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Thermally-induced structural dynamic response of flexural configurations influenced by linear/non-linear thermal effects

The thermally-induced strucural dynamic response of flexural configurations influenced by linear/nonlinear thermal effects is presented in conjunction with 'unified' transient approaches for effectively tackling this class of interdisciplinary problems. For illustrative purposes, the flexural structural models are assumed to be of the Euler-Bernoulli type. The purpose of the present paper is to not only provide an understanding of the influence of general linear/nonlinear thermal effects on flexural configurations, but also to provide to the analyst effective computational tools which help preserve a unified technology for the interdisciplinary areas encompassing structural mechanics/dynamics and thermal sciences. Several numerical test models illustrate the representative thermally-induced structural dynamic response of flexural configurations subjected to general linear/nonlinear temperature effects.

Namburu, Raju R.

Flexural models of trench/outer rise topography of coronae on Venus with axisymmetric spherical shell elastic plates

Magellan altimetry has revealed that many coronae on Venus have trenches or moats around their peripheries and rises outboard of the trenches. This trench/outer rise topographic signature is generally associated with the tectonic annulus of the corona. Sandwell and Schubert have interpreted the trench/outer rise topography and the associated tectonic annulus around coronae to be the result of elastic bending of the Venus lithosphere (though the tectonic structures are consequences of inelastic deformation of the lithosphere). They used two-dimensional elastic plate flexure theory to fit topographic profiles across a number of large coronae and inferred elastic lithosphere thicknesses between about 15 and 40 km, similar to inferred values of elastic thickness for the Earth's lithosphere at subduction zones around the Pacific Ocean. Here, we report the results of using axisymmetric elastic flexure theory for the deformation of thin spherical shell plates to interpret the trench/outer rise topography of the large coronae modeled by Sandwell and Schubert and of coronae as small as 250 km in diameter. In the case of a corona only a few hundred kilometers in diameter, the model accounts for the small planform radius of the moat and the nonradial orientation of altimetric traces across the corona. By fitting the flexural topography of coronae we determine the elastic thickness and loading necessary to account for the observed flexure. We calculate the associated bending moment and determine whether the corona interior topographic load can provide the required moment. We also calculate surface stresses and compare the stress distribution with the location of annular tectonic features.

Moore, W.

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.

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.

Effect of sintering temperature on feature resolution and flexural strength of ceramics fabricated through vat photopolymerization additive manufacturing

Although ceramic additive manufacturing (AM) could be used to fabricate complex, high-resolution parts for diverse, functional applications, one ongoing challenge is optimizing the post-process, particularly sintering, conditions to consistently produce geometrically accurate and mechanically robust parts. This study aims to investigate how sintering temperature affects feature resolution and flexural properties of silica-based parts formed by vat photopolymerization (VPP) AM. Test artifacts were designed to evaluate features of different sizes, shapes and orientations, and three-point bend specimens printed in multiple orientations were used to evaluate mechanical properties. Sintering temperatures were varied between 1000°C and 1300°C. Deviations from designed dimensions often increased with higher sintering temperatures and/or larger features. Higher sintering temperatures yielded parts with higher strength and lower strain at break. Many features exhibited defects, often dependent on geometry and sintering temperature, highlighting the need for further analysis of debinding and sintering parameters. To the best of the authors’ knowledge, this is the first time test artifacts have been designed for ceramic VPP. This work also offers insights into the effect of sintering temperature and print orientation on flexural properties. These results provide design guidelines for a particular material, while the methodology outlined for assessing feature resolution and flexural strength is broadly applicable to other ceramics, enabling more predictable part performance when considering the future design and manufacture of complex ceramic parts.

36 MATERIALS SCIENCE

Multi-faceted framework for extrapolating early age flexural strength to facilitate rapid lifting/handling of high-volume fly ash precast members

Maintaining adequate early-age structural performance for precast concrete components has grown in importance as more sustainable mix designs become more widespread. Achieving high-early flexural strength is particularly crucial to facilitate rapid removal of hardened concrete components from formwork, often within 24 h after fresh concrete placement. Limited research has assessed the effectiveness of traditional design methods in correlating flexural strength with compressive strength for next-generation mix designs, or demonstrated extrapolation of such material performance to larger-scale structural tests. This paper presents a multi-faceted framework to reassess early-age flexural strength for concretes made with relatively high proportions of fly ash from both fresh and harvested sources. Here, the framework provides several pathways, from which the user can select based upon available resources and the specific application, to improve accuracy of early-age cracking moment calculations. Furthermore, the scope includes evaluation of strength performance under curing conditions emulative of those in a precast facility, recommending modulus of rupture equations which are more performance-driven than current design provisions, and experimental tests on prefabricated concrete beams to validate the proposed methodologies. Correlations of early-age strength with both concrete age and maturity measurements compare the effectiveness of utilizing in-situ data to further enhance the prediction methods. Ultimately, the proposed framework helped reduce errors when calculating cracking moment capacity at early ages by tailoring calculations to reflect mix-dependent behavior. Furthermore, most estimates of cracking moment were within 25 % of their corresponding experimental test results, thus promoting confidence for using these strategies with high-volume fly ash precast structures.

42 ENGINEERING

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.

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.

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.

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

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

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

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.

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.

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

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.

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

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.