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NASA NTRS1987

Dynamic and thermal response finite element models of multi-body space structural configurations

Presented is structural dynamics modeling of two multibody space structural configurations. The first configuration is a generic space station model of a cylindrical habitation module, two solar array panels, radiator panel, and central connecting tube. The second is a 15-m hoop-column antenna. Discussed is the special joint elimination sequence used for these large finite element models, so that eigenvalues could be extracted. The generic space station model aided test configuration design and analysis/test data correlation. The model consisted of six finite element models, one of each substructure and one of all substructures as a system. Static analysis and tests at the substructure level fine-tuned the finite element models. The 15-m hoop-column antenna is a truss column and structural ring interconnected with tension stabilizing cables. To the cables, pretensioned mesh membrane elements were attached to form four parabolic shaped antennae, one per quadrant. Imposing thermal preloads in the cables and mesh elements produced pretension in the finite element model. Thermal preload variation in the 96 control cables was adjusted to maintain antenna shape within the required tolerance and to give pointing accuracy.

Edighoffer, Harold H.↗

NASA NTRS1986

On the numerical performance of three-dimensional thick shell elements using a hybrid/mixed formulation

Three-dimensional thick shell elements with 8, 16, and 18 nodes are formulated by using the hybrid/mixed method. In bending applications, these elements are free from locking effect and give improved stress predictions. Finite element equations are derived from the Hellinger-Reissner variational principle in which both the displacement and stress fields are approximated by independent interpolation functions. For the assumption of stress parameters, three guidelines are followed: (1) suppression of kinematic deformation modes, (2) invariant element property, and (3) the constraint index exhibited by the element, when applied to constrained-media problems, must be greater than or equal to one. Numerical results are presented to show the element's behavior characteristics regarding sensitivity to locking, distortion effect (patch tests), mesh convergence and the accuracy of stress evaluation.

Graf, W.↗

NASA NTRS1987

The trace element chemistry of CaS in enstatite chondrites and some implications regarding its origin

The trace element distribution in oldhamite (CaS) extracted from enstatite chondrites was determined by INAA. Prior to extraction, the petrologic setting of the grains was studied microscopically, and their minor element contents determined by microprobe analysis; samples that displayed a wide range of minor element contents were selected for detailed elementary analysis. Those samples of CaS suspected to be more primitive on the basis of their minor element and petrologic siting contain the entire inventory of the host meteorite's light REE (LREE) and Eu, plus 30-50 percent of the heavy-REE inventory. In less primitive samples, the LREE are less enriched although Eu remains highly concentrated. Several other elements, including lithophiles and chalcophiles, are most enriched in the most primitive CaS. It is suggested that oldhamite played a key role in the redistribution of these elements during the metamorphism and evolution of enstatite-rich material.

Larimer, John W.↗

NASA NTRS1988

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Kim, Sang-Wook↗

NASA NTRS1988

Cosmological quantum chromodynamics, neutron diffusion, and the production of primordial heavy elements

A simple one-dimensional model is used to describe the evolution of neutron density before and during nucleosynthesis in a high-entropy bubble left over from the cosmic quark-hadron phase transition. It is shown why cosmic nucleosynthesis in such a neutron-rich environment produces a surfeit of elements heavier than lithium. Analytical and numerical techniques are used to estimate the abundances of carbon, nitrogen, and heavier elements up to Ne-22. A high-density neutron-rich region produces enough primordial N-14 to be observed in stellar atmospheres. It shown that very heavy elements may be created in a cosmological r-process; the neutron exposure in the neutron-rich regions is large enough for the Ne-22 to trigger a catastrophic r-process runaway in which the quantity of heavy elements doubles in much less than an expansion time due to fission cycling. A primordial abundance of r-process elements is predicted to appear as an excess of rare earth elements in extremely metal-poor stars.

Applegate, J. H.↗

NASA NTRS1988

A re-evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. The ratio of crack depth to crack length ranged form 0.4 to 2; the ratio of crack depth to plate thickness ranged from 0.2 to 0.8; and the ratio of notch radius to the plate thickness ranged from 1 to 3. The models had about 15,000 degrees-of-freedom. Stress-intensity factors were calculated by using the nodal-force method.

Tan, P. W.↗

NASA NTRS1989

Gain of circularly polarised arrays composed of linearly polarised elements

The gain of circularly polarized (CP) array antennas realized by proper phasing of sequentially rotated linearly polarized (LP) elements is compared to that of arrays using CP elements and demonstrated by calculations for microstrip patch elements. When element spacing is large and array size is small, the advantages of LP elements are offset by the significant reduction in gain due to high cross polarized lobes in the diagonal planes. For large arrays of closely spaced elements, this gain loss reduces to a negligible amount. However, for spacings above a critical value of about 0.7 wavelengths, unacceptably high gain losses will be incurred.

Hall, P. S.↗

NASA NTRS1988

Refractory lithophile elements

The abundance and distributions of refractory lithophile elements in chondritic meteorites and calcium-aluminum inclusions (CAIs) are presently noted to indicate that protoplanetary material was heated to very high temperatures. Three subsequent elemental fractionations have since been resolved: (1) that within the CAIs, indicating temperatures high enough to evaporate much of the refractory element content; (2) that of the refractory lithophile elements; and (3) that of Mg and Si, which indicates that the high temperatures were prevalent throughout the chondrite-formation region. Attention is given to models that have been proposed to explain elemental and isotopic abundances of refractory lithophile elements in chondritic material.

Larimer, John W.↗

NASA NTRS1989

Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows

Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number laminar flows are presented. In both methods the pressure has been interpolated using linear shape functions for a triangular element which is contained inside the biquadratic flow element. It has been shown previously that the pressure interpolation method, when used in conjunction with the velocity-pressure integrated method, yields accurate computational results for high-Reynolds-number flows. It is shown in this paper that use of the same pressure interpolation method in the consistent penalty finite element method yields computational results which are comparable to those of the velocity-pressure integrated method for both the velocity and the pressure fields. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine grid finite difference computational results. Advantages and disadvantages of the two finite element methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow of Reynolds number 10000, a laminar backward-facing step flow and a laminar flow through a nest of cylinders.

Kim, S.-W.↗

NASA NTRS1989

Trace element abundance determinations by Synchrotron X Ray Fluorescence (SXRF) on returned comet nucleus mineral grains

Trace element analyses were performed on bulk cosmic dust particles by Proton Induced X Ray Emission (PIXE) and Synchrotron X Ray Fluorescence (SXRF). When present at or near chondritic abundances the trace elements K, Ti, Cr, Mn, Cu, Zn, Ga, Ge, Se, and Br are presently detectable by SXRF in particles of 20 micron diameter. Improvements to the SXRF analysis facility at the National Synchrotron Light Source presently underway should increase the range of detectable elements and permit the analysis of smaller samples. In addition the Advanced Photon Source will be commissioned at Argonne National Laboratory in 1995. This 7 to 8 GeV positron storage ring, specifically designed for high-energy undulator and wiggler insertion devices, will be an ideal source for an x ray microprobe with one micron spatial resolution and better than 100 ppb elemental sensitivity for most elements. Thus trace element analysis of individual micron-sized grains should be possible by the time of the comet nucleus sample return mission.

Flynn, G. J.↗

NASA NTRS1989

Abundances of ultraheavy elements in the cosmic radiation - Results from HEAO 3

An analysis is presented that, for the first time, systematically normalizes the data from the HEAO 3 heavy nuclei experiment on the cosmic-ray abundances of all the elements heavier than germanium to that of iron. In the range of atomic number Z from 33 to 60, the analysis yields abundances of odd-even element pairs. The abundances are consistent with a cosmic-ray source having a composition similar to that of the solar system, but subject to source fractionation correlated with the first ionization potential (FIP) of each element. For Z greater than 60, the analysis yields abundances of element groups. For these heaviest nuclei, we find an enhancement of the abundance of the platinum group, elements with Z of 74-80, relative to that in propagated solar system source, and a corresponding increase in the abundance of the largely secondary elements in the 62-73 range. These abundances suggest that there is an enhancement of the r-process contribution to the source nuclei in the Z greater than 60 charge region. Over the entire region of charge, standard leaky box models of propagation satisfactorily model secondary production.

Binns, W. R.↗

NASA NTRS1989

Asteroid family identifications and proper elements

This paper lists proper elements and family memberships for the first 2065 numbered asteroids plus 20 higher numbered objects. All proper elements were calculated using the Williams (1969) theory. The information contained in the 13 columns of the table is discussed in detail. It is noted that the proper elements and family assignments for the first 1796 numbered objects are mostly identical to those reported previously by Williams (1979). However, proper elements were recalculated for 68 objects in the earlier list, and entries were made for asteroids omitted from that list. Family identifications have changed for several objects as a result of the improvement of the osculating elements and a recalculation of the proper elements of asteroids which formerly had poor orbits.

Williams, J. G.↗

NASA NTRS1990

Generalized Transition Finite-Boundary Elements for high speed flight structures

A new class of 'Generalized Transition Finite-Boundary Elements' formulation is presented to predict temperature and/or stress distribution of flight structures at high speeds. A tweleve-noded three-dimensional transition element and a variable degree of freedom eight-noded element are formulated. These elements are incorporated into the formulation of the heat transfer and structural analysis problems by utilizing a newly introduced 'material approximation functions' concept. Results obtained from limited examples compared with the solutions from analytical and other finite element analysis solution. Numerical examples presented illustrate the effectiveness of these elements.

Sarigul-Klijn, Nesrin↗

NASA NTRS1991

Experiences with the use of axisymmetric elements in cosmic NASTRAN for static analysis

Discussed here are some recent finite element modeling experiences using the axisymmetric elements CONEAX, TRAPAX, and TRIAAX, from the COSMIC NASTRAN element library. These experiences were gained in the practical application of these elements to the static analysis of helicopter rotor force measuring systems for two design projects for the NASA Ames Research Center. These design projects were the Rotor Test Apparatus and the Large Rotor Test Apparatus, which are dedicated to basic helicopter research. Here, a genetic axisymmetric model is generated for illustrative purposes. Modeling considerations are discussed, and the advantages and disadvantages of using axisymmetric elements are presented. Asymmetric mechanical and thermal loads are applied to the structure, and single and multi-point constraints are addressed. An example that couples the axisymmetric model to a non-axisymmtric model is demonstrated, complete with DMAP alters. Recommendations for improving the elements and making them easier to use are offered.

Cooper, Michael J.↗

NASA NTRS1991

A finite dynamic element for laminated composite plates and shells

Development of finite dynamic elements can result in a significant reduction of computing time and cost for calculation of natural frequencies and mode shapes, which is an essential part of flutter prediction. Analysis with and without the dynamic terms is an alternative to constructing a new finite element mesh, to determine whether the mesh is sufficiently refined. Finite dynamic elements show spectacular improvement in convergence of higher modes with mesh refinement, but the improvement for lower modes is not so great. Cost reduction ratios greater than 20 have been observed for some modes. An average cost reduction ratio of 12 was achieved for the first six modes of a swept, tapered sandwich composite plate, at the 3 percent error level. Another set of calculations was made to determine the mesh density and cost parameters for which none of the first 12 frequencies was in error by more than 3 percent. It was found that the computing cost parameter for the dynamic element was about three times lower than the basic triangular element and 5.9 times lower than an eight-node isoparametric element.

Martin, C. W.↗

NASA NTRS1991

Developments in variational methods for high performance plate and shell elements

High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational foundations of high-performance elements, with emphasis on plate and shell elements constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parameterized variational principles are studied that provide a common foundation for the FF and ANS methods, as well as for a combination of both. From this unified formulation a variant of the ANS formulation, called the assumed natural deviatoric strain (ANDES) formulation, emerges as an important special case. The first ANDES element, a high-performance 9 degrees of freedom triangular Kirchhoff plate bending element, is briefly described to illustrate the use of the new formulation.

Felippa, Carlos A.↗

NASA NTRS1991

Finite element structural redesign by large admissible perturbations

In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.

Bernitsas, Michael M.↗

NASA NTRS1991

A geometric nonlinear degenerated shell element using a mixed formulation with independently assumed strain fields

A mixed formulation is chosen to overcome deficiencies of the standard displacement-based shell model. Element development is traced from the incremental variational principle on through to the final set of equilibrium equations. Particular attention is paid to developing specific guidelines for selecting the optimal set of strain parameters. A discussion of constraint index concepts and their predictive capability related to locking is included. Performance characteristics of the elements are assessed in a wide variety of linear and nonlinear plate/shell problems. Despite limiting the study to geometric nonlinear analysis, a substantial amount of additional insight concerning the finite element modeling of thin plate/shell structures is provided. For example, in nonlinear analysis, given the same mesh and load step size, mixed elements converge in fewer iterations than equivalent displacement-based models. It is also demonstrated that, in mixed formulations, lower order elements are preferred. Additionally, meshes used to obtain accurate linear solutions do not necessarily converge to the correct nonlinear solution. Finally, a new form of locking was identified associated with employing elements designed for biaxial bending in uniaxial bending applications.

Graf, Wiley E.↗