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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.↗

NASA NTRS1978

New alloys to conserve critical elements

Previous studies and surveys on availability of domestic reserves have shown that chromium is a most critical element within the U.S. metal industry. More precisely, the bulk of chromium is consumed in the production of stainless steels, specifically Type 304 stainless steel (304SS) which contains 18% Cr. The present paper deals with means of reducing chromium in commercial stainless steels by substituting more abundant or less expensive elements with the intent of maintaining the properties of 304SS. The discussion focuses on some of the oxidation and corrosion properties of new substitute stainless steels with only 12% Cr, which represents a potential saving of 33% of the chromium consumed in the production of 304SS. The alloying elements substituted for Cr in 304SS are selected according to their potential for protective oxide formation during high-temperature oxidation; these are Al, Si, Ti, Y, and misch metal which is 99.7% rare-earth metals containing 50 to 55% cerium. Other alloying elements to impart corrosion resistance are Mn, Mo, and V.

Stephens, J. R.↗

NASA NTRS1978

A finite element thermal analysis procedure for several temperature-dependent parameters

A finite-element thermal analysis procedure for elements with several temperature-dependent thermal parameters is presented. The procedure, based on an application of the Newton-Raphson iteration technique, is formulated by resolving element matrices into component matrices, one component for each thermal parameter. Component conductance matrices are evaluated by assuming constant thermal parameters within an element and are computed once per unit thermal parameter. Significant savings in computer time result from the unit thermal parameter concept. The solution procedure applied to a convectively cooled structure with significantly varying thermal parameters converged in four iterations.

Thornton, E. A.↗

NASA NTRS1978

Development of a finite dynamic element for free vibration analysis of two-dimensional structures

The paper develops an efficient free-vibration analysis procedure of two-dimensional structures. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and inertia matrices. A plane rectangular dynamic element is developed in detail. Numerical solution results of free-vibration analysis presented herein clearly indicate that these dynamic elements combined with a suitable quadratic matrix eigenproblem solution technique effect a most economical and efficient solution for such an analysis when compared with the usual finite element method.

Gupta, K. K.↗

NASA NTRS1978

Finite element analysis in a minicomputer/mainframe environment

Design considerations were evaluated for general purpose finite element systems to maximize performance when installed on distributed computer hardware/software systems. It is shown how the features of current minicomputers complement those of a modular implementation of the finite element method for increasing the control, speed, and visibility (interactive graphics) in solving structural problems at reduced cost. The approach used is to implement a finite element system in a distributed computer environment to solve structural problems and to explore alternatives in distributing finite element computations.

Storaasli, O. O.↗

NASA NTRS1978

Elemental characteristics of aerosols emitted from a coal-fired heating plant

Size differentiated aerosols were collected downstream from a heating plant fueled with eastern coal and analyzed using particle induced X-ray emission technique. Based on aerosol masses collected in various size ranges, the aerosol size distribution is determined to be trimodal, with the three peaks centered at 0.54 microns, 4.0 microns, and 11.0 microns, respectively. Of the various trace elements present in the aerosols, sulphur is the only element that shows very strong concentration in the smallest size group. Iron is strongly concentrated in the 4.0 micron group. Potassium, calcium, and titanium also exhibit stronger concentration in the 4.0 micron group than any other group. Other trace elements - vanadium, chromium, manganese, nickel, copper, and barium - are equally divided between the 0.54 microns and the 4.0 microns groups. Apparently, all of the trace elements - except S - enter aerosols during the initial formation and subsequent condensation phases in the combustion process. Excess concentration of sulphur in the 0.54 microns group can only be accounted for by recondensation of sulphur vapors on the combustion aerosols and gas-to-particle phase conversion of sulfate vapors at the stack top.

Singh, J. J.↗

NASA NTRS1979

Applications of velocity potential function to acoustic duct propagation and radiation from inlets using finite element theory

A finite element velocity potential program was developed to study acoustic wave propagation in complex geometries. For irrotational flows, relatively low sound frequencies, and plane wave input, the finite element solutions showed significant effects of inlet curvature and flow gradients on the attenuation of a given acoustic liner in a realistic variable area turbofan inlet. The velocity potential approach can not be used to estimate the effects of rotational flow on acoustic propagation, since the potential acoustic disturbances propagate at the speed of the media in sheared flow. Approaches are discussed that are being considered for extending the finite element solution to include the far field, as well as the internal portion of the duct. A new matrix partitioning approach is presented that can be incorporated in previously developed programs to allow the finite element calculation to be marched into the far field. The partitioning approach provided a large reduction in computer storage and running times.

Baumeister, K. J.↗

NASA NTRS1978

A Special Purpose Architecture for Finite Element Analysis

The analysis of aerospace structures by the finite element method consumes considerable computer time. The cost of this resource and the designer's desire to have rapid feedback concerning such questions as the effect of a change in loading of the structure or in a parameter of some structural material led to the design of a special purpose parallel computing system for finite element analysis. As a special purpose computer, the architecture of this finite element computer is closely tied to computational aspects of the particular problem. Various aspects of an MIMD array of microprocessors are related to the requirements of the class of finite element analysis problems which it is intended to solve.

Jordan, H. F.↗

NASA NTRS1979

Optimization of multi-element airfoils for maximum lift

Two theoretical methods are presented for optimizing multi-element airfoils to obtain maximum lift. The analyses assume that the shapes of the various high lift elements are fixed. The objective of the design procedures is then to determine the optimum location and/or deflection of the leading and trailing edge devices. The first analysis determines the optimum horizontal and vertical location and the deflection of a leading edge slat. The structure of the flow field is calculated by iteratively coupling potential flow and boundary layer analysis. This design procedure does not require that flow separation effects be modeled. The second analysis determines the slat and flap deflection required to maximize the lift of a three element airfoil. This approach requires that the effects of flow separation from one or more of the airfoil elements be taken into account. The theoretical results are in good agreement with results of a wind tunnel test used to corroborate the predicted optimum slat and flap positions.

Lawrence E Olson↗