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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.↗

NASA NTRS1993

Implementation of mixed formulation elements in PC/NASTRAN

The purpose of this paper is to describe the implementation and use of a consistent family of two and three dimensional elements in NASTRAN. The elements which are based on a mixed formulation include a replacement of the original NASTRAN shear element and the addition of triangular quadrilateral shell elements and tetrahedral, pentahedral and hexahedral solid elements. These elements support all static loads including temperature gradient and pressure load. The mass matrix is also generated to support all dynamic rigid formats.

Schaeffer, Harry G.↗

NASA NTRS1993

An efficient formulation of the coupled finite element-integral equation technique for solving large 3D scattering problems

It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.

Cwik, T.↗

NASA NTRS1993

Life assessment of structural components using inelastic finite element analyses

The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such finite element solution technologies (in conjunction with the finite element program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other finite element programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic finite element solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this finite element solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding finite element analyses.

Arya, Vinod K.↗

NASA NTRS1993

Apparatus for testing high pressure injector elements

An apparatus for testing and evaluating the spray pattern of high pressure fuel injector elements for use in supplying fuel to combustion engines is presented. Prior art fuel injector elements were normally tested by use of low pressure apparatuses which did not provide a purge to prevent mist from obscuring the injector element or to prevent frosting of the view windows; could utilize only one fluid during each test; and had their viewing ports positioned one hundred eighty (180 deg) apart, thus preventing optimum use of laser diagnostics. The high pressure fluid injector test apparatus includes an upper hub, an upper weldment or housing, a first clamp and stud/nut assembly for securing the upper hub to the upper weldment, a standoff assembly within the upper weldment, a pair of window housings having view glasses within the upper weldment, an injector block assembly and purge plate within the upper weldment for holding an injector element to be tested and evaluated, a lower weldment or housing, a second clamp and stud/nut assembly for securing the lower weldment to the upper weldment, a lower hub, a third clamp and stud/nut assembly for securing the lower hub to the lower weldment, mechanisms for introducing fluid under high pressure for testing an injector element, and mechanisms for purging the apparatus to prevent frosting of view glasses within the window housings and to permit unobstructed viewing of the injector element.

Myers, William Neill↗

NASA NTRS1994

Alkali element constraints on Earth-Moon relations

Given their range of volatilities, alkali elements are potential tracers of temperature-dependent processes during planetary accretion and formation of the Earth-Moon system. Under the giant impact hypothesis, no direct connection between the composition of the Moon and the Earth is required, and proto-lunar material does not necessarily experience high temperatures. Models calling for multiple collisions with smaller planetesimals derive proto-lunar materials mainly from the Earth's mantle and explicitly invoke vaporization, shock melting and volatility-related fractionation. Na/K, K/Rb, and Rb/Cs should all increase in response to thermal volatization, so theories which derive the Moon substantially from Earth's mantle predict these ratios will be higher in the Moon than in the primitive mantle of the Earth. Despite the overall depletion of volatile elements in the Moon, its Na/K and K/Rb are equal to or less than those of Earth. A new model presented here for the composition of Earth's continental crust, a major repository of the alkali elements, suggests the Rb/Cs of the Moon is also less than that of Earth. Fractionation of the alkali elements between Earth and Moon are in the opposite sense to predictions based on the relative volatilities of these elements, if the Moon formed by high-T processing of Earth's mantle. Earth, rather than the Moon, appears to carry a signature of volatility-related fractionation in the alkali elements. This may reflect an early episode of intense heating on Earth with the Moon's alkali budget accreting from cooler material.

Norman, M. D.↗

NASA NTRS1994

Transportation of volatile elements in thermally evolving planetesimals: An important role of metallic iron

Ordinary chondrites are considered to have experienced thermal metamorphism in small bodies. We are interested in behaviors of volatile elements in such a kind of thermally evolving planetesimals. Volatile elements generally have high vapor pressures at high temperature. In porous bodies, with a high gas permeability, volatile elements are transported efficiently over a long range. Behavior of volatile elements transported by permeable gas flow can be handled by an equation whose form is similar to that of the equation of thermal diffusion. We can follow transportation of heats and volatile elements in planetesimals, when parameters in these equations, initial conditions and chemical behavior of volatile elements are given. Recently, we discovered that nitrogen in equilibrated H-chondrites is mainly trapped in taenite (f.c.c. Fe-Ni), probably dissolved in interstitial sites. Fegley suggests that metallic iron cannot trap nitrogen in the solar nebula gas due to its very low nitrogen partial pressure. Approximately 1 bar of nitrogen pressure is required to explain the nitrogen content in taenite. We may expect high nitrogen gas partial pressure (possibly produced by vaporization of nitrogen-bearing solids such as organic materials) at the interior of thermally evolving planetesimals. Kinetic behavior of nitrogen in taenite suggests that it can easily be equilibrated with the ambient nitrogen gas at temperatures of approximately 500 C or higher. We consider that nitrogen is trapped in taenite through a nitrogen redistribution process occurred during the thermal metamorphic event.

Hashizume, K.↗

NASA NTRS1995

Apparatus for testing high pressure injector elements

An apparatus for testing and evaluating the spray pattern of high pressure fuel injector elements for use in supplying fuel to combustion engines is presented. Prior art fuel injector elements were normally tested by use of low pressure apparatuses which did not provide a purge to prevent mist from obscuring the injector element or to prevent frosting of the view windows; could utilize only one fluid during each test; and had their viewing ports positioned one hundred eighty (180 deg) apart, thus preventing optimum use of laser diagnostics. The high pressure fluid injector test apparatus includes an upper hub, an upper weldment or housing, a first clamp and stud/nut assembly for securing the upper hub to the upper weldment, a standoff assembly within the upper weldment, a pair of window housings having view glasses within the upper weldment, an injector block assembly and purge plate within the upper weldment for holding an injector element to be tested and evaluated, a lower weldment or housing, a second clamp and stud/nut assembly for securing the lower weldment to the upper hub, a third clamp and stud/nut assembly for securing the lower hub to the lower weldment, mechanisms for introducing fluid under high pressure for testing an injector element, and mechanisms for purging the apparatus to prevent frosting of view glasses within the window housings and to permit unobstructed viewing of the injector element.

Myers, William Neill↗

NASA NTRS1994

Advance finite element modeling of rotor blade aeroelasticity

An advanced beam finite element has been developed for modeling rotor blade dynamics and aeroelasticity. This element is part of the Element Library of the Second Generation Comprehensive Helicopter Analysis System (2GCHAS). The element allows modeling of arbitrary rotor systems, including bearingless rotors. It accounts for moderately large elastic deflections, anisotropic properties, large frame motion for maneuver simulation, and allows for variable order shape functions. The effects of gravity, mechanically applied and aerodynamic loads are included. All kinematic quantities required to compute airloads are provided. In this paper, the fundamental assumptions and derivation of the element matrices are presented. Numerical results are shown to verify the formulation and illustrate several features of the element.

Straub, F. K.↗

NASA NTRS1995

Efficient finite element simulation of slot spirals, slot radomes and microwave structures

This progress report contains the following two documents: (1) 'Efficient Finite Element Simulation of Slot Antennas using Prismatic Elements' - A hybrid finite element-boundary integral (FE-BI) simulation technique is discussed to treat narrow slot antennas etched on a planar platform. Specifically, the prismatic elements are used to reduce the redundant sampling rates and ease the mesh generation process. Numerical results for an antenna slot and frequency selective surfaces are presented to demonstrate the validity and capability of the technique; and (2) 'Application and Design Guidelines of the PML Absorber for Finite Element Simulations of Microwave Packages' - The recently introduced perfectly matched layer (PML) uniaxial absorber for frequency domain finite element simulations has several advantages. In this paper we present the application of PML for microwave circuit simulations along with design guidelines to obtain a desired level of absorption. Different feeding techniques are also investigated for improved accuracy.

Gong, J.↗

NASA NTRS1996

Finite Element Simulation of Smart Structures

Finite element equations representing the behavior of piezoelectric materials when bounded to a typical structure and used as sensors and actuators were developed. Emphasis was placed on generating sensor output equations of piezoelectric sensors and responses of a typical structure bonded with piezoelectric sensors and actuators on the basis of finite element formulation. The model can predict not only structural responses due to both mechanical and electrical loading but also electrical potential due to mechanical or thermal effects. The resulted finite element equations were then used for simple control design and performance evaluation. In the control algorithm, voltages coming out from piezoelectric sensors, which are proportional to strains at sensing locations, are taken as input. The voltages applied to the piezoelectric actuators are used as output. The feasibility of integrating control algorithm with the element routine developed herein and FEAP was demonstrated. In particular, optimal independent modal space control was implemented in a software package on the basis of finite element formulation. A rudimentary finite element-control algorithm package was also developed to evaluate the performance of candidate control laws. A few numerical simulations using the software package developed herein were given. The integrated software package will provide a design tool to address issues such as how adaptive smart systems will scale to a full size aircraft, the amount of piezoelectric materials and the powers needed to actuate it for desired performance. It will also provide a viable new structural control design concept for practical applications in large flexible structures such as aerospace vehicles and aircraft.

Cui, Y. Lawrence↗

NASA NTRS1997

Elemental composition before, during and after the January 6, 1997, CME event measured by CELIAS/SOHO

Using solar wind particle data from the charge, element and isotope analysis system (CELIAS) experiment on the SOHO mission, densities of the elements O, Ne, Mg, Si, S, Ca, and Fe are derived, and their abundance is analyzed before, during and after the 6 Janaury 1997 coronal mass ejection event (CME). In the interstream and coronal hole regions before and after this event, typical solar wind abundances for the elements investigated were found. However, during the passage of the coronal mass ejection and during the passage of the erupted filament, the elemental composition differed markedly from typical solar wind. For the passage of the CME and for the passage of the erupted filament, a mass-dependent enhancement of the elements was found, with a monotonic increase towards heavier elements. Si/O and Fe/O ratios of the order of one during these time periods were observed.

Wurz, P.↗

NASA NTRS1999

Stratified Volume Diffractive Optical Elements as Low-Mass Coherent Lidar Scanners

Transmissive scanning elements for coherent laser radar systems are typically optical wedges, or prisms, which deflect the lidar beam at a specified angle and are then rotated about the instrument optical axis to produce a scan pattern. The wedge is placed in the lidar optical system subsequent to a beam-expanding telescope, implying that it has the largest diameter of any element in the system. The combination of the wedge diameter and asymmetric profile result in the element having very large mass and, consequently, relatively large power consumption required for scanning. These two parameters, mass and power consumption, are among the instrument requirements which need to be minimized when designing a lidar for a space-borne platform. Reducing the scanner contributions in these areas will have a significant effect on the overall instrument specifications, Replacing the optical wedge with a diffraction grating on the surface of a thin substrate is a straight forward approach with potential to reduce the mass of the scanning element significantly. For example, the optical wedge that will be used for the SPAce Readiness Coherent Lidar Experiment (SPARCLE) is approximately 25 cm in diameter and is made from silicon with a wedge angle designed for 30 degree deflection of a beam operating at approx. 2 micrometer wavelength. The mass of this element could be reduced by a factor of four by instead using a fused silica substrate, 1 cm thick, with a grating fabricated on one of the surfaces. For a grating to deflect a beam with a 2 micrometer wavelength by 30 degrees, a period of approximately 4 micrometers is required. This is small enough that fabrication of appropriate high efficiency blazed or multi-phase level diffractive optical gratings is prohibitively difficult. Moreover, bulk or stratified volume holographic approaches appear impractical due to materials limitations at 2 micrometers and the need to maintain adequate wavefront quality. In order to avoid the difficulties encountered in these approaches, we have developed a new type of high-efficiency grating which we call a Stratified Volume Diffractive Optical Element (SVDOE). The features of the gratings in this approach can be easily fabricated using standard photolithography and etching techniques and the materials used in the grating can be chosen specifically for a given application, In this paper we will briefly discuss the SVDOE technique and will present an example design of a lidar scanner using this approach. We will also discuss performance predictions for the example design.

Chambers, Diana M.↗

NASA NTRS2001

Thermal Analysis of a High-Speed Aircraft Wing Using p-Version Finite Elements

This paper presents the results of conceptual level thermal analyses of a High Speed Civil Transport (HSCT) wing using p-version finite elements. The work was motivated by a thermal analysis of a HSCT wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining a traditional finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Further study indicated using p-version finite elements might improve computation performance for this class of problem. Methods for determining internal radiation heat transfer were then developed and demonstrated on test problems representative of the geometry found in an aircraft wing structure. This paper presents the results of the application of these new methods to the analysis of a high speed aircraft wing. Results for both a wing box model as well as a full wing model are presented. 'Me reduced wing box model allows for a comparison of the traditional finite element method with mesh refinement (h-refinement) to the new p-version finite elements while the full wing model demonstrates the applicability and efficiency of p-version finite elements for large models.

Gould, Dana C.↗