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At least 307 records · Page 17

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NASA NTRS1976

Finite element representations for thin shell instability analysis

The development of finite element calculational procedures for thin-shell instability analysis has involved the definition of appropriate element representations (i.e. the geometric form of the element and the approximation of displacement and/or stress), constitutive expressions, and computational algorithms. Among these, the status of thin-shell finite element representations remains unsettled. This paper, therefore, emphasizes recent developments in the basic aspects of thin-shell finite element analysis and discusses one simplified approach in more detail. Formulative and computational procedures for elastic instability analysis are then summarized, and numerical results are shown for the simplified shell element formulation.

Gallagher, R. H.↗

NASA NTRS1976

On a 3-D singularity element for computation of combined mode stress intensities

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

Atluri, S. N.↗

NASA NTRS1977

Test of a model for trace element partition during closed-system solidification of a silicate liquid

Trace-element concentrations in separated minerals and rock fragments from a coarsely crushed and sieved sample of medium-grained lunar basalt are determined by high-precision instrumental neutron activation analysis for three main purposes. These are: (1) to test a previously proposed model for describing trace-element behavior during solidification of a silicate liquid under conditions of a closed system; (2) to compare trace-element concentrations among different size fractions of a comminuted basalt; and (3) to investigate small-scale heterogeneity within a single medium-grained basalt. It is found that an excellent mass balance for the whole rock is attained in terms of the trace-element concentrations of the component minerals and mesostasis, that the mixing model describing this mass balance yields a superior modal analysis for the whole rock, and that different size fractions of the coarsely crushed basalt vary in mineral composition. The closed-system model is shown to account properly for the average behavior of the trace elements during solidification of the basalt, and values of distribution coefficients are obtained for incompatible elements in that rock.

Haskin, L. A.↗

NASA NTRS1977

Singular plastic element: NASTRAN implementation and application

The elastic and plastic singularities near a crack tip are obtained from higher order isoparametric elements. This is simply accomplished by collapsing the quadrilateral element into the triangular element and by judicious choice of adjacent mid-side nodes. Specifically for the cubic element the elastic singularity is obtained by placing the mid-side nodes adjacent to the crack tip at 1/9th and 4/9th locations. The plastic singularity is constructed using the sliding node concept. These elements have been implemented in NASTRAN as user dummy elements.

Hussain, M. A.↗

NASA NTRS1978

Heavy element abundances in Ap stars from ultraviolet data. I - The bright reference stars Alpha Lyrae and Alpha Canis Majoris A

Curve-of-growth analysis is used to derive chemical abundances in Alpha Lyr and Alpha CMa, based on ultraviolet spectra obtained with Copernicus. This analysis is part of a program to study the abundances of the heavy elements mercury and platinum and the short-lived element technetium in the atmospheres of Ap and Am stars. Ultraviolet Fe II lines are used to establish the curves of growth for Alpha Lyr and Alpha CMa A; abundances of a variety of elements, along with upper limits on Hg, Pt, and Tc, are derived. In cases where previous studies based on visual spectra have included elements in common with the present analysis, the agreement is good within the known uncertainties. One new element, cadmium, is observed for these two stars. The upper limits on Pt and Hg, as well as Tc, show that these elements are probably not enhanced in Alpha CMa A by more than about one order of magnitude.

Boiarchuk, A. A.↗

NASA NTRS1980

An improved sensing element for skin-friction balance measurements

A nulling, parallel-linkage sensing element has been developed for a skin-friction balance in order to minimize the introduction of extraneous forces. Advantages of the present element over the conventional single-pivot sensing element include its insensitivity to element misalignment and off-center normal forces. Wind tunnel tests of the effects of gap size and element misalignment on parallel-linkage balance measurements indicate the greater sensitivity of the device to misalignment at small gap sizes and large lip sizes, as well as its relative insensitivity to off-center normal forces. It is concluded that a parallel-linkage device with a small lip is virtually insensitive to gap size and element misalignment, representing an improvement in skin-friction-measuring characteristics.

Allen, J. M.↗

NASA NTRS1981

Composition of the earth's upper mantle. I - Siderophile trace elements in ultramafic nodules

The considered investigation is concerned with a reexamination of the question of the distribution of siderophile elements in the earth's upper mantle, taking into account a more unified data base which is now available. A comprehensive suite of ultramafic inclusions was collected as part of the Basaltic Volcanism Study Project and has been analyzed by instrument neutron activation analysis for major, minor, and some lithophile trace elements. In addition, 18 of these rocks and the important sheared garnet lherzolite PHN 1611 have been analyzed by means of radiochemical neutron activation analysis for 7 siderophile elements (Au, Ge, Ir, Ni, Os, Pd, and Re) and 9 volatile elements (Ag, Bi, Cd, In, Sb, Se, Te, Tl, and Zn). The siderophile element data reveal interesting inter-element correlations, which were not apparent from the compiled abundance tables of Ringwood and Kesson (1976) and Chou (1978).

Morgan, J. W.↗

NASA NTRS1981

Time elements in rectangular coordinates

In a paper by the second author (Nacozy, 1981), various time elements are presented for use with the Sundman time transformation. In that paper, the time elements are given in terms of Keplerian orbital elements. We give here the corresponding time elements in terms of rectangular coordinates. Extensive references are given in the previous paper and will be omitted here. We present additional numerical experiments comparing the use of time elements and time transformations together with the use of time transformations alone. The results indicate a reduction in computational error when time elements are used.

Kwok, J. H.↗

NASA NTRS1982

Evaluation of an improved finite-element thermal stress calculation technique

A procedure for generating accurate thermal stresses with coarse finite element grids (Ojalvo's method) is described. The procedure is based on the observation that for linear thermoelastic problems, the thermal stresses may be envisioned as being composed of two contributions; the first due to the strains in the structure which depend on the integral of the temperature distribution over the finite element and the second due to the local variation of the temperature in the element. The first contribution can be accurately predicted with a coarse finite-element mesh. The resulting strain distribution can then be combined via the constitutive relations with detailed temperatures from a separate thermal analysis. The result is accurate thermal stresses from coarse finite element structural models even where the temperature distributions have sharp variations. The range of applicability of the method for various classes of thermostructural problems such as in-plane or bending type problems and the effect of the nature of the temperature distribution and edge constraints are addressed. Ojalvo's method is used in conjunction with the SPAR finite element program. Results are obtained for rods, membranes, a box beam and a stiffened panel.

Camarda, C. J.↗

NASA NTRS1982

Integrated finite element thermal-structural analysis with radiation heat transfer

An integrated approach for efficiently coupling thermal and stress analyses of structures with radiation heat transfer is presented. A new integrated one dimensional element based on a nodeless variable formulation is introduced. Lumped and consistent formulations of the nonlinear radiation heat transfer matrix are presented. The accuracy of the integrated approach is assessed by comparisons with analytical solutions and conventional finite element thermal-structural analyses. Results show that the nodeless variable thermal element yields accuracy equivalent to a higher order element but permits a common discretization with a lower order congruent structural element. The integrated element thus provides improved accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.

Thornton, E. A.↗

NASA NTRS1983

Wave envelope and infinite element schemes for fan noise radiation from turbofan inlets

Finite element models are presented for the calculation of radiated fan noise in the vicinity of turbofan inlets. The models involve the use of conventional axisymmetric finite elements in an inner region close to the inlet. The far field is represented by infinite elements or wave envelope elements. Theory and results are presented for the case with no mean flow. Comparisons of computed data with analytic solutions and measured values establish the utility of both the infinite element and wave envelope element schemes. The wave envelope scheme is shown to be effective also in the far field. Both schemes use meshes which are much sparser than would be required in conventional numerical discretizations and may be applied to real inlet configurations at modest computational cost.

Astley, R. J.↗

NASA NTRS1984

Accuracy of Three Dimensional Solid Finite Elements

The results of a study to determine the accuracy of the three dimensional solid elements available in NASTRAN for predicting displacements is presented. Of particular interest in the study is determining how to effectively use solid elements in analyzing thick optical mirrors, as might exist in a large telescope. Surface deformations due to thermal and gravity loading can be significant contributors to the determination of the overall optical quality of a telescope. The study investigates most of the solid elements currently available in either COSMIC or MSC NASTRAN. Error bounds as a function of mesh refinement and element aspect ratios are addressed. It is shown that the MSC solid elements are, in general, more accurate than their COSMIC NASTRAN counterparts due to the specialized numerical integration used. In addition, the MSC elements appear to be more economical to use on the DEC VAX 11/780 computer.

Case, W. R.↗

NASA NTRS1984

Numerical formulation for a higher order plane finite dynamic element

The paper describes the development of an eight-node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices. Numerical test results of free vibration analyses are presented in detail for the newly developed eight-node element and also the corresponding four-node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures. Such results indicate a superior pattern of solution convergence of the presently developed dynamic element.

Gupta, K. K.↗

NASA NTRS1983

The cosmic ray abundances of the platinum-lead elements as measured on HEAO-3

The relative abundances of elements in the charge ranges of Z = 75-79 (platinum) and Z = 80-83 (lead) should be a sensitive indication of the contributions of the r- and s-processes in nucleosynthesis. Data from the HEAO 3 Heavy Nuclei Experiment are used to establish abundances, relative to iron, of these elements in the cosmic radiation, as well as the ratio of 'secondary' elements, in the Z = 62-74 range, to the primary lead-platinum elements. These results appear to suggest that either the source abundances are deficient in s-process elements or that they are not organized solely by first ionization potential. In addition, present propagation models can adequately represent the relative abundances of primary and secondary elements.

Fixsen, D. J.↗

NASA NTRS1986

Supercomputer implementation of finite element algorithms for high speed compressible flows

Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes.

Thornton, E. A.↗

NASA NTRS1985

Finite elements based on consistently assumed stresses and displacements

Finite element stiffness matrices are derived using an extended Hellinger-Reissner principle in which internal displacements are added to serve as Lagrange multipliers to introduce the equilibrium constraint in each element. In a consistent formulation the assumed stresses are initially unconstrained and complete polynomials and the total displacements are also complete such that the corresponding strains are complete in the same order as the stresses. Several examples indicate that resulting properties for elements constructed by this consistent formulation are ideal and are less sensitive to distortions of element geometries. The method has been used to find the optimal stress terms for plane elements, 3-D solids, axisymmetric solids, and plate bending elements.

Pian, T. H. H.↗

NASA NTRS1985

Simplex finite element analysis of viscous incompressible flow with penalty function formulation

Viscous flow calculations are important for the determination of separated flows, recirculating flows, secondary flows and so on. This paper presents a penalty function approach for the finite element analysis of steady incompressible viscous flow. A simplex element is used with linear velocity and constant pressure in contrast to other works which usually employ higher order elements. Simplex elements yield analytical expressions for the element matrices which in turn lead to efficient solutions. Earlier works have partially indicated how constraint and lock-up problems might be avoided for simplex elements. This paper extends the earlier works by indicating the approach in detail and verifying that it is successful for several applications not discussed in the literature so far. Solution times and accuracy considerations are discussed for Couette flow, plane Poiseuille flow, a driven cavity problem, and laminar and turbulent flow over a step.

Allaire, P. E.↗

NASA NTRS1987

Stochastic and hybrid-stress plate/shell finite elements for hot-section components

The research effort in the Center for the Advancement of Computational Mechanics at Georgia Tech has two main thrusts. The first of these is the development of special approaches for the numerical stress analysis of solids and structures whose material and geometric properties are uncertain. The second seeks to develop and implement high-efficiency plate and shell elements. The stochastic element method, currently being implemented, will be able to more accurately portray the probabilistic nature of stress, strain, and displacement in actual structures. Current research has provided a hybrid-stress shell element whose behavior is acceptable for aspect ratios as high as 30 to 1. Thus, substantially more complex analyses will be practicable as soon as this element is fully implemented. An additional advantage of the hybrid approach is that it permits more accurate stress-recovery at the upper and lower surfaces of the shell, an important consideration in high thickness-gradient applications. The software associated with the above research is being implemented in the form of extensions to the Nessus code. The hybrid shell element has been successfully tested in several small-deformation elastic analyses. The theoretical formulation of the stochastic elements is essentially complete; its implementation is just beginning.

Atluri, S. N.↗