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NASA NTRS1988

Refractory lithophile elements

The abundance and distributions of refractory lithophile elements in chondritic meteorites and calcium-aluminum inclusions (CAIs) are presently noted to indicate that protoplanetary material was heated to very high temperatures. Three subsequent elemental fractionations have since been resolved: (1) that within the CAIs, indicating temperatures high enough to evaporate much of the refractory element content; (2) that of the refractory lithophile elements; and (3) that of Mg and Si, which indicates that the high temperatures were prevalent throughout the chondrite-formation region. Attention is given to models that have been proposed to explain elemental and isotopic abundances of refractory lithophile elements in chondritic material.

Larimer, John W.↗

NASA NTRS1989

Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows

Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number laminar flows are presented. In both methods the pressure has been interpolated using linear shape functions for a triangular element which is contained inside the biquadratic flow element. It has been shown previously that the pressure interpolation method, when used in conjunction with the velocity-pressure integrated method, yields accurate computational results for high-Reynolds-number flows. It is shown in this paper that use of the same pressure interpolation method in the consistent penalty finite element method yields computational results which are comparable to those of the velocity-pressure integrated method for both the velocity and the pressure fields. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine grid finite difference computational results. Advantages and disadvantages of the two finite element methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow of Reynolds number 10000, a laminar backward-facing step flow and a laminar flow through a nest of cylinders.

Kim, S.-W.↗

NASA NTRS1989

Trace element abundance determinations by Synchrotron X Ray Fluorescence (SXRF) on returned comet nucleus mineral grains

Trace element analyses were performed on bulk cosmic dust particles by Proton Induced X Ray Emission (PIXE) and Synchrotron X Ray Fluorescence (SXRF). When present at or near chondritic abundances the trace elements K, Ti, Cr, Mn, Cu, Zn, Ga, Ge, Se, and Br are presently detectable by SXRF in particles of 20 micron diameter. Improvements to the SXRF analysis facility at the National Synchrotron Light Source presently underway should increase the range of detectable elements and permit the analysis of smaller samples. In addition the Advanced Photon Source will be commissioned at Argonne National Laboratory in 1995. This 7 to 8 GeV positron storage ring, specifically designed for high-energy undulator and wiggler insertion devices, will be an ideal source for an x ray microprobe with one micron spatial resolution and better than 100 ppb elemental sensitivity for most elements. Thus trace element analysis of individual micron-sized grains should be possible by the time of the comet nucleus sample return mission.

Flynn, G. J.↗

NASA NTRS1989

Abundances of ultraheavy elements in the cosmic radiation - Results from HEAO 3

An analysis is presented that, for the first time, systematically normalizes the data from the HEAO 3 heavy nuclei experiment on the cosmic-ray abundances of all the elements heavier than germanium to that of iron. In the range of atomic number Z from 33 to 60, the analysis yields abundances of odd-even element pairs. The abundances are consistent with a cosmic-ray source having a composition similar to that of the solar system, but subject to source fractionation correlated with the first ionization potential (FIP) of each element. For Z greater than 60, the analysis yields abundances of element groups. For these heaviest nuclei, we find an enhancement of the abundance of the platinum group, elements with Z of 74-80, relative to that in propagated solar system source, and a corresponding increase in the abundance of the largely secondary elements in the 62-73 range. These abundances suggest that there is an enhancement of the r-process contribution to the source nuclei in the Z greater than 60 charge region. Over the entire region of charge, standard leaky box models of propagation satisfactorily model secondary production.

Binns, W. R.↗

NASA NTRS1989

Asteroid family identifications and proper elements

This paper lists proper elements and family memberships for the first 2065 numbered asteroids plus 20 higher numbered objects. All proper elements were calculated using the Williams (1969) theory. The information contained in the 13 columns of the table is discussed in detail. It is noted that the proper elements and family assignments for the first 1796 numbered objects are mostly identical to those reported previously by Williams (1979). However, proper elements were recalculated for 68 objects in the earlier list, and entries were made for asteroids omitted from that list. Family identifications have changed for several objects as a result of the improvement of the osculating elements and a recalculation of the proper elements of asteroids which formerly had poor orbits.

Williams, J. G.↗

NASA NTRS1990

Generalized Transition Finite-Boundary Elements for high speed flight structures

A new class of 'Generalized Transition Finite-Boundary Elements' formulation is presented to predict temperature and/or stress distribution of flight structures at high speeds. A tweleve-noded three-dimensional transition element and a variable degree of freedom eight-noded element are formulated. These elements are incorporated into the formulation of the heat transfer and structural analysis problems by utilizing a newly introduced 'material approximation functions' concept. Results obtained from limited examples compared with the solutions from analytical and other finite element analysis solution. Numerical examples presented illustrate the effectiveness of these elements.

Sarigul-Klijn, Nesrin↗

NASA NTRS1991

Experiences with the use of axisymmetric elements in cosmic NASTRAN for static analysis

Discussed here are some recent finite element modeling experiences using the axisymmetric elements CONEAX, TRAPAX, and TRIAAX, from the COSMIC NASTRAN element library. These experiences were gained in the practical application of these elements to the static analysis of helicopter rotor force measuring systems for two design projects for the NASA Ames Research Center. These design projects were the Rotor Test Apparatus and the Large Rotor Test Apparatus, which are dedicated to basic helicopter research. Here, a genetic axisymmetric model is generated for illustrative purposes. Modeling considerations are discussed, and the advantages and disadvantages of using axisymmetric elements are presented. Asymmetric mechanical and thermal loads are applied to the structure, and single and multi-point constraints are addressed. An example that couples the axisymmetric model to a non-axisymmtric model is demonstrated, complete with DMAP alters. Recommendations for improving the elements and making them easier to use are offered.

Cooper, Michael J.↗

NASA NTRS1991

A finite dynamic element for laminated composite plates and shells

Development of finite dynamic elements can result in a significant reduction of computing time and cost for calculation of natural frequencies and mode shapes, which is an essential part of flutter prediction. Analysis with and without the dynamic terms is an alternative to constructing a new finite element mesh, to determine whether the mesh is sufficiently refined. Finite dynamic elements show spectacular improvement in convergence of higher modes with mesh refinement, but the improvement for lower modes is not so great. Cost reduction ratios greater than 20 have been observed for some modes. An average cost reduction ratio of 12 was achieved for the first six modes of a swept, tapered sandwich composite plate, at the 3 percent error level. Another set of calculations was made to determine the mesh density and cost parameters for which none of the first 12 frequencies was in error by more than 3 percent. It was found that the computing cost parameter for the dynamic element was about three times lower than the basic triangular element and 5.9 times lower than an eight-node isoparametric element.

Martin, C. W.↗

NASA NTRS1991

Developments in variational methods for high performance plate and shell elements

High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational foundations of high-performance elements, with emphasis on plate and shell elements constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parameterized variational principles are studied that provide a common foundation for the FF and ANS methods, as well as for a combination of both. From this unified formulation a variant of the ANS formulation, called the assumed natural deviatoric strain (ANDES) formulation, emerges as an important special case. The first ANDES element, a high-performance 9 degrees of freedom triangular Kirchhoff plate bending element, is briefly described to illustrate the use of the new formulation.

Felippa, Carlos A.↗

NASA NTRS1991

Finite element structural redesign by large admissible perturbations

In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.

Bernitsas, Michael M.↗

NASA NTRS1991

A geometric nonlinear degenerated shell element using a mixed formulation with independently assumed strain fields

A mixed formulation is chosen to overcome deficiencies of the standard displacement-based shell model. Element development is traced from the incremental variational principle on through to the final set of equilibrium equations. Particular attention is paid to developing specific guidelines for selecting the optimal set of strain parameters. A discussion of constraint index concepts and their predictive capability related to locking is included. Performance characteristics of the elements are assessed in a wide variety of linear and nonlinear plate/shell problems. Despite limiting the study to geometric nonlinear analysis, a substantial amount of additional insight concerning the finite element modeling of thin plate/shell structures is provided. For example, in nonlinear analysis, given the same mesh and load step size, mixed elements converge in fewer iterations than equivalent displacement-based models. It is also demonstrated that, in mixed formulations, lower order elements are preferred. Additionally, meshes used to obtain accurate linear solutions do not necessarily converge to the correct nonlinear solution. Finally, a new form of locking was identified associated with employing elements designed for biaxial bending in uniaxial bending applications.

Graf, Wiley E.↗

NASA NTRS1992

Improved inhomogeneous finite elements for fabric reinforced composite mechanics analysis

There is a need to do routine stress/failure analysis of fabric reinforced composite microstructures to provide additional confidence in critical applications and guide materials development. Conventional methods of 3-D stress analysis are time consuming to set up, run and interpret. A need exists for simpler methods of modeling these structures and analyzing the models. The principal difficulty is the discrete element mesh generation problem. Inhomogeneous finite elements are worth investigating for application to these problems because they eliminate the mesh generation problem. However, there are penalties associated with these elements. Their convergence rates can be slow compared to homogeneous elements. Also, there is no accepted method for obtaining detailed stresses in the constituent materials of each element. This paper shows that the convergence rate can be significantly improved by a simple device which substitutes homogeneous elements for the inhomogeneous ones. The device is shown to work well in simple one and two dimensional problems. However, demonstration of the application to more complex two and three dimensional problems remains to be done. Work is also progressing toward more realistic fabric microstructural geometries.

Foye, R. L.↗

NASA NTRS1993

Approximating the stress field within the unit cell of a fabric reinforced composite using replacement elements

This report concerns the prediction of the elastic moduli and the internal stresses within the unit cell of a fabric reinforced composite. In the proposed analysis no restrictions or assumptions are necessary concerning yarn or tow cross-sectional shapes or paths through the unit cell but the unit cell itself must be a right hexagonal parallelepiped. All the unit cell dimensions are assumed to be small with respect to the thickness of the composite structure that it models. The finite element analysis of a unit cell is usually complicated by the mesh generation problems and the non-standard, adjacent-cell boundary conditions. This analysis avoids these problems through the use of preprogrammed boundary conditions and replacement materials (or elements). With replacement elements it is not necessary to match all the constitutional material interfaces with finite element boundaries. Simple brick-shaped elements can be used to model the unit cell structure. The analysis predicts the elastic constants and the average stresses within each constituent material of each brick element. The application and results of this analysis are demonstrated through several example problems which include a number of composite microstructures.

Foye, R. L.↗

NASA NTRS1993

Implementation of a mesh adaptive scheme based on an element-level error indicator

We investigate the formulation and application of element-level error indicators based on parametrized variational principles. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited to drive adaptive mesh refinement on parallel computers where access to neighboring elements resident on different processors may incur significant computational overhead. Furthermore, such indicators are not affected by physical jumps at junctures or interfaces. An element-level indicator has been derived from the higher-order element energy and applied to r and h mesh adaptation of meshes in plates and shell structures. We report on our initial experiments with a cylindrical shell that intersects with fist plates forming a simplified 'wing-body intersection' benchmark problem.

Keating, Scott↗

NASA NTRS1990

On the effects of grid ill-conditioning in three dimensional finite element vector potential magnetostatic field computations

The effects of finite element grid geometries and associated ill-conditioning were studied in single medium and multi-media (air-iron) three dimensional magnetostatic field computation problems. The sensitivities of these 3D field computations to finite element grid geometries were investigated. It was found that in single medium applications the unconstrained magnetic vector potential curl-curl formulation in conjunction with first order finite elements produce global results which are almost totally insensitive to grid geometries. However, it was found that in multi-media (air-iron) applications first order finite element results are sensitive to grid geometries and consequent elemental shape ill-conditioning. These sensitivities were almost totally eliminated by means of the use of second order finite elements in the field computation algorithms. Practical examples are given in this paper to demonstrate these aspects mentioned above.

Wang, R.↗

NASA NTRS1993

Directionally adaptive finite element method for multidimensional Euler and Navier-Stokes equations

A directionally adaptive finite element method for multidimensional compressible flows is presented. Quadrilateral and hexahedral elements are used because they have several advantages over triangular and tetrahedral elements. Unlike traditional methods that use quadrilateral/hexahedral elements, our method allows an element to be divided in each of the three directions in 3D and two directions in 2D. Some restrictions on mesh structure are found to be necessary, especially in 3D. The refining and coarsening procedures, and the treatment of constraints are given. A new implementation of upwind schemes in the constrained finite element system is presented. Some example problems, including a Mach 10 shock interaction with the walls of a 2D channel, a 2D viscous compression corner flow, and inviscid and viscous 3D flows in square channels, are also shown.

Tan, Zhiqiang↗

NASA NTRS1988

A proposed method for enhanced eigen-pair extraction using finite element methods: Theory and application

The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.

Jara-Almonte, J.↗

NASA NTRS1993

SXRF determination of trace elements in chondrule rims in the unequilibrated CO3 chondrite, ALH A77307

The concentrations of Ni, Cu, Zn, Ga, Ge, and Se in five chondrule rims in the CO3 chondrite ALH A77307 (3.0) using the synchrotron x-ray fluorescence (SXRF) microprobe at Brookhaven National Laboratory were determined. The data show that the trace element chemistry of rims on different chondrules is remarkably similar, consistent with data obtained for the major elements by electron microprobe. These results support the idea that rims are not genetically related to individual chondrules, but all sampled the same reservoir of homogeneously mixed dust. Of the trace elements analyzed Zn and Ga show depletions relative to CI chondrite values, but in comparison with bulk CO chondrites all the elements are enriched by approximately 1.5 to 3.5 x CO. The high concentrations of the highly volatile elements Se and Ga and moderately volatile Zn (1.5 to 2 x CO) in rims show that matrix is the major reservoir of volatile elements in ALH A77307.

Brearley, Adrian J.↗