Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “element”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,279 records · Page 71
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Time elements

Time elements are introduced for use with Sundman time transformations for satellite equations of motion. Two time elements are presented, one providing maximum accuracy when the exponent of the governing equation equals 1, the other when the exponent equals 2. Time elements and time transformations reduce local truncation error and Liapunov (in-track) instability, and provide analytical step size control. Numerical results show accuracy improvements of more than one order of magnitude when time elements are employed with time transformations in the numerical integration of the satellite equations, compared with using time transformations alone.

Nacozy, P. E.↗
NASA NTRS1975

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Cooke, C. H.↗
NASA NTRS1975

Elemental composition and size distribution of particulates in Cleveland, Ohio

Measurements were made of the elemental particle size distribution at five contrasting urban environments with different source-type distributions in Cleveland, Ohio. Air quality conditions ranged from normal to air pollution alert levels. A parallel network of high-volume cascade impactors (5-state) were used for simultaneous sampling on glass fiber surfaces for mass determinations and on Whatman-41 surfaces for elemental analysis by neutron activation for 25 elements. The elemental data are assessed in terms of distribution functions and interrelationships and are compared between locations as a function of resultant wind direction in an attempt to relate the findings to sources.

King, R. B.↗
NASA NTRS1975

A finite element analysis of the exact nonlinear formulation of a lifting surface in steady incompressible flow, with the evaluation of the correct wake geometry

The problem of steady incompressible flow for lifting surfaces is considered. An integral equation is solved relating the values of the potential discontinuity on the lifting surface and its wake to the values of the normal derivative of the potential which are known from the boundary conditions. The lifting surface and the wake are divided into small quadrilateral surface elements. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each lifting surface element and equal to their values at the centroids of the lifting surface elements. This yields a set of linear algebraic equations. An iteration procedure is used to obtain the wake geometry: the velocities at the corner points of the wake elements are calculated and the wake streamlines are aligned to be parallel to the velocity vector. The procedure is repeated until convergence is attained.

Suciu, E. O.↗
NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗
NASA NTRS1975

Extinct superheavy element in the Allende meteorite

Radiochemical neutron activation analysis of seven Allende samples for 26 trace elements were conducted. In addition, Cr and Fe were studied with the aid of instrumental neutron activation analysis. The investigation had the objective to identify the extinct superheavy element which was present in meteorites and decayed to Xe isotopes by spontaneous fission. The superheavy element was found to reside mainly in a rare mineral (probably a Fe, Ni, Cr, Al-sulfide), comprising only 0.04% of the meteorite. It is pointed out that of the nine volatile superheavy elements 111 to 119, only 115, 114, and 113 are expected to condense as sulfides in the temperature interval between 400 and 500 K corresponding to mineral formation conditions in the solar nebula.

Anders, E.↗
NASA NTRS1974

The simultaneous determination of 20 trace elements in terrestrial, lunar and meteoritic material by radiochemical neutron activation analysis

A radiochemical neutron activation method has been developed and applied to determine the content of 20 trace elements (Ag, Au, Bi, Br, Cd, Co, Cs, Cu, Ga, Ge, In, Ir, Ni, Rb, Re, Sb, Te, Tl, and Zn) in 45 terrestrial, 230 lunar, and 70 meteoritic samples. Results obtained for the U.S.G.S. standard basalt BCR-1 indicate that the inherent precision for most elements is 10% or better. The values obtained for the trace elements investigated are compared to those previously reported in the literature. Data for Type I carbonaceous chondrites show their compositions to be far more uniform than previously supposed. The values obtained for several elements represent significant revisions in the accepted cosmic abundances. These new values include: Zn, 1250; Cd, 1.51; and Ir, 0.72 atoms/million Si atoms. Further results have provided insight into the meteoritic material and accretion of the moon, and give evidence of lunar highland vulcanism.

Keays, R. R.↗
NASA NTRS1975

Elemental composition and size distribution of particulates in Cleveland, Ohio

Measurements have been made of the elemental particle size distribution at five contrasting urban environments with different source-type distributions in Cleveland, Ohio. Air quality conditions ranged from normal to air pollution alert levels. A parallel network of high-volume cascade impactors (5-stage) were used for simultaneous sampling on glass fiber surfaces for mass determinations and on Whatman-41 surfaces for elemental analysis by neutron activation for 25 elements. The elemental data are assessed in terms of distribution functions and interrelationships and are compared between locations as a function of resultant wind direction in an attempt to relate the findings to sources.

Leibecki, H. F.↗
NASA NTRS1976

Evolution of major mineral compositions and trace element abundances during fractional crystallization of a model lunar composition

The evolution of major mineral compositions and trace element abundances during perfect fractional crystallization of a model lunar magma ocean was calculated. The minerals in the model lunar composition were olivine, orthopyroxene, clinopyroxene, and plagioclase. Lunar bulk composition data, major mineral/melt equilibria data, and trace element partition data were taken from published sources. The results show olivine beginning to crystallize at 1380 C. Approximately 50% of the system crystallizes as olivine. From 50 to 60% solidification, orthopyroxene crystallizes alone. During the final 40% solidification, Ca-rich clinopyroxene and plagioclase crystallize together. Various changes in composition of all these minerals are also noted during the process. Concomitant evolution of major element abundances in the melt is followed along with that of trace element abundances. Consequences of the results for constraints on some aspects of the composition of the lunar magma ocean and of the primitive moon are discussed.

Drake, M. J.↗
NASA NTRS1975

Spacelab - A key element in the Space Shuttle Space Transportation System

Spacelab will be a key element in the Space Transportation System (STS) to be initiated with the advent of the first operational flight of Space Shuttle in 1980. Spacelab is an international, cooperative venture between the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA), which is structured to provide the scientific community an earthlike laboratory in space by 1980. The responsibilities of both ESA and NASA are divided into design and development to be accomplished by ESA and the experiment integration and operation with the Space Shuttle by NASA. While the Spacelab is a key element in the STS, it is highly dependent on other elements in the system for its resources and payload support capabilities. This paper presents the relationship of the Spacelab to other elements and the operational planning that NASA is undertaking to make the Spacelab a flexible and efficient laboratory in space.

Lee, T. J.↗
NASA NTRS1976

Rare earth element abundances in rocks and minerals from the Fiskenaesset Complex, West Greenland

The paper reports activation-analysis determinations of rare-earth-element (REE) and other trace-element concentrations in selected rocks, plagioclase, and mafic separates from the Fiskenaesset Complex. The REE abundances are found to be very low and atypical in comparison with other terrestrial anorthosites. The plagioclases are shown to be characterized by a deficiency in heavy RE elements relative to light ones and a positive Eu anomaly, while the mafic separates are enriched in heavy rare earths and have no Eu anomaly, except in one sample. It is found that the bulk and trace-element abundances of the plagioclases are similar to those observed in some lunar anorthosites, but the degree of Eu anomaly is less in the plagioclases. The data are taken as confirmation of the idea that fractionation processes were involved in the origin of the Complex, and it is concluded that the Complex may have been produced from a magma generated by partial melting of a garnet-bearing source.

Henderson, P.↗
NASA NTRS1976

Application of finite element approach to transonic flow problems

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed.

Hafez, M. M.↗
NASA NTRS1977

Development of a curved pipe capability for the NASTRAN finite element program

A curved pipe element capability for the NASTRAN structural analysis program is developed using the NASTRAN dummy element feature. A description is given of the theory involved in the subroutines which describe stiffness, mass, thermal and enforced deformation loads, and force and stress recovery for the curved pipe element. Incorporation of these subroutines into NASTRAN is discussed. Test problems are proposed. Instructions on use of the new element capability are provided.

Jeter, J. W., Jr.↗
NASA NTRS1977

PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.

Pifko, A.↗
NASA NTRS1977

Doubly-curved variable-thickness isoparametric heterogeneous finite element

This paper describes an element streamlined for the analysis of doubly-curved, variable-thickness structural components and illustrates its effective application to vibration and static problems. The element is isoparametric, doubly-curved, thin-shell and triangular with variable thickness and accounts for anisotropic, inhomogeneous elastic material behavior. The element has six nodes (three corner and three mid-side) with five degrees-of-freedom (DOF) per node - three translations and two rotations. Quadratic isoparametric interpolation polynomials are used to express the element geometry and displacement variables in terms of corresponding nodal variables.

Minich, M. D.↗
NASA NTRS1976

Application of finite element approach to transonic flow problems

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions. Blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, non-rectangular elements and discontinuous approximation of shock waves are also discussed.

Hafez, M. M.↗
NASA NTRS1976

The development of the Poincare-similar elements with true anomaly as the independent variable

In reference 1, the Hamiltonian of the unperturbed two-body problem in extended phase space is established. Depending on the type of time transformation, eight canonical elements were developed with the true anomaly or the eccentric anomaly as the independent variable. These two new sets, DS(phi) and DS(u), however contain singularities for small eccentricities and inclinations. In reference 2, these singularities are removed by a transformation from DS(u) to eight canonical PS(u) elements. In reference 3, the DS(phi) variables are transformed to the PS(phi) elements to remove the singularities. However, no direct relation was established between the eight canonical PS(phi) elements and the Cartesian coordinates. It is the purpose of this report to establish those relations and to develop the perturbed equations of motion in the PS(phi) space. This report also demonstrates the accuracy of this new set when it is applied to numerical orbit prediction problems.

Mueller, A.↗
NASA NTRS1977

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The continuous cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗