observable constructed with the fpfs shapelets and detection modes utilizing autodifferentiation (ad), generalizing the formalism to include a family of shear estimators with corrections for detection and selection biases. Using the ad capability of jax, it calculates the full Hessian matrix of the non-linear observables, which improves the previously presented second-order noise bias correction in the shear estimation. As an illustration of the power of the new anacal framework, we optimize the effective galaxy number density in the space of the generalized shear estimators using an LSST-like galaxy image simulation for the 10 yr LSST. For the generic shear estimator, the magnitude of the multiplicative bias |m| is below 3 × 10 –3 (99.7 per cent confidence interval), and the effective galaxy number density is improved by 5 per cent. We also discuss some planned future additions to the anacal software suite to extend its applicability beyond the fpfs measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Analytical noise bias correction for precise weak lensing shear inference

Noise bias is a significant source of systematic error in weak gravitational lensing measurements that must be corrected to satisfy the stringent standards of modern imaging surveys in the era of precision cosmology. This paper reviews the analytical noise bias correction method and provides analytical derivations demonstrating that we can recover shear to its second order using the ‘renoising’ noise bias correction approach introduced by METACALIBRATION. We implement this analytical noise bias correction within the AnaCal shear estimation framework and propose several enhancements to the noise bias correction algorithm. We evaluate the improved AnaCal using simulations designed to replicate Rubin Legacy Survey of Space and Time (LSST) imaging data. These simulations feature semi-realistic galaxies and stars, complete with representative distributions of magnitudes and Galactic spatial density. We conduct tests under various observational challenges, including cosmic rays, defective CCD columns, bright star saturation, bleed trails, and spatially variable point spread functions. Our results indicate a multiplicative bias in weak lensing shear recovery of less than a few tenths of a per cent, meeting LSST Dark Energy Science Collaboration requirements without requiring calibration from external image simulations. Additionally, our algorithm achieves rapid processing, handling one galaxy in less than a millisecond.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2011

Measurement of Phased Array Point Spread Functions for Use with Beamforming

Microphone arrays can be used to localize and estimate the strengths of acoustic sources present in a region of interest. However, the array measurement of a region, or beam map, is not an accurate representation of the acoustic field in that region. The true acoustic field is convolved with the array s sampling response, or point spread function (PSF). Many techniques exist to remove the PSF's effect on the beam map via deconvolution. Currently these methods use a theoretical estimate of the array point spread function and perhaps account for installation offsets via determination of the microphone locations. This methodology fails to account for any reflections or scattering in the measurement setup and still requires both microphone magnitude and phase calibration, as well as a separate shear layer correction in an open-jet facility. The research presented seeks to investigate direct measurement of the array's PSF using a non-intrusive acoustic point source generated by a pulsed laser system. Experimental PSFs of the array are computed for different conditions to evaluate features such as shift-invariance, shear layers and model presence. Results show that experimental measurements trend with theory with regard to source offset. The source shows expected behavior due to shear layer refraction when observed in a flow, and application of a measured PSF to NACA 0012 aeroacoustic trailing-edge noise data shows a promising alternative to a classic shear layer correction method.

Bahr, Chris↗

NASA NTRS1974

Dissipative heating effects and end corrections for viscous Newtonian flow in high shear capillary tube viscometry

The effect of dissipation heating on the apparent viscosity measured in capillary tube viscometry is described in this paper. Conditions of low Reynolds number and high shear are assumed. End corrections to the tube flow are incorporated. The flow curves show decreasing apparent viscosity when the shear stress increases. The configuration of the flow curves plotted in logarithmic presentation are found to be identical for fluids with Newtonian behavior. Convection is the predominant mechanism in removal of the heat in short capillary tube. The estimated upper bound for the shear stress obtainable in short length capillary tubes appears to be of the order of magnitude of 10 MPa limited primarily by the pressure drop associated with the constant end correction from the flat ended inlet and exit of the tube.

Jakobsen, J.↗