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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

An In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials

An in-depth tutorial on the constitutive equations for elastic, anisotropic materials is presented. Basic concepts are introduced that are used to characterize materials, and notions about how anisotropic material deform are presented. Hooke s law and the Duhamel-Neuman law for isotropic materials are presented and discussed. Then, the most general form of Hooke s law for elastic anisotropic materials is presented and symmetry requirements are given. A similar presentation is also given for the generalized Duhamel-Neuman law for elastic, anisotropic materials that includes thermal effects. Transformation equations for stress and strains are presented and the most general form of the transformation equations for the constitutive matrices are given. Then, specialized transformation equations are presented for dextral rotations about the coordinate axes. Next, concepts of material symmetry are introduced and criteria for material symmetries are presented. Additionally, engineering constants of fully anisotropic, elastic materials are derived from first principles and the specialized to several cases of practical importance.

Nemeth, Michael P.↗
NASA NTRS1983

Thermal elastohydrodynamic lubrication of line contacts

A numerical solution to the problem of thermal elastohydrodynamic lubrication of line contacts was obtained by using a finite difference formulation. The solution procedure consists of simultaneous solution of the thermal Reynolds equation, the elasticity equation, and the energy equation subject to appropriate boundary conditions. Pressure distribution, film shape, and temperature distribution were obtained for fully flooded conjunctions, a paraffinic lubricant, and various dimensionless speed parameters while the dimensionless load and materials parameters were held constant. Reduction in the minimum film thickness due to thermal effects (as a ratio of thermal to isothermal minimum film thickness) is given by a simple formula as a function of the thermal loading parameter Q: H(min)/H(min,I) = 10/10+ Q(0.4). Plots of pressure distribution, film shape, temperature distribution, and flow are shown for some representative cases.

Ghosh, M. K.↗
NASA NTRS1985

Thermal elastohydrodynamic lubrication of line contacts

A numerical solution to the problem of thermal elastohydrodynamic lubrication of line contacts was obtained by using a finite difference formulation. The solution procedure consists of simultaneous solution of the thermal Reynolds equation, the elasticity equation, and the energy equation subject to appropriate boundary conditions. Pressure distribution, film shape, and temperature distribution were obtained for fully flooded conjunctions, a paraffinic lubricant, and various dimensionless speed parameters while the dimensionless load and materials parameters were held constant. Reduction in the minimum film thickness due to thermal effects (as a ratio of thermal to isothermal minimum film thickness) is given by a simple formula as a function of the thermal loading parameter Q: H(min)/H(min, I) = 10/10 + Q(0.4). Plots of pressure distribution, film shape, temperature distribution, and flow are shown for some representative cases.

Ghosh, M. K.↗
NASA NTRS1992

Acoustic intensity calculations for axisymmetrically modeled fluid regions

An algorithm for calculating acoustic intensities from a time harmonic pressure field in an axisymmetric fluid region is presented. Acoustic pressures are computed in a mesh of NASTRAN triangular finite elements of revolution (TRIAAX) using an analogy between the scalar wave equation and elasticity equations. Acoustic intensities are then calculated from pressures and pressure derivatives taken over the mesh of TRIAAX elements. Intensities are displayed as vectors indicating the directions and magnitudes of energy flow at all mesh points in the acoustic field. A prolate spheroidal shell is modeled with axisymmetric shell elements (CONEAX) and submerged in a fluid region of TRIAAX elements. The model is analyzed to illustrate the acoustic intensity method and the usefulness of energy flow paths in the understanding of the response of fluid-structure interaction problems. The structural-acoustic analogy used is summarized for completeness. This study uncovered a NASTRAN limitation involving numerical precision issues in the CONEAX stiffness calculation causing large errors in the system matrices for nearly cylindrical cones.

Hambric, Stephen A.↗
NASA NTRS1986

Multigrid method for the equilibrium equations of elasticity using a compact scheme

A compact difference scheme is derived for treating the equilibrium equations of elasticity. The scheme is inconsistent and unstable. A multigrid method which takes into account these properties is described. The solution of the discrete equations, up to the level of discretization errors, is obtained by this method in just two multigrid cycles.

Taasan, S.↗
NASA NTRS1987

Multigrid method for the equilibrium equations of elasticity using a compact scheme

A compact difference scheme is derived for treating the equilibrium equations of elasticity. The scheme is inconsistent and unstable. A multigrid method which takes into account these properties is described. The solution of the discrete equations, up to the level of discretization errors, is obtained by this method in just two multigrid cycles.

Taasan, Shlomo↗
NASA NTRS1973

Effect of surface asperity on elastohydrodynamic lubrication

The important aspects of elastohydrodynamic lubrication, with a single, one-dimensional asperity, have been found by solving numerically the coupled transient Reynolds equation and the elasticity equation. Even though the assumption of a single asperity is highly ideal, this study sheds some light on the effect of surface roughness on elastohydrodynamic lubrication. The results show that the film pressure tends to increase more than the steady state pressure, and in particular, the increase in pressure reaches a maximum as the asperity approaches the inlet of the contact region. The asperity height and the pressure increase above the steady state pressure are closely related to each other; the higher the asperity height, the larger the pressure increase. In the pure rolling case, it has been found that a local pressure peak is not developed. However, in the cases of sliding and rolling, a small, local pressure peak is developed on the pressure profile when the asperity moves into the contact region. In general, the overall film thickness profile increases with increasing asperity height, but is not significantly affected by the asperity width. Moreover, the slope of the overall film thickness profile for the transient cases is much greater than the steady state profile, which is approximately constant across the contact width. The increase in the center film thickness also depends upon the width and height of the asperity.

Lee, K.↗
NASA NTRS1985

Elastohydrodynamic lubrication calculations used as a tool to study scuffing

A new Reynolds equation was developed that takes into account the nonlinear viscous behavior of the fluid. The new Reynolds equation considers the nonlinear viscous fluid model of Eyring, the equilibrium equation, the constant mass flow, and the kinematic boundary condition. The new Reynolds equation and the elasticity equation are solved simultaneously by using a system approach and a Newton-Raphson technique. Comparisons are made with results obtained from the classical Reynolds equation. The effects of sliding speed and introducing a bump or a groove within the conjunction are studied. Results are shown for both moderate and heavy loads.

Houpert, L. G.↗
NASA NTRS1981

Basic lubrication equations

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

Hamrock, B. J.↗
NASA NTRS1992

An integrated development of the equations of motion for elastic hypersonic flight vehicles

An integrated, consistent analytical framework is developed for modeling the dynamics of elastic hypersonic flight vehicles. A Lagrangian approach is used in order to capture the dynamics of rigid-body motion, elastic deformation, fluid flow, rotating machinery, wind, and a spherical rotating earth model, and to account for their interactions with each other. A vector form of the force, moment and elastic-deformation equations is developed from Lagrange's equation; a useable scalar form of these equations is also presented. The appropriate kinematic equations are developed, and are presented in a useable form. A preliminary study of the significance of selected terms in the equations of motion is conducted. Using generic data for a single-stage-to-orbit vehicle, it was found that the Coriolis force can reach values of up to 6 percent of the vehicle weight, and that the forces and moments attributable to fluid-flow terms can be significant.

Bilimoria, Karl D.↗
NASA NTRS1994

Refined Estimation Of Thermal Tensile Stresses In Bolts

Thermal changes in tensile stresses and strains in bolt and in corresponding compressive stresses and strains in bolted material estimated more accurately by use of equations incorporating two refinements over previous equations. Elasticity of bolted material and radial thermal expansion also taken into account. Refined equations improve design and analysis of bolted joints assembled at one temperature (e.g., room temperature) and in which specified minimum tension must be maintained (and/or specified maximum tension not exceeded) at higher or lower operational temperature.

Rash, Larry C.↗
NASA NTRS1982

Frictional heating due to asperity interaction of elastohydrodynamic line-contact surfaces

A numerical solution of an elastohydrodynamically lubricated (EHL) line contact between two long, rough-surface cylinders that considers the frictional heating of asperities was obtained. Pressure distribution, temperature distribution, film thickness and EHL load for given speeds, lubricant properties, material properties of surfaces, and surface roughness parameters were theoretically solved by simultaneous solution of the elasticity equation and the Reynolds equation for two partially lubricated rough surfaces. The pressure due to asperity contact was calculated by assuming a Gaussian distribution of surface irregularities. The elastic deformation used for film thickness computation was found from the two kinds of pressure by plane strain analysis. The temperature rise in the contact zone was calculated by using the Blok-Jaeger flash temperature model. The effects of surface roughness on EHL load for various slide-role ratios, surface roughness parameters, surface patterns, and temperature parameters was studied. It was found that the maximum temperature rise in most cases occurred in the inlet zone, and that the minimum film thickness decreased and the maximum temperature increased as the surface roughness was increased.

Majumdar, B. C.↗