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NASA NTRS1999

Implications of Flexural Flanks at the Valles Marineris, Mars

The presence or absence of flexural flanks at the Valles Marineris (VM), Mars, have strong implications for the properties of the lithosphere, information which is critical for models of compensation state and formation of the troughs. Two hypotheses are favored for the formation of the VM, tectonic extension or subsurface withdrawal potentially related to dike emplacement; in either case, the formation of the large troughs at the VM requires a flexural response. After discussing preliminary models of flexure for VM from released Mars Global Surveyor (MGS) Mars Orbiting Laser Altimeter (MOLA) topography, this abstract considers the implications of flexure for gravity modeling and the lithosphere at VM. With future MGS topography and gravity data, and constraints on T(sub e) from this study, significantly better gravity modeling can be done to understand the state of the lithosphere at VM. Additional information is contained in the original extended abstract.

Anderson, F. S.↗

NASA NTRS1994

Elevated Temperature Slow Crack Growth of Silicon Nitride Under Dynamic, Static and Cyclic Flexural Loading

The slow crack growth parameters of a hot-pressed silicon nitride were determined at 1200 and 1300 C in air by statically, dynamically and cyclicly loading bend specimens. The fatigue parameters were estimated using the recently developed CARES/Life computer code. Good agreement exists between the flexural results. However, fatigue susceptibility under static uniaxial tensile loading, reported elsewhere, was greater than in flexure. Cyclic flexural loading resulted in the lowest apparent flexural fatigue susceptibility.

Choi, Sung R.↗

NASA NTRS1978

Studies on the influence on flexural wall deformations on the development of the flow boundary layer

Flexural wave-like deformations can be used to excite boundary layer waves which in turn lead to the onset of turbulence in the boundary layer. The investigations were performed with flow velocities between 5 m/s and 40 m/s. With four different flexural wave transmissions a frequency range from 0.2 kc/s to 1.5 kc/s and a phase velocity range from 3.5 m/s to 12 m/s was covered. The excitation of boundary layer waves becomes most effective if the phase velocity of the flexural wave coincides with the phase velocity region of unstable boundary layer waves.

Schilz, W.↗

NASA NTRS1983

SEASAT observations of lithospheric flexure seaward of trenches

Lithospheric flexure seaward of deep ocean trenches in SEASAT altimeter observations of the marine geoid. In fact, mechanical models of lithospheric flexure can be tested directly on the SEASAT altimeter data. A simple elastic model was used for the oceanic lithosphere and, after least squares adjustments, estimates of model parameters were recovered including Outer Rise (OR) amplitude, OR wavelength, and effective lithospheric thickness. Effective lithospheric thickness was recovered for five regions: the Mariana, the Kuril, the Philippine, the Aleutian and the Middle America OR. These results support the suggestion of Bodine et al. (1981) that effective thickness, T, increased with age of lithosphere in approximate accord with the relation T approximately equals x age to the 1/2 power where C approximately equals 4 km x my to the -1/2 power. Altimetric results agree more closely with this relation than do published results based on bathymetric data. The close agreement with the thickness-age relation suggests that there is no longer any need to assume that significant horizontal compression acts across the Kuril, Marianas and Izo-Bonin trenches. This thickness-age relation implies that flexural strength of the oceanic lithosphere is temperature controlled.

Mcadoo, D. C.↗

NASA NTRS1984

Seasat observations of lithospheric flexure seaward of trenches

Lithospheric flexure seaward of deep ocean trenches is evident in Seasat altimeter observations of the marine geoid. In fact, mechanical models of lithospheric flexure can be tested directly on the Seasat altimeter data. A simple elastic model has been used for the oceanic lithosphere and, after least squares adjustments, estimates have been recovered of model parameters including outer rise (OR) amplitude, OR wavelength, and effective lithospheric thickness. Effective lithospheric thicknesses have been recovered for six regions: the Mariana, the Kuril, the Philippine, the Aleutian, the Izu-Bonin, and the Middle America OR's. These results support the proposition that effective thickness Te increases with age of lithosphere in approximate accord with the relation Te approximately C x square root of age where C approximately 4 km/square root of (m.y.). In fact, altimetric results agree more closely with this relation than do published results based on bathymetric data. The close agreement with the thickness-age relation suggests that there is no longer any need to assume that significant horizontal compression acts across the Kuril, Marianas, and Izu-Bonin trenches. This thickness-age relation implies that flexural strength of the oceanic lithosphere is temperature controlled.

Mcadoo, D. C.↗

NASA NTRS1988

Flexural behavior of the continental lithosphere in Italy - Constraints imposed by gravity and deflection data

This paper presents a simple model that describes the geometry of subducted continental lithosphere as the result of flexural loading of a thin elastic sheet. The method involves a procedure for systematically matching the plate flexure and gravity data to the best-fitting two-dimensional flexural geometry obtained by a thin elastic sheet of specified elastic strength. It is shown that the model can explain both the deflection of the lithosphere and the gravity anomalies observed along four profiles across the Apennine convergent system in Italy. The results of calculations suggest that in subduction systems, like the Apennines, that are characterized by backarc extension, forces acting on subducted lithosphere at depth can be expressed at the surface in the geometry of the foredeep basin that forms adjacent to the subduction zone.

Royden, Leigh↗

NASA NTRS1988

Effect of actuator dynamics on control of beam flexure during nonlinear slew of SCOLE model

The effect of actuator dynamics on the control of beam flexure during nonlinear slewing of the SCOLE model is discussed. Two aspects of physical limitations on the regulation of beam flexure are similated, i.e., (1) a one foot travel limitation of displacement of proof-mass actuators; and (2) a time delay of 0.1 secs. in application of controls. The goal was to assess the magnitude of induced errors and, comparing the results to the ideal, and to determine how much flexure there is during slew and settling.

Fisher, Shalom↗

NASA NTRS1989

Design of a flexure mount for optics in dynamic and cryogenic environments

The design of a flexure mount for a mirror operating in a cryogenic environment is presented. This structure represents a design effort recently submitted to NASA Ames for the support of the primary mirror of the Space Infrared Telescope Facility (SIRTF). The support structure must passively accommodate the differential thermal contraction between the glass mirror and the aluminium structure of the telescope during cryogenic cooldown. Further, it must support the one meter diameter, 116 kilogram (258 pound) primary mirror during a severe launch to orbit without exceeding the micro-yield of the material anywhere in the flexure mount. Procedures used to establish the maximum allowable radial stiffness of the flexural mount, based on the finite element program NASTRAN and the optical program FRINGE, are discussed. Early design concepts were evaluated using a parametric design program, and the development of that program is presented. Dynamic loading analyses performed with NASTRAN are discussed. Methods of combining modal responses resulting from a displacement response spectrum analysis are discussed, and a combination scheme called MRSS, modified root of sum of squares, is presented. Model combination schemes using MRSS, SRSS, and ABS are compared to the results of the modal frequency response analysis performed with NASTRAN.

Pollard, Lloyd Wayne↗

NASA NTRS1989

The flexure assembly design for the SIRTF one-meter primary mirror

A titanium flexure assembly for the Space Infrared Telescope Facility (SIRTF) 1-m primary mirror has been designed to accommodate: (1) the cryogenic cool-down effect on the optical performance of the mirror, (2) the Shuttle launch-load environment, and (3) the support-baseplate manufacturing tolerances. Numerous iterations involving a multidimensional design space search led to an assembly design that provides the stiffness and strength in the vertical (optical axis) and tangential directions to accommodate launch loads, but is compliant radially to accommodate cryogenic cool down. A 'folded back' titanium flexure system was required because of the differential thermal contraction of the aluminum telescope baseplate support and the fused-silica mirror. This unique and innovative flexure assembly represents a totally passive mechanism for accommodating the design launch loads, cryogenic cool down, and out-of-plane baseplate effects.

Richard, R. M.↗

NASA NTRS1990

Simultaneous active control of flexural and extensional waves in beams

The simultaneous active control of flexural and extensional vibrations in elastic beams is experimentally investigated. The results demonstrate that using pairs of piezoceramic transducers, whose elements are symmetrically located and independently controlled by a multichannel adaptive controller, enables the high attenuation of both flexural and extensional response. This capability is due to the nature of the piezoceramic element, which when bonded to the surface of the structure and electrically excited, exerts a surface strain on the structure. This strain enables input of both shear forces and moments into the structural system. The results are applicable to many situations where extensional vibrations couple to large flexural vibrations and subsequently radiate significant sound levels.

Fuller, C. R.↗

NASA NTRS1991

Servo Reduces Friction In Flexure Bearing

Proposed servocontrol device reduces such resistive torques as stiction, friction, ripple, and cogging in flexure bearing described in LAR-14348, "Flexure Bearing Reduces Startup Friction". Reduces frictional "bump" torque encountered when bearing ball runs into buildup of grease on bearing race. Also used as cable follower to reduce torque caused by cable and hoses when they bend because of motion of bearing. New device includes torquer across ball race. Torquer controlled by servo striving to keep flexure at null, removing torque to outer ring. In effect, device is inner control loop reducing friction, but does not control platforms or any outer-control-loop functions.

Clingman, W. Dean↗

NASA NTRS1992

Flexure-torsion behavior of sheat-deformable beams with applications to aircraft wing sections

The flexure-torsion 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 represent a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-section properties including: the torsion constant, shear deformation coefficients, shear correction factors, and the shear center location. A new linear relation is developed for locating the shear center using the Saint-Venant flexure and torsion solutions, where the twist rate is zero about the line of shear centers (not the centroidal axis). Numerical results are presented for a triangular cross-section and different NACA airfoils.

Kosmatka, J. B.↗

NASA NTRS1992

Fatigue and flexural response of advanced carbon-carbon composites at room and elevated temperatures

The flexural response of SiC-coated carbon-carbon composites (ACC-4) at room and elevated temperatures is presented. Three-point bending tests were performed on virgin and mission-cycled specimens, and the variation in flexural strength is examined. The load-deflection behavior of the material at various temperatures is investigated, and the Weibull (1939) analysis of the strength data is performed. Micrographs of various cross sections in the damaged zone were taken, and the failure mechanisms are discussed. Fatigue tests were conducted under flexural loads, and the S-N diagram with the corresponding Weibull analysis are presented. Untested as well as fractured specimens under static and dynamic loading were C-scanned to identify the damaged zone and visualize the extent of the damage. Failure analyses are presented for both static and cyclic loading on the basis of NDE, the micrographs, and the experimental data.

Mahfuz, Hassan↗

NASA NTRS1993

Fuzzy sets predict flexural strength and density of silicon nitride ceramics

In this work, we utilize fuzzy sets theory to evaluate and make predictions of flexural strength and density of NASA 6Y silicon nitride ceramic. Processing variables of milling time, sintering time, and sintering nitrogen pressure are used as an input to the fuzzy system. Flexural strength and density are the output parameters of the system. Data from 273 Si3N4 modulus of rupture bars tested at room temperature and 135 bars tested at 1370 C are used in this study. Generalized mean operator and Hamming distance are utilized to build the fuzzy predictive model. The maximum test error for density does not exceed 3.3 percent, and for flexural strength 7.1 percent, as compared with the errors of 1.72 percent and 11.34 percent obtained by using neural networks, respectively. These results demonstrate that fuzzy sets theory can be incorporated into the process of designing materials, such as ceramics, especially for assessing more complex relationships between the processing variables and parameters, like strength, which are governed by randomness of manufacturing processes.

Cios, Krzysztof J.↗

NASA NTRS1993

A combined experimental and finite element study to predict the failure mechanisms in SiC coated carbon/carbon composites at room and elevated temperatures under flexural loading

Response of quasi-isotropic laminates of SiC coated Carbon/Carbon (C/C) composites have been investigated under flexural loading at various temperatures. Variation of load-deflection behavior with temperatures are studied. Increase in flexural strength and stiffness are observed with the rise in temperature. Extensive analyses through Optical Microscope (OM) and Non-Destructive Evaluation (NDE) have been performed to understand the failure mechanisms. Damage zone is found only within the neighborhood of the loading plane. Isoparametric layered shell elements developed on the basis of the first order shear deformation theory have been used to model the thin laminates of C/C under flexural loading. Large deformation behavior has been considered in the finite element analysis to account for the non-linearities encountered during the actual test. Data generated using finite element analysis are presented to corroborate the experimental findings, and a comparison in respect of displacement and stress-strain behavior are given to check the accuracy of the finite element analysis. Reasonable correlation between the experimental and finite element results have been established.

Mahfuz, Hassan↗

NASA NTRS1936

The stress criterion of a tension member with graded flexural stiffness : contribution to the problem of "clamping effect" outside of the elastic range

The approximate size of the stress criterion of a bar on two supports stressed beyond the elastic range is assessed by an approximation. The calculation proceeds from the premise of "substitute flexural stiffness" so defined that the part stressed beyond the elastic range may be considered as following Hooke's law when determining the flexural deformation quantities. For the determination of the substitute flexural stiffness, it is presumed that the material is already stressed so much beyond the yield point as to be strain-hardened. The data are directly applicable to materials having no definite yield point. For the rest, von Karman's method for compressed and subsequently deflected bars serves as basis for the calculation.

Kaul, Hans W↗

NASA NTRS1993

Flexure and the role of inplane force around coronae on Venus

Large coronae on Venus, such as Artemis and Latona, are rimmed by conspicuous trenches and associated outer rises. Sandwell and Schubert have observed that these systems resemble terrestrial subduction zones in planform and have succeeded in fitting an elastic plate bending equation to the inferred flexural topography. However, the first zero crossing bending moments required are -2.5 x 10(exp 17) N for Artemis and -5.0 x 10(exp 16) N for Latona. Since these moments are similar in magnitude to those of subducting slabs on Earth, a rollback subduction mechanism was proposed to explain the flexure around the largest coronae, although a differential thermal subsidence model is sufficient to account for the topography around some coronae. The purpose is to investigate the effect of inplane force as a possible alternative to large applied moments in producing flexure at Artemis and Latona. The close correlation of gravity to topography on Venus implies the absence of a low viscosity zone and the strong coupling of the lithosphere to mantle convection. If coronae are the surface manifestations of mantle plumes, they may be the sites of active convective stress coupling. As the upwelling reaches the lithosphere, it spreads radially outward, inducing shear tractions on the base of the plate. In addition, the hot, expanding corona may load the surrounding plate horizonally. Both the basal shear stresses and radial loading can be treated as an equivalent compressive inplane force in the mechanical lithosphere, which contributes to the bending of the outlying plate. Using a model that relates inplane force to the measured gravity anomalies, a rough value of the inplane force at Artemis was calculated. Recent Pioneer Venus spherical harmonic gravity models indicate a geoid anomaly of about 75 m over Artemis, which corresponds to an estimated inplane force on the order of -1x10(exp 13) N/m. The gravity model is unable to resolve Latona, but an inplane force of similar dimensions is assumed. The maximum possible inplane force based on the expected rheology can be constrained by using the approximate 5 K/km thermal gradient inferred from the best fit 30 km elastic plate at Artemis and Latona. For a dry olivine flow law in the upper mantle, the compressional load limit of the 60 km thick mechanical lithosphere is -4 x 10(exp 13) N/m. This value is equivalent to a load of -8 x 10(exp 13) N/m on a 30 km thick elastic plate.

Brown, C. David↗

NASA NTRS1994

Erosional dynamics, flexural isostasy, and long-lived escarpments: A numerical modeling study

Erosional escarpments common features of high-elevation rifted continets. Fission track data suffest that these escarpments form by base level lowering and/or marginal uplift during rifting, followed by lateral retreat of an erosion front across tens to hundreds of kioometers. Previous modeling studies have shown that this characteristic pattern of denudation can have a profound impact upon marginal isostatic uplift and the evolution of offshore sedimentary basins. Yet at present there is only a rudimentary understanding of the geomorphic mechanisms capable of driving such prolonged escarpment retreat. In this study we present a nonlinear, two-dimensional landscape evolution model tha tis used to asses the necessary and sufficient conditions for long-term retreat of a rift-generated escarpment. The model represents topography as a grid of cells, with drainage networkds evolving as water flows across the grid in the direction of steepest descent. The model accounts for sediment production by weathering, fluvial sediment transport, bedrock channel erosion, and hillslope sediment transport by diffusive mechanisms and by mass failure. Numerical experiments presented explore the effects of different combinations of erosion processes and of dynamic coupling between denudation and flexural isostatic uplift. Model results suggest that the necessary and sufficient conditions for long-term escarpment retreat are (1) incising bedrock channels in which the erosion rate increases with increasing drainage area, so that the channels steepen and propagate headward; (2) a low rate of sediment production relative to sediment transport efficiency, which promotes relief-generating processes over diffusive ones; (3) high continental elevation, which allows greater freedom for fluvial dissection; and (4) any process, including flexural isostatic uplift, that helps to maintain a drainage divide near an escarpment crest. Flexural isostatic uplift also facilitates escarpment, thereby increasing channel gradients and accelerating erosion which in turn generates additional isostatic uplift. Of all the above conditions, high continental elevation is common ot most rift margin escarpments and may ultimately be the most important factor.

Tucker, Gregory E.↗