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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Mechanics of couple-stress fluid coatings

The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors.

Waxman, A. M.↗
NASA NTRS1982

Mathematical models for the synthesis and optimization of spiral bevel gear tooth surfaces

The geometry of spiral bevel gears and to their rational design are studied. The nonconjugate tooth surfaces of spiral bevel gears are, in theory, replaced (or approximated) by conjugated tooth surfaces. These surfaces can be generated by two conical surfaces, and by a conical surface and a revolution. Although these conjugated tooth surfaces are simpler than the actual ones, the determination of their principal curvatures and directions is still a complicated problem. Therefore, a new approach, to the solution of these is proposed. Direct relationships between the principal curvatures and directions of the tool surface and those of the generated gear surface are obtained. With the aid of these analytical tools, the Hertzian contact problem for conjugate tooth surfaces can be solved. These results are useful in determining compressive load capacity and surface fatigue life of spiral bevel gears. A general theory of kinematical errors exerted by manufacturing and assembly errors is developed. This theory is used to determine the analytical relationship between gear misalignments and kinematical errors. This is important to the study of noise and vibration in geared systems.

Litvin, F. L.↗
NASA NTRS1982

The optimal design of involute gear teeth with unequal addenda

The design of a gear mesh is treated with the objective of minimizing the gear size for a given gear ratio, pinion torque, pressure angle, and allowable tooth lengths. Tooth strengths considered include scoring, pitting fatigue, and bending fatigue. Kinematic involute interference is avoided. The design variation on standard spur gear teeth called the long and short addendum system, is considered. In this system the mesh center distance and pressure angle are maintained as is the ability to manufacture the teeth with standard tooling. However, the pinion and gear tooth proportions are altered in order to obtain fewer teeth numbers for the same ratio as standard gears without kinematic involute interference. The effect of this nonstandard gearing geometry with on tooth strengths and gear mesh size are studied. For a 2:1 gearing ratio, the optimal nonstandard gear design is compared with the optimal standard gear design.

Savage, M.↗
NASA NTRS1981

Sodium remote from Io

Measurements of sodium emission lines originating in the middle Jupiter magnetosphere are measured, confirming the wide dispersal of neutral sodium in the Jovian system in at least two distinct manifestations. Candidate neutral transport processes in the context of the observed kinematical signatures are discussed. It is argued that the normal emission feature is produced by sodium atoms on bound elliptical orbits originating in the Io sodium cloud but with apojove in the field of view. Observations of the fast sodium feature indicate that atoms episodically acquire a broad range of line-of-sight velocities above the Jupiter gravitational escape speed and far above the speeds characteristic of surface-sputtered atoms. Three suggested reactions are distinguished according to (1) production rates based on estimated plasmaspheric properties, (2) kinematical signature, and (3) the timing of occurrences of the fast sodium feature.

Brown, R. A.↗
NASA NTRS1982

Materials constitutive models for nonlinear analysis of thermally cycled structures

Effects of inelastic materials models on computed stress-strain solutions for thermally loaded structures were studied by performing nonlinear (elastoplastic creep) and elastic structural analyses on a prismatic, double edge wedge specimen of IN 100 alloy that was subjected to thermal cycling in fluidized beds. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic kinematic, and combined plus transient creep) were exercised for the problem by using the MARC nonlinear, finite element computer program. Maximum total strain ranges computed from the elastic and nonlinear analyses agreed within 5 percent. Mean cyclic stresses, inelastic strain ranges, and inelastic work were significantly affected by the choice of inelastic constitutive model. The computing time per cycle for the nonlinear analyses was more than five times that required for the elastic analysis.

Kaufman, A.↗
NASA NTRS1983

A basis for the analysis of surface geometry of spiral bevel gears

Geometrical procedures helpful in the fundamental studies of the surface geometry of spiral bevel gears are summarized. These procedures are based upon: (1) fundamental gear geometry and kinematics as exposited by Buckingham, et al; (2) formulas developed from differential geometry; and (3) geometrical concepts developed in recent papers and reports on spiral bevel gear surface geometry. Procedures which characterize the geometry so that the surface parametric equations, the principal radii of curvature, and the meshing kinematics are systematically determined are emphasized. Initially, the focus in on theoretical, logarithmic spiral bevel gears as defined by Buckingham. The gears, however, are difficult to fabricate and are sometimes considered to be too straight. Circular-cut spiral bevel gears are an alternative to this. Surface characteristics of crown circular cut gears are analyzed.

Huston, R. L.↗
NASA NTRS1983

The optimal design of standard gearsets

A design procedure for sizing standard involute spur gearsets is presented. The procedure is applied to find the optimal design for two examples - an external gear mesh with a ratio of 5:1 and an internal gear mesh with a ratio of 5:1. In the procedure, the gear mesh is designed to minimize the center distance for a given gear ratio, pressure angle, pinion torque, and allowable tooth strengths. From the methodology presented, a design space may be formulated for either external gear contact or for internal contact. The design space includes kinematics considerations of involute interference, tip fouling, and contact ratio. Also included are design constraints based on bending fatigue in the pinion fillet and Hertzian contact pressure in the full load region and at the gear tip where scoring is possible. This design space is two dimensional, giving the gear mesh center distance as a function of diametral pitch and the number of pinion teeth. The constraint equations were identified for kinematic interference, fillet bending fatigue, pitting fatigue, and scoring pressure, which define the optimal design space for a given gear design. The locus of equal size optimum designs was identified as the straight line through the origin which has the least slope in the design region.

Savage, M.↗
NASA NTRS1983

Grabens, basin tectonics, and the maximum total expansion of the moon

Information from lunar grabens is used to address the question of whether the grabens and wrinkle ridges are tectonic or volcanic in origin. The geometry of simple grabens is discussed, and the kinematics and mechanics are addressed in terms of an elastic response model, a brittle response model, the mechanics of the megaregolith, and total extension for all lunar grabens. Constraints on the thermal evolution of the moon are considered, including thermal history calculations and grabens in space and time. Mare basin tectonics is discussed in terms of two kinematic models/ subsidence by increased radius of curvature and subsidence with no increase in radius of curvature. It is concluded that the observable geological history of the moon is inconsistent with any significant expansion of the moon since about 3.9 billion years ago. Both thermal and tectonic models of lunar evolution are critized.

Golombek, M. P.↗
NASA NTRS1982

Properties of a constricted-tube air-flow levitator

The properties of a constricted-tube gas flow levitator first developed by Berge et al. (1981) have been investigated experimentally in order to predict its behavior in a gravity-free environment and at elevated temperatures. The levitator consists of a constricted (quartz) tube fed at one end by a source of heated air or gas. A spherical sample is positioned by the air stream on the downstream side of the constriction, where it can be melted and resolidified without touching the tube. It is shown experimentally that the kinematic viscosity is the important fluid parameter for operation in thermal equilibrium at high temperatures. If air is heated from room temperature to 1200 C, the kinematic viscosity increases by a factor of 14. To maintain a given value of the Reynolds number, the flow rate would have to be increased by the same factor for a specific geometry of tube and sample. Thus, to maintain stable equilibrium, the flow rate should be increased as the air or other gas is heated. The other stability problem discussed is associated with changes in the shape of a cylindrical sample as it melts.

Rush, J. E.↗
NASA NTRS1983

Wrinkling phenomenon in structures. I - Model formulations

Those structural element models which can suffer the wrinkling phenomenon are analyzed. A laminated elastic material, defined as a one-parametrical family of surfaces whose in-plane strains are negligible in comparison to the strains in the transverse direction, is analyzed in terms of its geometry, geometrical compatibility equations, layer geometry, kinematics, kinematical compatibility equations, and governing dynamical equations. These aspects are also examined for the case of a soft shell, defined as a shell for which the in-plane strains of the middle surface are negligible compared to the strains in the transverse direction, and for the case of a soft rod, defined as a rod for which the strains along the axis are negligible compared to the strains in the transverse direction. The influence of internal fluid flow on the wrinkling phenomenon for layers of laminated material and for a flexible pipe containing an inviscid and incompressible fluid is also analyzed.

Zak, M.↗
NASA NTRS1984

Geodynamics of crustal deformation and seismotectonic block movements in central Europe

Geological observations reveal the style of neotectonic near-surface stresses and deformations in central Europe. Seismic activity, focal depths and fault plane solutions of earthquakes indicate kinematic reactions within the crust. A crustal deformation model which may account for the Rhine graben systems and the associated seismotectonic block movements in Europe is presented. A computer aided tomography to gravity anomalies is used in determining the crustal stresses in central Europe. Tomographical interpretations of gravity data with respect to seismic stresses are discussed. Kinematics and dynamics are integrated to show that the measured regional stresses in central Europe are derivable from the convection generated traction on the boundary of the elastic spherical shell of the crust as inferred from satellite derived gravity data.

Liu, H. S.↗
NASA NTRS1983

On the suppression of zero energy deformation modes

Based on the Hellinger-Reissner principle and the deformation energy due to assumed stresses and displacements, the problem of the kinematic deformation modes in assumed stress hybrid/mixed finite elements has been examined. Basic schemes are developed for the choice of assumed stress terms that will suppress all kinematic deformation modes. Quadrilateral membrane and axisymmetric elements, and three-dimensional hexahedral elements, are used to illustrate the suggested procedure.

Pian, T. H. H.↗
NASA NTRS1985

Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations

Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.

Hodges, D. H.↗
NASA NTRS1985

Spiral bevel and circular arc helical gears: Tooth contact analysis and the effect of misalignment on circular arc helical gears

A computer aided method for tooth contact analysis was developed and applied. Optimal machine-tool settings for spiral bevel gears are proposed and when applied indicated that kinematic errors can be minimized while maintaining a desirable bearing contact. The effect of misalignment for circular arc helical gears was investigated and the results indicted that directed pinion refinishing can compensate the kinematic errors due to misalignment.

Litvin, F. L.↗
NASA NTRS1984

The eccentric Saturnian ringlets at 1.29 R(s) and 1.45 R(s)

The shapes and kinematics of the Titan and Maxwell ringlets of Saturn's C ring are studied. The ringlets are narrow and eccentric, with mean widths of about 25 km for Titan and abut 64 km for Maxwell, and with eccentricities of order 10 to the -4th. They have sharp edges on a scale of about 1 km, normal optical depths of roughly 0.5-2.0, normal optical depth of the surrounding region, and positive linear width-radius relations. The Titan ringlet is the only feature whose dynamics appears to be completely determined by an external satellite; the kinematics of the Maxwell ringlet are determined solely by Saturn's nonspherical gravity field. The comparatively large measured optical depths and large inferred mass extinction coefficients for the ringlets suggest an environment and particle size distribution different from the remainder of the C ring and presumably caused by the mechanism responsible for ring confinement.

Porco, C.↗
NASA NTRS1984

Extension of constrained incremental Newton-Raphson scheme to generalized loading fields

This paper develops numerical strategies which enable the constrained incremental Newton-Raphson scheme to handle the static response of structure to loading fields with completely generalized histories. This is made possible through the use of specially warped hyperelliptic constraint surfaces which control successive or clustered load steps in the vicinity of loading events with specific timing schedules. Such an approach enables improved convergence and stability characteristics. Due to the generality of the methodology, pre- and postbuckling behavior caused by both kinematic and material nonlinearity can be handled. To demonstrate the scheme, the results of several bench-mark problems are also presented. These include situations involving nonlinear kinematics as well as highly history-dependent elastic-plastic and thermoelastic-plastic material behavior.

Padovan, J.↗
NASA NTRS1985

Pantographing self adaptive gap elements

This paper develops a so-called pantographing self adaptive gap element type contact strategy. Due to the manner of formulation, the scheme has the capability to handle large deformations in the contact zone; contact initiation in structure exhibiting either positive or indefinite stiffness characteristics; kinematic and material nonlinearity as well as; self adaptively adjusts load/time stepping. In this context, contact in pre and postbuckling structure can be treated. To illustrate the scheme, several benchmark problems are presented. These include contacting structure involving large deformation kinematics, inelastic behavior as well as pre and postbuckling stiffness characteristics.

Padovan, J.↗
NASA NTRS1985

Constitutive modeling and computational implementation for finite strain plasticity

This paper describes a simple alternate approach to the difficult problem of modeling material behavior. Starting from a general representation for a rate-tpe constitutive equation, it is shown by example how sets of test data may be used to derive restrictions on the scalar functions appearing in the representation. It is not possible to determine these functions from experimental data, but the aforementioned restrictions serve as a guide in their eventual definition. The implications are examined for hypo-elastic, isotropically hardening plastic, and kinematically hardening plastic materials. A simple model for the evolution of the 'back-stress,' in a kinematic-hardening plasticity theory, that is entirely analogous to a hypoelastic stress-strain relation is postulated and examined in detail in modeling finitely plastic tension-torsion test. The implementation of rate-type material models in finite element algorithms is also discussed.

Reed, K. W.↗