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At least 577 records · Page 32

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NASA NTRS1978

Graphical evaluation of relativistic matrix elements

A graphical representation of angular momentum was used to evaluate relativistic matrix elements between antisymmetrized states of many particle configurations having any number of open shells. The antisymmetrized matrix element was expanded as a sum of semisymmetrized matrix elements. The diagram representing a semisymmetrized matrix element was composed of four diagram blocks; the bra block, the ket block, the spectator block, and the interaction block. The first three blocks indicate the couplings of the two interacting configurations while the last depends on the interaction and is the replaceable component. Interaction blocks for relativistic operators and commonly used potentials were summarized in ready to use forms. A simple step by step procedure was prescribed generally for calculating antisymmetrized matrix elements of one and two particle operators.

Huang, K. N.↗

NASA NTRS1977

Trace elements in the Allende meteorite. III - Coarse-grained inclusions revisited

Radiochemical neutron activation analytic determinations of several elements in coarse-grained inclusions of the Allende meteorite are reported. The condensation and fractionation behavior of these and other elements are described. Evidence was found for a post-accretion thermal event which redistributed some trace elements. The solar system ratio of Zr/Hf is computed on the basis of the minimum variation in the inclusion, and the percentage of high-temperature condensates in the earth and moon are calculated on the basis of the mean U content of the inclusions. The mean value of the enrichment factors of 21 refractory elements relative to C1 chondrites is provided, and the elements that did or did not condense in a solid solution of melilite are listed.

Grossman, L.↗

NASA NTRS1979

Development and demonstration of manufacturing processes for fabricating graphite/PMR-15 polyimide structural elements

The processing requirements for graphite/PMR-15 polyimide composites developed to demonstrate the structural integrity of polyimide composite structural elements at temperatures up to 589K (600 F) are described. Major tasks included: quality assurance development; materials and process development; specification verification; flat panel fabrication; stiffened panel fabrication; honeycomb panel fabrication; chopped fiber moldings; and demonstration component fabrication. Materials, processing, and quality assurance documents were prepared from experimentally derived data. Structural elements consisting of flat panels, corrugated stiffeners, I-beams, hat stiffeners, honeycomb panels, and chopped fiber moldings were made and tested. Property data from 219K (-65 F) to 589K (600 F) were obtained. All elements were made in a production environment. The size of each element was sufficient to insure production capability and structural component applicability. Problems associated with adhesive bonding, laminate and structural element analysis, material variability, and test methods were addressed.

Sheppard, C. H.↗

NASA NTRS1979

Finite element methodology for transient conduction/forced-convection thermal analysis

Finite element methodology for steady state thermal analysis of convectively cooled structures has been extended for transient analysis. The finite elements are based on representing the fluid passages by fluid bulk-temperature nodes and fluid-solid interface nodes. The formulation of the finite element equations for a typical flow passage is based on the weighted residual method with upwind weighting functions. Computer implementation of the convective finite element methodology using explicit and implicit time integration algorithms is described. Accuracy and efficiency of the methodology is evaluated by comparisons with analytical solutions and finite-difference lumped-parameter analyses. The comparative analyses demonstrate that finite element conduction/conduction methodology may be used to predict transient temperatures with an accuracy equal or superior to the lumped-parameter finite-difference method.

Thornton, E. A.↗

NASA NTRS1978

Major and trace element chemistry of separated fragments from a hibonite-bearing Allende inclusion

The major and trace elements of separated fragments and a bulk sample from CG-11, a hibonite-bearing inclusion in the Allende meteorite, were analyzed. Major element abundances were used to determine the minerology of separated fragments. The high degree of correlation between Eu/Sm ratios and Lu/Yb ratios for the samples studied indicates that their rare earth element (REE) distributions are governed by two components. One, Lu-, Eu-rich, is probably hibonite; the other, depleted in these elements, seems to be associated with the secondary alteration phases, grossular, nepheline and anorthite. The REE distribution in CG-11 precludes melting events after formation of the secondary alteration phases, but a melting event involving the primary minerals cannot be excluded. The enrichment of Lu with respect to other measured REE in hibonite can be explained by present REE condensation models. Two Hf-bearing components, most likely hibonite and perovskite, are necessary to account for variations in Sc/Hf ratios in the fragments studied. The lithophile volatiles Na, Mn, Fe, Zn, and probably Cr increase in the same order as the amount of secondary alteration minerals; the volatile siderophile elements Co and Au, however, do not.

Davis, A. M.↗

NASA NTRS1979

A finite element formulation of the eigenvalue problem in lined ducts with flow

A finite element method is used to formulate the eigenvalue problem for a lined duct with flow. Either two dimensional or axially symmetric ducts with sheared flows can be studied, although the examples cited are two dimensional. The primitive variables of velocity and pressure are used with quadratic shape functions in each element. Results indicate that a useful level of accuracy can be achieved with a modest number of elements. Spurious eigenvalues, easily identified by obviously inconsistent eigenvectors, occur in certain instances. If the number of elements is not too small, these spurious modes are among the higher order eigenvalues of otherwise questionable accuracy. The possibility of using higher order elements which have slope continuity is proposed for future investigations to eliminate the spurious results.

Astley, R. J.↗

NASA NTRS1979

Evaluation of finite element formulations for transient conduction forced-convection analysis

Numerical studies clarifying the advantages and disavantages of conventional versus upwind convective finite elements are presented along with lumped versus consistent formulations for practical conduction forced-convection analysis. A finite-element procedure for treatment of negligible capacitance fluid nodes is presented. The procedure is based on procedures used in finite-element structural dynamics to treat nodes with negligible structural mass. Two finite-element programs and a finite-difference lumped-parameter program used in the studies are discussed. Evaluation studies utilizing three convection and two combined conduction-convection problems are then presented and discussed. Additionally, the computational time saving offered by the finite element procedure is considered for a practical combined conduction-convection problem.

Thornton, E. A.↗

NASA NTRS1980

Trace elements as quantitative probes of differentiation processes in planetary interiors

The characteristic trace element signature that each mineral in the source region imparts on the magma constitutes the conceptual basis for trace element modeling. It is shown that abundances of trace elements in extrusive igneous rocks may be used as petrological and geochemical probes of the source regions of the rocks if differentiation processes, partition coefficients, phase equilibria, and initial concentrations in the source region are known. Although compatible and incompatible trace elements are useful in modeling, the present review focuses primarily on examples involving the rare-earth elements.

Drake, M. J.↗

NASA NTRS1981

Integrated transient thermal-structural finite element analysis

An integrated thermal-structural finite element approach for efficient coupling of transient thermal and structural analysis is presented. New integrated thermal-structural rod and one dimensional axisymmetric elements considering conduction and convection are developed and used in transient thermal-structural applications. The improved accuracy of the integrated approach is illustrated by comparisons with exact transient heat conduction-elasticity solutions and conventional finite element thermal-finite element structural analyses. Results indicate that the approach offers significant potential for further development with other elements.

Thornton, E. A.↗

NASA NTRS1982

Application of the Finite Element Method to Rotary Wing Aeroelasticity

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.

Straub, F. K.↗

NASA NTRS1981

Finite element analyses of plane thermal entry-length flows

It is pointed out that the design of actively cooled engine and airframe structures for hypersonic flight requires strong interaction between fluid, thermal, and structural analyses. Research programs are being conducted to develop an integrated thermal-structural analysis capability based upon the finite element method. In connection with these programs, a finite element engineering approach has been developed based upon a number of assumptions customarily used in practical heat transfer analysis. An evaluation is conducted of the finite element engineering approach for entry-length flows. The evaluation makes use of an analysis of plane thermal entry-length flows by a finite element approach utilizing mean fluid temperatures with a convection coefficient. Another analysis is based on a finite element continuum approach, taking into account the rigorous momentum, mass, and energy equations of viscous, incompressible flow. The engineering approach was found to give excellent agreement with the rigorous continuum approach for Peclet number values not less than 100.

Thornton, E. A.↗

NASA NTRS1982

Alternative ways for formulation of hybrid stress elements

An element stiffness matrix can be derived by the conventional potential energy principle and, indirectly, also by generalized variational principles, such as the Hu-Washizu principle and the Hellinger-Reissner principle. The present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle. It is found that the resulting scheme is equivalent to that considered by Tong (1982) for the construction of hybrid stress elements. In Tong's scheme the inversion of a large flexibility matrix can be avoided. It is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the Hellinger-Reissner principle and the Hu-Washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method.

Pian, T. H. H.↗

NASA NTRS1982

The effects of C, P, and S on trace element partitioning during solidification in Fe-Ni alloys

Trace and minor element distributions in the iron meteorites are generally ascribed to partitioning during solidification of the parent body core or to partial melting within the parent body. A model involving fractional crystallization is considered. The model cannot account for differences between the measured values for the slopes on the log Ir-log Ni plots and the slopes predicted using experimentally determined distribution coefficients obtained in an investigation conducted by Goldstein and Friel (1978). The model has also other weaknesses. Part of the answer concerning the existing problems was provided by Narayan and Goldstein (1981, 1982). The present investigation is concerned with a further clarification of the effect of the minor elements P, S, and C on the distribution behavior of trace elements. Attention is given to measurements of the distribution coefficients for various elements (Ir, Ge, Ga, Au, Cu, Cr) in the presence of these minor elements.

Willis, J.↗

NASA NTRS1982

Chemical studies of L chondrites. II - Shock-induced trace element mobilization

Data for 13 trace elements in 14 L4-6 chondrites of established shock history are reported and discussed. These data are combined with data for an additional 13 L4-6 chondrites to delineate the full extent of losses by shock. Trace element contents vary with petrologic type, S/Fe subgroup, and shock history, the last dominating strongly. Absolute abundances and interelement relationships for the six or seven most mobile elements vary with degree of shock-loading established from mineralogic and petrologic study. Shock-heating, previously known to have affected radiogenic Ar-40 and/or He-4 in meteorites but not other elements, apparently was at least as effective as other open-system processes in establishing mobile trace element contents of L chondrites and probably others.

Walsh, T. M.↗

NASA NTRS1983

Kinetic effects on trace element partitioning

A potential difficulty regarding the application of trace element abundance data to problems in igneous petrogenesis is related to the possibility that partitioning of trace elements among minerals and melt may not be an equilibrium process. It may rather be controlled by kinetic processes, specifically the interplay between crystal growth and diffusion of the trace elements in crystals and melt. The present investigation has the objective to quantify kinetic effects on trace element partitioning. Crystals of olivine, pyroxene, and plagioclase were grown rapidly from synthetic melts resembling naturally-occurring mafic melts and doped with La, Sm, and Lu to quantify the magnitude of the effect of crystal growth rate on concentration of excluded trace elements. Olivine melt partitioning failed to show any appreciable kinetic effects, while diopside/melt distribution coefficients increased by 70 percent when the crystals grew very rapidly.

Lindstrom, D. J.↗

NASA NTRS1984

Application of finite element substructuring to composite micromechanics

Finite element substructuring is used to predict unidirectional fiber composite hygral (moisture), thermal, and mechanical properties. COSMIC NASTRAN and MSC/NASTRAN are used to perform the finite element analysis. The results obtained from the finite element model are compared with those obtained from the simplified composite micromechanics equations. A unidirectional composite structure made of boron/HM-epoxy, S-glass/IMHS-epoxy and AS/IMHS-epoxy are studied. The finite element analysis is performed using three dimensional isoparametric brick elements and two distinct models. The first model consists of a single cell (one fiber surrounded by matrix) to form a square. The second model uses the single cell and substructuring to form a nine cell square array. To compare computer time and results with the nine cell superelement model, another nine cell model is constructed using conventional mesh generation techniques. An independent computer program consisting of the simplified micromechanics equation is developed to predict the hygral, thermal, and mechanical properties for this comparison. The results indicate that advanced techniques can be used advantageously for fiber composite micromechanics.

Caruso, J. J.↗

NASA NTRS1984

A simple rectangular element for 2-dimensional analysis of laminated composites

A simple rectangular finite element was developed for two dimensional analysis of laminated composite materials. The rectangular laminated composite element eliminates the need to add elements to a model simply to account for the material properties of various laminae. This is particularly advantageous for thick laminates with many lamina. Explicit integration in terms of generalized displacements minimizes the algebraic effort required to derive the element stiffness and the thermal load vector. A substitute shape function technique is used to improve the performance of the element in modeling bending type deformation. Results for several example problems are discussed.

Whitcomb, J. D.↗

NASA NTRS1983

A posteriori error indicators for the p-version of the finite element method

The existence of local a posteriori error indicators for the p-version of the finite element method is demonstrated through numerical examples. It is shown that it is possible to construct reliable error indicators from the residuums and tractions which have the same rate of convergence as the strain energy. The error indicators contribution of an element can be estimated by considering only the element and its immediate neighbors. The optimal sequence of p-distributions can be closely followed by the indicators even when there are only a very few elements, the elements vary greatly in size, the polynomial orders vary, the mesh grading is poor, and the smoothness indices and relative errors vary between wide limits.

Dunavant, D. A.↗