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NASA NTRS1988

Numerical simulations of the bending of narrow-angle-tail radio jets by ram pressure or pressure gradients

Three-dimensional numerical hydrodynamic simulations are used to study the bending of radio jets. The simulations are compared with observations of jets in narrow-angle-tail radio sources. Two mechanisms for the observed bending are considered: direct bending of quasi-continuous jets by ram pressure from intergalactic gas and bending by pressure gradients in the interstellar gas of the host galaxy, the pressure gradients themselves being the result of ram pressure by intergalactic gas. It is shown that the pressure gradients are much less effective in bending jets, implying that the jets have roughly 30 times lower momentum fluxes if they are bent by this mechanism. Ram-pressure bending produces jets with 'kidney-shaped' cross sections; when observed from the side, these jets appear to have diffuse extensions on the downstream side. On the other hand, pressure-gradient bending causes the jets to be densest near their upstream side.

Soker, Noam↗

NASA NTRS2008

Ares-I Bending Filter Design using a Constrained Optimization Approach

The Ares-I launch vehicle represents a challenging flex-body structural environment for control system design. Software filtering of the inertial sensor output is required to ensure adequate stable response to guidance commands while minimizing trajectory deviations. This paper presents a design methodology employing numerical optimization to develop the Ares-I bending filters. The design objectives include attitude tracking accuracy and robust stability with respect to rigid body dynamics, propellant slosh, and flex. Under the assumption that the Ares-I time-varying dynamics and control system can be frozen over a short period of time, the bending filters are designed to stabilize all the selected frozen-time launch control systems in the presence of parameter uncertainty. To ensure adequate response to guidance command, step response specifications are introduced as constraints in the optimization problem. Imposing these constrains minimizes performance degradation caused by the addition of the bending filters. The first stage bending filter design achieves stability by adding lag to the first structural frequency to phase stabilize the first flex mode while gain stabilizing the higher modes. The upper stage bending filter design gain stabilizes all the flex bending modes. The bending filter designs provided here have been demonstrated to provide stable first and second stage control systems in both Draper Ares Stability Analysis Tool (ASAT) and the MSFC MAVERIC 6DOF nonlinear time domain simulation.

Hall, Charles↗

NASA NTRS1971

Bend ductility of columbium alloys WC3015 and Cb752.

Bend angles for columbium-base alloys, WC3015 and Cb752, at temperatures between -300 F and +500 F are reported. WC3015 exhibited a bend transition temperature well below -100 F, but was severely embrittled by silicide coatings. Cb 752 exhibited a bend transition temperature below -300 F, and the silicide coating application did not influence bend angle of the substrate. However, coating failure on both alloys was observed at less than 60 deg bend, even at 500 F. The effect of electron beam welding and gas tungsten-arc welding on the properties of WC3015 and Cb752 are also reported. Both techniques are shown to produce a marked reduction in the bend angle of WC3015. Unlike WC3015, ductility is restored in Cb752 after a suitable postweld anneal. Microstructural and hardness tests results for both alloys are reported and discussed.

Tavassoli, A. A.↗

NASA NTRS1986

Analysis of Delamination Growth from Matrix Cracks in Laminates Subjected to Bending Loads

A major source of delamination damage in laminated composite materials is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies, and delaminations then grow from these cracks at the ply interfaces. The purpose of this study was to quantify the combined effects of bending and transverse shear loads on delamination initiation from matrix cracks. Graphite-epoxy laminates with 90 deg. plies on the outside were used to provide a two-dimensional simulation of the damage due to low-velocity impact. Three plate bending problems were considered: a 4-point bending, 3-point bending, and an end-clamped center-loaded plate. Under bending, a matrix crack will form on the tension side of the laminate, through the outer 90 deg. plies and parallel to the fibers. Delaminations will then grow in the interface between the cracked 90 deg. ply and the next adjacent ply. Laminate plate theory was used to derive simple equations relating the total strain energy release rate, G, associated with the delamination growth from a 90 deg. ply crack to the applied bending load and laminate stiffness properties. Three different lay-ups were tested and results compared. Test results verified that the delamination always formed at the interface between the cracked 90 deg. ply and the next adjacent ply. Calculated values for total G sub c from the analysis showed good agreement for all configurations. The analysis was able to predict the delamination onset load for the cases considered. The result indicated that the opening mode component (Mode I) for delamination growth from a matrix crack may be much larger than the component due to interlaminar shear (Mode II).

Murri, G. B.↗

NASA NTRS1989

Characterization of the bending stiffness of large space structure joints

A technique for estimating the bending stiffness of large space structure joints is developed and demonstrated for an erectable joint concept. Experimental load-deflection data from a three-point bending test was used as input to solve a closed-form expression for the joint bending stiffness which was derived from linear beam theory. Potential error sources in both the experimental and analytical procedures are identified and discussed. The bending stiffness of a mechanically preloaded erectable joint is studied at three applied moments and seven joint orientations. Using this technique, the joint bending stiffness was bounded between 6 and 17 percent of the bending stiffness of the graphite/epoxy strut member.

Wu, K. Chauncey↗

NASA NTRS1988

Analysis of delamination growth from matrix cracks in laminates subjected to bending loads

A major source of delamination damage in laminated composite materials is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies, and delaminations then grow from these cracks at the ply interfaces. The purpose of this study was to quantify the combined effects of bending and transverse shear loads on delamination initiation from matrix cracks. Graphite-epoxy laminates with 90 deg plies on the outside were used to provide a two-dimensional simulation of the damage due to low-velocity impact. Three plate bending problems were considered: a 4-point bending, 3-point bending, and an end-clamped center-loaded plate. Under bending, a matrix crack will form on the tension side of the laminate, through the outer 90 deg plies and parallel to the fibers. Delaminations will then grow in the interface between the cracked 90 deg ply and the next adjacent ply. Laminate plate theory was used to derive simple equations relating the total strain energy release rate, G, associated with the delamination growth from a 90 deg ply crack to the applied bending load and laminate stiffness properties. Three different lay-ups were tested and results compared. Test results verified that the delamination always formed at the interface between the cracked 90 deg ply and the next adjacent ply. Calculated values for total G sub c from the analysis showed good agreement for all configurations. The analysis was able to predict the delamination onset load for the cases considered. The result indicated that the opening mode component (Mode I) for delamination growth from a matrix crack may be much larger than the component due to interlaminar shear (Mode II).

Murri, Gretchen Bostaph↗

NASA NTRS1959

A Dynamic Model Investigation of the Effect of a Sharp-Edge Vertical Gust on Blade Periodic Flapping Angles and Bending Moments of a Two-Blade Rotor

A two-blade rotor having a diameter of 4 feet and a solidity of 0.037 was subjected to sharp-edge vertical gusts while being operated at various forward speeds to study the effect of the gusts on the blade periodic bending moments and flapping angles. Variables studied included gust velocity, collective pitch angle, flapping hinge offset, and tip-speed ratio. Dimensionless coefficients are derived for the periodic components of the incremental changes in blade flapping angles and bending moments which arise when a rotor blade penetrates a sharp-edge gust. Mental changes in both the flapping angles and bending moments are essentially proportional to gust velocity, and the coefficients express the ratio of these increments to gust velccity. The results show that the flapping coefficient usually increases with an increase in collective pitch angle, is generally dependent on tip-speed ratio, and is essentially independent of the amount of flapping hinge offset. The bending-moment coefficient is also dependent on collective pitch angle and tip-speed ratio. Expected reductions in bending moments are realized by the use of flapping hinges, and further reductions in bending moments are achieved as the amount of flapping hinge offset is increased. Comparison of the experimental results of this investigation with limited available theoretical results shows substantial agreement but indicates that the assumption that the response of the rotor to a sharp-edge gust is independent of the collective pitch angle prior to gust entry is probably inadequate.

McCarty, John Locke↗

NASA NTRS1997

An Experimental Study of Fatigue Crack Growth in Aluminum Sheet Subjected to Combined Bending and Membrane Stresses

An experimental study was conducted to determine the effects of combined bending and membrane cyclic stresses on the fatigue crack growth behavior of aluminum sheet material. The materials used in the tests were 0.040-in.- thick 2024-T3 alclad and 0.090-in.-thick 2024-T3 bare sheet. In the tests, the membrane stresses were applied as a constant amplitude loading at a stress ratio (minimum to maximum stress) of 0.02, and the bending stresses were applied as a constant amplitude deflection in phase with the membrane stresses. Tests were conducted at ratios of bending to membrane stresses (B/M) of 0, 0.75, and 1.50. The general trends of the results were for larger effects of bending for the higher B/M ratios, the lower membrane stresses, and the thicker material. The addition of cyclic bending stresses to a test with cyclic membrane stresses had only a small effect on the growth rates of through-thickness cracks in the thin material, but had a significant effect on the crack growth rates of through-thickness cracks in the thick material. Adding bending stresses to a test had the most effect on the initiation and early growth of cracks and had less effect on the growth of long through-thickness cracks.

Phillips, Edward P.↗

NASA NTRS2000

Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells

An analytical, parametric study of the attenuation of bending boundary layers or edge effects in balanced and unbalanced, symmetrically and unsymmetrically laminated thin cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize and quantify the effects of laminate orthotropy and laminate anisotropy on the bending boundary-layer decay length in a very general and encompassing manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all the laminate constructions considered, the results show that the differences between results that were obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that in some cases neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and in other cases it results in an overestimation.

Nemeth, Michael P.↗

NASA NTRS2000

Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells

A study of the attenuation of bending boundary layers in balanced and unbalanced, symmetrically and unsymmetrically laminated cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize the effects of laminate orthotropy and anisotropy on the bending boundary-layer decay length in a very general manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all laminates considered, the results show that the differences between results obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that, in some cases, neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and, in other cases, results in an overestimation.

Nemeth, Michael P.↗

NASA NTRS2012

Bending of Light in Modified Gravity at Large Distances

We discuss the bending of light in a recent model for gravity at large distances containing a Rindler type acceleration proposed by Grumiller. We consider the static, spherically symmetric metric with cosmological constant and Rindler-like term 2ar presented in this model, and we use the procedure by Rindler and Ishak. to obtain the bending angle of light in this metric. Earlier work on light bending in this model by Carloni, Grumiller, and Preis, using the method normally employed for asymptotically flat space-times, led to a conflicting result (caused by the Rindler-like term in the metric) of a bending angle that increases with the distance of closest approach r(sub 0) of the light ray from the centrally concentrated spherically symmetric matter distribution. However, when using the alternative approach for light bending in nonasymptotically flat space-times, we show that the linear Rindler-like term produces a small correction to the general relativistic result that is inversely proportional to r(sub 0). This will in turn affect the bounds on Rindler acceleration obtained earlier from light bending and casts doubts on the nature of the linear term 2ar in the metric

Grumiller↗

NASA NTRS1972

Elasto-plastic bending of cracked plates, including the effects of crack closure

A capability for solving elasto-plastic plate bending problems is developed using assumptions consistent with Kirchhoff plate theory. Both bending and extensional modes of deformation are admitted with the two modes becoming coupled as yielding proceeds. Equilibrium solutions are obtained numerically by determination of the stationary point of a functional which is analogous to the potential strain energy. The stationary value of the functional for each load increment is efficiently obtained through use of the conjugate gradient. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.

Jones, D. P.↗

NASA NTRS1976

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Hodges, D. H., Roberta.↗

NASA NTRS1975

The influence of crack closure and elasto-plastic flow on the bending of a cracked plate

The influence of crack closure and elastoplastic flow on the bending behavior of thin cracked plates is investigated using an incremental elastoplastic plate bending finite element computer program. The finite element program was developed using assumptions consistent with Kirchhoff fourth-order plate theory while the material property treatment permits general isotropic work hardening with local elastic unloading. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.

Jones, D. P.↗

NASA NTRS1979

Noninvasive measures of bone bending rigidity in the monkey /M. nemestrina/

The in vivo bending rigidity and bone mineral content of monkey ulnae and tibiae were measured. Bending rigidity in the anteroposterior plane was measured by an impedance probe technique. Forced vibrations of the bones were induced with an electromechanical shaker, and force and velocity at the driving point were determined. The responses over the range of 100-250 Hz were utilized to compute the bending rigidity. Bone mineral content in the cross section was determined by a photon absorption technique. Seventeen male monkeys (Macaca nemestrina) weighing 6-14 kg were evaluated. Bending rigidity was correlated with the mineral content of the cross section, with a correlation coefficient of 0.899. Two monkeys were evaluated during prolonged hypodynamic restraint. Restraint produced regional losses of bone most obviously in the proximal tibia. The local bone mineral content declines 17 to 24% and the average bending rigidity declines 12 to 22%. Changes in bones leading to a reduction in mineral content and stiffness are discussed.

Young, D. R.↗

NASA NTRS1985

The effects of strong shock loading on coupled bending-torsion flutter of tuned and mistuned cascades

This paper presents an investigation of the effects of strong in-passage shock waves on coupled bending-torsion flutter of both tuned and mistuned cascades. The aerodynamic and inertial coupling between the bending and torsional motions of each blade are included in the analytical model. Analysis revealed (1) that the shock loading has a beneficial effect on torsional flutters of both tuned and mistuned cascades and (2) that alternating bending mistuning has a beneficial effect on shock load induced bending flutter. The latter finding becomes important when shock induced bending flutter is a problem.

Busbey, B. C.↗

NASA NTRS1988

The Titan-1:0 nodal bending wave in Saturn's Ring C

The most prominent oscillatory feature observed in the Voyager 1 radio occultation of Saturn's rings is identified as a one-armed spiral bending wave excited by Titan's-1:0 nodal inner vertical resonance. Ring particles in a bending wave move in coherently inclined orbits, warping the local mean plane of the rings. The Titan-1:0 wave is the only known bending wave that propagates outward, away from Saturn, and the only spiral wave yet observed in which the wave pattern rotates opposite to the orbital direction of the ring particles. It is also the first bending wave identified in ring C. Modeling the observed feature with existing bending wave theory gives a surface mass density of about 0.4 g/sq cm outside the wave region and a local ring thickness of less than about 5 meters, and suggests that surface mass density is not constant in the wave region.

Rosen, Paul A.↗

NASA NTRS1990

Thin-walled composite beams under bending, torsional, and extensional loads

Symmetric and antisymmetric layup graphite-epoxy composite beams with thin-walled rectangular cross sections are fabricated using an autoclave molding technique and tested under bending, torsional, and extensional loads. The bending slope and elastic twist at a station are measured using an optical system, and the results correlated with predicted values from a simple beam analysis as well as a refined finite element analysis. A symmetric ply layup results in bending-twist coupling whereas an antisymmetric layup causes extension-twist coupling. Simple analytical results with plane-stress assumption agree better with measured data as well as finite element predictions than with plane-strain assumption. For symmetric layup beams, the bending-induced twist and torsion-induced bending slope are predicted satisfactorily using simple analytical solution. Correlations with measured data, however, are generally improved using a finite element solution. For antisymmetric beams, axial force-induced twist is predicted satisfactorily by both methods.

Chandra, Ramesh↗