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At least 433 records · Page 24

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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.↗

NASA NTRS1983

A mixed finite element for the analysis of laminated plates

A new mixed shear-flexible finite element based on the Hellinger-Reissner's variational principle is developed. The element is constructed using a mixed formulation of the shear deformation theory of laminated composite plates, and consists of three displacements, two shear rotations, and three moments as the independent degrees of freedom. The numerical convergence and accuracy characteristics of the element are investigated for bending of laminated anisotropic composite plates. The element is relatively simple to construct and has better accuracy and convergence features when compared to other conventional finite elements.

Putcha, N. S.↗

NASA NTRS1984

A spectral element method for fluid dynamics - Laminar flow in a channel expansion

A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.

Patera, A. T.↗

NASA NTRS1984

Origin of the Moon: Constraints from volatile elements

Supporting arguments for the lunar fusion hypothesis include the low density of the Moon corresponding to the density of the Earth's mantle and the low volatile content of the lunar rocks vs. those of terrestrial origin. Vapor pressures of the alkali elements and their oxides increase in the following order: Na, K, Rb and Cs. The Moon should, therefore, be more depleted in Cs relative to Rb, Rb relative to K, and K relative to Na than the Earth if the fission model is correct. Analyses of lunar mare basalts and terrestrial mid-ocean ridge and other young basalts indicate that this behavior is not observed. It is possible that monovalent alkali elements might be lost from silicate materials in a different order than that inferred from elemental and oxide vapor pressures, as a result of differences in the way they are bound in silicate materials. To test this hypothesis a series of experiments was conducted to investigate alkali loss at high temperatures. Analyses indicate that the behavior of volatiles dissolved in a silicate melt is similar to that inferred from elemental and oxide vapor pressures. It is concluded that alkali element ratios in the Earth and Moon are not readily interpreted in terms of the fission hypothesis.

Kreutzberger, M. E.↗

NASA NTRS1985

A 4-node Bilinear Isoparametric Element in Rockwell NASTRAN

The development and evaluation of the Rockwell NASTRAN four node quadrilateral (QUAD4) element is presented. The element derivation utilizes bilinear isoparametric techniques both for membrane and bending characteristics. The QUAD4 element coordinate system, membrane properties, lumped mass matrix, and treatment of warping are based upon the COSMIC/NASTRAN QDMEMI element while the bending characteristics are based on a paper by T. J. R. Hughes. The effects of warping on the bending stiffness, consistent mass, and geometric stiffness are based upon a paper by R. H. MacNeal. Numerical integration is accomplished by Gaussian quadrature on a 2 x 2 grid. Practical user support features include variable element thickness, thermal analysis and layered composite material definitions.

Liao, C.↗

NASA NTRS1984

Rational approach for assumed stress finite elements

A new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element. The equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co-ordinates. The resulting element possesses all the ideal qualities, i.e. it is invariant, it is less sensitive to geometric distortion, it contains a minimum number of stress parameters and it provides accurate stress calculations. For the formulation of a 4-node plane stress element, a small perturbation method is used to determine the equilibrium constraint equations. The element has been proved to be always rank sufficient.

Pian, T. H. H.↗

NASA NTRS1985

Contributions to the finite element solution of the fan noise radiation problem

The radiation of fan generated noise to the far field from a nacelle of realistic geometry is investigated using the finite element method. Several innovations have been introduced to minimize the computational requirements and create a highly efficient numerical scheme. The innovations include: (1) formulation of the problem in terms of velocity potential and density in such a way that no inlet mean flow velocity derivatives are required in the field equations, (2) the use of 'wave envelope' elements in an outer region permitting a grid much coarser than would be used for conventional finite elements, (3) the use of a mesh which deforms with an increase of forward flight speed so that mesh lines are always lines of constant phase and rays for a point source, permitting the use of wave envelope elements and simple boundary conditions for any case of forward velocity, (4) an efficient scheme for introducing the noise source via modal amplitude coefficients, and (5) the use of a frontal solution technique which for physically realistic problems drastically reduces the active storage requirements. The finite element scheme is outlined, as are the specific details of the innovations. Results are given for cases where comparable experimental data are available.

Eversman, W.↗

NASA NTRS1985

Study of the Reactive-element Effect in Oxidation of Fe-cr Alloys Using Transverse Section Analytical Electron Microscopy

The role of trace additions of reactive elements like Y, Ce, Th, or Hf to Cr bearing alloys was studied by applying a new developed technique of transverse section analytical electron microscopy. This reactive-element effect improves the high temperature oxidation resistance of alloys by strongly reducing the high temperature oxidation rate and enhancing the adhesion of the oxide scale, however, the mechanisms for this important effect remain largely unknown. It is indicated that the presence of yttrium affects the oxidation of Fe-Cr-Y alloys in at least two ways. The reactive element alters the growth mechanism of the oxide scale as evidenced by the marked influence of the reactive element on the oxide scale microstructure. The present results also suggest that reactive-element intermetallic compounds, which internally oxidize in the metal during oxidation, act as sinks for excess vacancies thus inhibiting vacancy condensation at the scale-metal interface and possibly enhancing scale adhesion.

King, W. E.↗

NASA NTRS1986

Anisotropic constitutive model for nickel base single crystal alloys: Development and finite element implementation

A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.

Dame, L. T.↗