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NASA NTRS1987

The NESSUS finite element code

The objective of this development is to provide a new analysis tool which integrates the structural modeling versatility of a modern finite element code with the latest advances in the area of probabilistic modeling and structural reliability. Version 2.0 of the NESSUS finite element code was released last February, and is currently being exercised on a set of problems which are representative of typical Space Shuttle Main Engine (SSME) applications. NESSUS 2.0 allows linear elastostatic and eigenvalue analysis of structures with uncertain geometry, material properties and boundary conditions, which are subjected to a random mechanical and thermal loading environment. The NESSUS finite element code is a key component in a broader software system consisting of five major modules. NESSUS/EXPERT is an expert system under development at Southwest Research Institute, with the objective of centralizing all component-specific knowledge useful for conducting probabilistic analysis of typical Space Shuttle Main Engine (SSME) components. NESSUS/FEM contains the finite element code used for the structural analysis and parameter sensitivity evaluation of these components. The task of parametrizing a finite element mesh in terms of the random variables present is facilitated with the use of the probabilistic data preprocessor in NESSUS/PRE. An external database file is used for managing the bulk of the data generated by NESSUS/FEM.

Dias, J. B.↗
NASA NTRS1986

Conforming versus non-conforming boundary elements in three-dimensional elastostatics

A critical comparison of two basic formulations in three-dimensional elastostatics, using conforming and nonconforming boundary elements, is presented. The basic structure of the boundary element method is developed. The peculiarities that both types of boundary elements present in relation to the numerical implementation are discussed. Through selected examples, key issues such as the computational advantages and disadvantages of both formulations, mesh discretization and accuracy questions, and optimal location of the collocation nodes in the case of nonconforming elements are addressed. It is shown that conforming elements are able to produce more accurate results than nonconforming ones, with substantial economy in the final size of the system equations.

Manolis, G. D.↗
NASA NTRS1986

Siderophile and chalcophile element abundances in oceanic basalts, Pb isotope evolution and growth of the earth's core

The hypothesis that the mantle Pb isotope ratios reflect continued extraction of Pb into the earth's core over geologic time is evaluated by studying the depeletion of chalcophile and siderophile elements in the mantle. Oceanic basalt samples are analyzed in order to determine the Pb, Sr, and Nd isotropic compositions and the abundances of siderophile and chalcophile elements and incompatible lithophile elements. The data reveal that there is no systematic variation of siderophile or chalcophile element abundances relative to abundances of lithophile elements and the Pb/Ce ratio of the mantle is constant. It is suggested that the crust formation involves nonmagmatic and magmatic processes.

Newsom, H. E.↗
NASA NTRS1987

Al-26, Pu-244, Ti-50, REE, and trace element abundances in hibonite grains from CM and CV meteorites

Hibonites from the CM meteorites Murchison, Murray, and Cold Bokkeveld, and hibonites and Ti-rich pyroxene from the CV chondrite Allende are studied. Electron microprobe measurements of major element concentrations and track and ion probe measurements of Mg and Ti isotopic ratios, rare earth elements (REEs), and trace element abundances are analyzed. Correlations between isotopic anomalies in Ti, Al-26, Pu-244, and Mg-26(asterisk) are examined. Ti isotopic anomalies are compared with REE and trace element abundance patterns. Reasons for the lack of Al-26 in the hibonites are investigated and discussed. It is observed that there is no correlation between the Ti isotopic compositions, and the presence of Mg-26(asterisk), Pu-244, and REE and trace element patterns in individual hibonite samples. The data reveal that hibonites are not interstellar dust grains but formed on a short time scale and in localized regions of the early solar system.

Fahey, A. J.↗
NASA NTRS1987

A simple and efficient shear-flexible plate bending element

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

Chaudhuri, Reaz A.↗
NASA NTRS1987

An efficient quadrilateral element for plate bending analysis

A simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields. The crucial point of the selection of appropriate stress parameters is emphasized in the formulation. For this purpose, a set of guidelines is formulated based on the follwoing considerations: (1) suppression of all kinematic deformation modes, (2) the element has a favorable value for the constraint index in the thin plate limit, and (3) element properties are frame-invariant. For computer implementation the components of the element stiffness matrix are evaluated analytically using the symbolic manipulation package MACSYMA. The effectiveness and practical usefulness of the proposed element are demonstrated by the numerical results of a variety of problems involving thin and moderately thick plates under different loading and support conditions.

Saleeb, A. F.↗
NASA NTRS1987

A quadrilateral shell element using a mixed formulation

A simple quadrilateral shell element consisting of five nodes, four corner nodes and a central node, is developed for linear elastic analysis of thin as well as moderately thick shells. Based on a modified Hellinger-Reissner principle, finite element equations are derived from the assumed displacement and strain fields. By carefully choosing appropriate strain terms, all kinematic deformation modes are suppressed. Although the present element is similar to a displacement-based degenerated shell, no locking is experienced when it is applied to thin shell problems. Five examples are given to illustrate the analysis capability of the shell element. Numerical results indicate that the element shows fast mesh convergence and gives excellent stress predictions.

Saleeb, A. F.↗
NASA NTRS1988

Spectral element methods: Algorithms and architectures

Spectral element methods are high-order weighted residual techniques for partial differential equations that combine the geometric flexibility of finite element methods with the rapid convergence of spectral techniques. Spectral element methods are described for the simulation of incompressible fluid flows, with special emphasis on implementation of spectral element techniques on medium-grained parallel processors. Two parallel architectures are considered: the first, a commercially available message-passing hypercube system; the second, a developmental reconfigurable architecture based on Geometry-Defining Processors. High parallel efficiency is obtained in hypercube spectral element computations, indicating that load balancing and communication issues can be successfully addressed by a high-order technique/medium-grained processor algorithm-architecture coupling.

Fischer, Paul↗
NASA NTRS1987

Calculation of strain-energy release rates with higher order and singular finite elements

A general finite element procedure for obtaining strain-energy release rates for crack growth in isotropic materials is presented. The procedure is applicable to two-dimensional finite element analyses and uses the virtual crack-closure method. The procedure was applied to nonsingular 4-noded (linear), 8-noded (parabolic), and 12-noded (cubic) elements and to quarter-point and cubic singularity elements. Simple formulas for strain-energy release rates were obtained with this procedure for both nonsingular and singularity elements. The formulas were evaluated by applying them to two mode I and two mixed mode problems. Comparisons with results from the literature for these problems showed that the formulas give accurate strain-energy release rates.

Raju, I. S.↗
NASA NTRS1988

On the analytical treatment of impact in finite element modeling

Two simplified impact models which could be used in conjunction with finite element modeling of impacted structures are considered. The two methods are: a previously developed localized finite element impulse-momentum procedure for nondissipative impacts, and a simple gap element consisting of a parallel linear spring and damper useful in dissipative impacts. Results are presented for axial impact of an initially stationary rod. Impulse-momentum theory used in conjunction with finite element modeling was found to result in energy variations unrelated to physical behavior; these variations are reduced as the finite element model is refined.

Jeffrey, Glenda L.↗
NASA NTRS1988

A mixed formulaton of C(0)-linear triangular plate/shell element - The role of edge shear constraints

A simple and effective linear C(0)-tiangular element for plates and shells is developed on the basis of the Hellinger-Reissner mixed variational principle with independently assumed stress and displacement fields. Two main features are emphasized in this development concerning the assumed transverse shear stress field. First, this assumption results in edge-type penalty constraints in the thin plate/shell regimes. Second, the element is used in the form of a four-triangle, cross-diagonal macroelement mesh. As a result, the element is shown to be free from shear locking in thin plate/shell applications, and it satisfies all the appropriate patch tests required for Kirchhoff plate models. In addition, the element exhibits good overall convergence properties in a variety of test problems for plates and shells. Finally, from the computational standpoint, the element is very efficient since all stiffness component matrices are derived in explicit forms.

Saleeb, A. F.↗
NASA NTRS1988

A finite element study of the EIDI system

This paper presents a method for modeling the structural dynamics of an Electro-Impulse De-Icing System, using finite element analyses procedures. A guideline for building a representative finite element model is discussed. Modeling was done initially using four noded cubic elements, four noded isoparametric plate elements and eight noded isoparametric shell elements. Due to the size of the problem and due to the underestimation of shear stress results when compared to previous analytical work an approximate model was created to predict possible areas of shedding of ice. There appears to be good agreement with the test data provided by The Boeing Commercial Airplane Company. Thus these initial results of this method were found to be encouraging. Additional analytical work and comparison with experiment is needed in order to completely evaluate this approach.

Khatkhate, A. A.↗
NASA NTRS1988

An accurate and efficient satellite long-term orbit predictor employing 'fictitious' mean orbital elements

By using Von Zeipel's generating function procedure the perturbing earth gravitational potential is averaged with respect to the fast variable (mean anomaly) and a set of 'fictitous' mean orbital elements which can be used as a long-term satellite orbit predictor is obtained. The set of elements is shown to be a function of the nonlinear square of the second zonal harmonic coefficient. It is found that the long-term orbit prediction using the 'fictitous' mean elements is as accurate as that using the osculating elements, but has a computing speed about two orders of magnitude faster. For short-term orbit predictions, the osculating elements approach must be used.

Tang, Charles C. H.↗
NASA NTRS1988

Trace element and isotope geochemistry of Cretaceous-Tertiary boundary sediments: identification of extra-terrestrial and volcanic components

Trace element and stable isotope analyses were performed on a series of sediment samples crossing the Cretaceous-Tertiary (K-T) boundary from critical sections at Aumaya and Sopelano, Spain. The aim is to possibly distinguish extraterrestrial vs. volcanic or authigenic concentration of platinum group and other elements in K-T boundary transitional sediments. These sediments also have been shown to contain evidence for step-wise extinction of several groups of marine invertebrates, associated with negative oxygen and carbon isotope excursions occurring during the last million years of the Cretaceous. These isotope excursions have been interpreted to indicate major changes in ocean thermal regime, circulation, and ecosystems that may be related to multiple events during latest Cretaceous time. Results to date on the petrographic and geochemical analyses of the Late Cretaceous and Early Paleocene sediments indicate that diagenesis has obviously affected the trace element geochemistry and stable isotope compositions at Zumaya. Mineralogical and geochemical analysis of K-T boundary sediments at Zumaya suggest that a substantial fraction of anomalous trace elements in the boundary marl are present in specific mineral phases. Platinum and nickel grains perhaps represent the first direct evidence of siderophile-rich minerals at the boundary. The presence of spinels and Ni-rich particles as inclusions in aluminosilicate spherules from Zumaya suggests an original, non-diagenetic origin for the spherules. Similar spherules from southern Spain (Caravaca), show a strong marine authigenic overprint. This research represents a new approach in trying to directly identify the sedimentary mineral components that are responsible for the trace element concentrations associated with the K-T boundary.

Margolis, S. V.↗
NASA NTRS1989

Application of the p-version of the finite-element method to global-local problems

A brief survey is given of some recent developments in finite-element analysis technology which bear upon the three main research areas under consideration in this workshop: (1) analysis methods; (2) software testing and quality assurance; and (3) parallel processing. The variational principle incorporated in a finite-element computer program, together with a particular set of input data, determines the exact solution corresponding to that input data. Most finite-element analysis computer programs are based on the principle of virtual work. In the following, researchers consider only programs based on the principle of virtual work and denote the exact displacement vector field corresponding to some specific set of input data by vector u(EX). The exact solution vector u(EX) is independent of the design of the mesh or the choice of elements. Except for very simple problems, or specially constructed test problems, vector u(EX) is not known. Researchers perform a finite-element analysis (or any other numerical analysis) because they wish to make conclusions concerning the response of a physical system to certain imposed conditions, as if vector u(EX) were known.

Szabo, Barna A.↗
NASA NTRS1989

Launch packaging options for the photovoltaic power module cargo element

The National Aeronautics and Space Administration recently embarked on the Space Station Freedom program, which will utilize the Shuttle Orbiter for transportation to orbit. This task will be accomplished with a number of flights over several years. Each flight is unique in terms of the hardware that is manifested and the method by which it is integrated to form viable cargo elements. Work Package 4 is responsible for the electric power system for Space Station Freedom, and was delegated the authority to develop a photovoltaic (PV) power module cargo element. The PV power module consists of several unique assemblies. The first of these is the combined solar array/beta gimbal assembly. The remaining assemblies form the single combined integrated equipment assembly for each PV power module. These three combined assemblies are packaged into a launch cradle to form the PV power module cargo element, which is placed in the cargo bay of the Shuttle Orbiter for transportation to orbit. Various constraints determine the packaging options for the three PV power module combined assemblies. The size and shape of the combined assemblies in relation to the Shuttle Orbiter cargo bay dimensions and other manifested hardware are ultimately a factor in determining the acceptable packaging schemes for the PV power module cargo element. Several packaging options for the PV power module cargo element are presented. These options are discussed in terms of their impact on the overall flight hardware manifest as determined by the various constraints.

Hoberecht, Mark A.↗
NASA NTRS1989

Derivation of a Tappered p-Version Beam Finite Element

A tapered p-version beam finite element suitable for dynamic applications is derived. The taper in the element is represented by allowing the area moments of inertia to vary as quartic polynomials along the length of the beam, and the cross-sectional area to vary as a quadratic polynomial. The p-version finite-element characteristics are implemented through a set of polynomial shape functions. The lower-order shape functions are identical to the classical cubic and linear shape functions normally associated with a beam element. The higher-order shape functions are a hierarchical set of polynomials that are integrals of orthogonal polynomials. Explicit expressions for the mass and stiffness matrices are presented for an arbitrary value of p. The element has been verified to be numerically stable using shape functions through 22nd order.

Hinnant, Howard E.↗
NASA NTRS1988

A 20-DOF hybrid stress general shell element

A hybrid-stress general shell element is developed based on the Hellinger-Reissner principle modified for relaxed element compatibility conditions. The element is based on a thin-shell theory with Love-Kirchhoff hypothesis. It is of quadrilateral shape with only four corner nodes and five degrees of freedom per node. The geometry of the element is approximated through a cubic polynomial surface patch. Numerical examples consisting of torsion-loaded slit cylinder and pinched cylinders with open ends and rigid diaphragmed ends demonstrate excellent performance of the present element.

Kang, David S.↗