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NASA NTRS1984

New Variational Formulations of Hybrid Stress Elements

In the variational formulations of finite elements by the Hu-Washizu and Hellinger-Reissner principles the stress equilibrium condition is maintained by the inclusion of internal displacements which function as the Lagrange multipliers for the constraints. These versions permit the use of natural coordinates and the relaxation of the equilibrium conditions and render considerable improvements in the assumed stress hybrid elements. These include the derivation of invariant hybrid elements which possess the ideal qualities such as minimum sensitivity to geometric distortions, minimum number of independent stress parameters, rank sufficient, and ability to represent constant strain states and bending moments. Another application is the formulation of semiLoof thin shell elements which can yield excellent results for many severe test cases because the rigid body nodes, the momentless membrane strains, and the inextensional bending modes are all represented.

Pian, T. H. H.↗

NASA NTRS1984

Finite Element Prediction of Acoustic Scattering and Radiation from Submerged Elastic Structures

A finite element formulation is derived for the scattering and radiation of acoustic waves from submerged elastic structures. The formulation uses as fundamental unknowns the displacement in the structure and a velocity potential in the field. Symmetric coefficient matrices result. The outer boundary of the fluid region is terminated with an approximate local wave-absorbing boundary condition which assumes that outgoing waves are locally planar. The finite element model is capable of predicting only the near-field acoustic pressures. Far-field sound pressure levels may be determined by integrating the surface pressures and velocities over the wet boundary of the structure using the Helmholtz integral. Comparison of finite element results with analytic results show excellent agreement. The coupled fluid-structure problem may be solved with general purpose finite element codes by using an analogy between the equations of elasticity and the wave equation of linear acoustics.

Everstine, G. C.↗

NASA NTRS1983

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm - Applications

A new hybrid-stress finite element algorithm suitable for analyzing large quasistatic deformations of inelastic solids is presented and its feasibility and performance are demonstrated with examples. The algorithm provides extremely accurate bifurcation analysis which is stable with respect to variation in the finite element mesh, so long as the same type of element is used in every mesh. When the mesh element is varied, the result changes in a predictable manner. The method does not necessarily lead to an upper or lower bound for the critical load. An explicit forward gradient scheme is used to improve stability and is shown to be useful also for elongation-dominated deformations. The application of the method to the onset of necking in plane extension and to deformation and stress in plane extension of an elasticoviscous fluid with an array of cylindrical voids is given in detail.

Reed, K. W.↗

NASA NTRS1984

The chemistry and origin of the ordinary chondrites Implications from refractory-lithophile and siderophile elements

Thirty-eight ordinary chondrites (17 H, 20 L, and 1 LL) have been analyzed for major and selected trace elements. These data indicate that the lithophile elements Mg, Ca, Al, Cr, and V normalized to Si are in higher abundance in the H than in the L chondrites. The siderophile elements Ni, Co, and Fe show very good correlation within, as well as between, the two major ordinary chondrite groups. Twenty-four of the analyses are of Antarctic finds, while ten are samples of falls. Comparing the Antarctic data with the fall data reveals no evidence that any of the elements studied here have been mobilized by terrestrial weathering processes. Within the H and L chondrite groups there is little chemical variation, indicating that the source of these samples is remarkably homogeneous. Equilibrium condensate fractionation from a nebula of CI composition can result in the observed ordinary chondrite compositions. The fractionation of metal at about 1440 K (and 0.001 atm) into high and low iron groups, followed by a gas-solid fractionation at about 1380 K with the H group losing more solids than the L, will produce the observed H and L compositions and intragroup trends.

Fulton, C. R.↗

NASA NTRS1982

Integrating 128 element InSb array - Recent results

There has been a continuing evolution toward larger arrays of infrared detectors, and the technology base derived from the Galileo Near Infrared Mapping Spectrometer (NIMS) has been expanded to linear arrays including from 128 to 512 elements. This advance is based on the commercial availability of high-quality InSb photodiodes and 128/256 element FET switch MUX's (multiplexing elements). The present investigation is concerned with an experimental 128-element linear imager using InSb detectors and silicon MUX for readout. Attention is given to detector array electrical characteristics, the detector readout architecture, noise, and special effects.

Bailey, G.↗

NASA NTRS1984

Error analysis and correction of discrete solutions from finite element codes

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Thurston, G. A.↗

NASA NTRS1984

Trace elements in rims and interiors of Chainpur chondrules

Trace elements were measured in the rims and interiors of nine chondrules separated from the Chainpur LL-3 chondrite. Whole rock samples of Chainpur and samples of separated rims were also measured. Chondrule rims are moderately enriched in siderophile and volatile elements relative to the chondrule interiors. The enriched volatile elements include the lithophilic volatile element Zn. The moderate enrichment of volatiles in chondrule rims and the lack of severe depletion in chondrules can account for the complete volatile inventory in Chainpur. These results support a three-component model of chondrite formation in which metal plus sulfide, chondrules plus rims and matrix silicates are mixed to form chondrites.

Wilkening, L. L.↗

NASA NTRS1984

A mixed shear flexible finite element for the analysis of laminated plates

A mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated. The element consists of three displacements, two rotations, and three moments as the generalized degrees of freedom per node. The numerical convergence and accuracy characteristics of the element are investigated by comparing the finite element solutions with the exact solutions. The present study shows that reduced-order integration of the stiffness coefficients due to shear is necessary to obtain accurate results for thin plates.

Putcha, N. S.↗

NASA NTRS1984

A triangular finite element for thin plates and shells

A finite element modeling technique which utilizes a triangular element called TSHEL with 45 degrees of freedom and seven point integration was tested for analysis of thin plate and shell structures. The element formulation is based on the degenerate solid shell concept and the mixed formulation with assumed independent inplane and transverse shear strains. The effectiveness of the present modeling technique which features combined use of elements with kinematic modes and those without kinematic modes to eliminate both locking and spurious kinematic modes at the global structural levels are shown.

Lee, S. W.↗

NASA NTRS1984

Finite element modelling of buried structures

In many structures the final stress states are dependent on the sequence of construction or the stress states at various stages of construction are of interest. Such problems can be analyzed using finite element programs that have the capability of adding (birthing) elements to simulate the progress of construction. However, the usual procedure of assembling elements may lead to numerical instabilities or stress states that are unrealistic. Both problems are demonstrated in the analysis of a structure using the program ADINA. A technique which combines application of a preload with element birthing to overcome these problems is described and illustrated.

Playdon, D. K.↗

NASA NTRS1984

Constraints on the origin of the Moon from molybdenum and other siderophile elements

New data on the concentration of molybdenum in the mantle of the Earth and in lunar rocks confirm that most siderophile elements in lunar crustal rocks and lunar basalts derived from the interior have significantly lower concentrations than in the Earth's mantle and much lower concentrations compared to chrondritic meteorites. Different but correlated depletions of Co and P have been found in different lunar samples. The Mo data appear to be correlated with the P and Co depletions. The variations siderophile contents may be explained by small variations in the segregation of the siderophile element data which are consistent with theories for either a terrestrial gran independent origin for the Moon. It is suggested that the Moon formed from the Earth's mantle (depleted in siderophile elements) and segregation of metal within the Moon further lowered the concentrations compared to the Earth's mantle. The Mo data support evidence from other siderophile elements that the Moon almost certainly contains a metal core or pools of segregated metal.

Newsom, H. E.↗

NASA NTRS1984

Volatile elements in and on lunar volcanic glasses: What do they tell us about lunar genesis?

There are good reasons to believe that lunar volcanic glasses originated from a deep interior source. The presence of a thin layer of surface correlated elements on these glasses may indicate that the Moon has some reservoirs that are enriched in volatiles. Since the glasses themselves do not show similar enrichment, the source should be of limited extent. Three scenarios are advanced for the origin of these elements. The mechanism for lunar volcanism differs from the mechanism for volcanism on Earth since the former produces bubbling and the latter explosive fountaining. From the condensation behavior of the volatile compounds, which leads to heterogeneous condensation, it is concluded that comparing element ratios of surface correlated elements gives little sense. It seems as if the volatile reservoirs are of rather limited extent and that they do not enlarge the volatile content of the bulk Moon significantly.

Koeberl, C.↗

NASA NTRS1984

Method and apparatus for mapping the distribution of chemical elements in an extended medium

Contaminants in an extended medium such as the wall of a building are mapped by locating neutron excitation source on one side of the wall and a gamma ray spectrometer, including a gamma ray detector on the opposite side of the wall facing the excitation source. The source and detector are moved in unison in discrete steps over opposing wall surfaces so as to determine the chemical composition of the elements in a hemispheric region of the wall adjacent the detector with the radius of the region being substantially that of the mean free path distance of gamma rays emitted from elements interacting with neutrons on the detector side of the wall. The source and detector are reversed for relatively thick walls for mapping the distribution of elements on the other side of the wall thickness. The output of the detector is fed to a multichannel pulse height analyzer where the intensity of the various gamma ray spectral lines are indicated relative to a dominant constituent element such as silicon. Resolution of anomalies such as the presence of voids and/or determining the bulk density of the medium is achieved by substituting a gamma ray source technique is also applied to metal alloys, such as iron alloys, in either the solid or molten state.

Evans, L. G.↗

NASA NTRS1985

Crack elements for COSMIC/NASTRAN

A crack element was developed and incorporated into COSMIC/NASTRAN. The element is considered linear, isotropic, and homogeneous. Mode 1 and 2 stress intensity factors are automatically calculated. Comparisons to theoretical plane strain solutions for several geometries are presented and demonstrate the accuracy of the developed element. Extensions of the element to three dimensions, anisotropic material, and plastic analysis are discussed.

Woytowitz, P. J.↗

NASA NTRS1985

Probabilistic Finite Element Development

The probabilistic finite element computer program known as Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) is being developed for the analysis of critical structural components for reusable space propulsion systems. First year efforts involve the formulation of the probabilistic analysis strategy and the development of a probabilistic linear analysis code. The ultimate goal of the 3-year program is the development of a finite element code capable of performing nonlinear dynamic analysis of structures having stochastic material properties, geometry, and boundary conditions and subjected to random loading. Three levels of sophistication are envisioned for the stochastic description of the structural problem, namely: (1) homogeneous random variable for stiffness, mass, damping, and external loading; (2) stochastic characterization of variables at the element level, with specified interelement correlations; and (3) stochastic interpolation of variables within a finite element. Two alternative probabilistic analysis methods will be developed, allowing for all three levels of modeling sophistication.

Nagtegaal, J.↗

NASA NTRS1985

Probabilistic Finite Element: Variational Theory

The goal of this research is to provide techniques which are cost-effective and enable the engineer to evaluate the effect of uncertainties in complex finite element models. Embedding the probabilistic aspects in a variational formulation is a natural approach. In addition, a variational approach to probabilistic finite elements enables it to be incorporated within standard finite element methodologies. Therefore, once the procedures are developed, they can easily be adapted to existing general purpose programs. Furthermore, the variational basis for these methods enables them to be adapted to a wide variety of structural elements and to provide a consistent basis for incorporating probabilistic features in many aspects of the structural problem. Tasks concluded include the theoretical development of probabilistic variational equations for structural dynamics, the development of efficient numerical algorithms for probabilistic sensitivity displacement and stress analysis, and integration of methodologies into a pilot computer code.

Belytschko, T.↗

NASA NTRS1984

The 'North American shale composite' - Its compilation, major and trace element characteristics

North American shale composite (NASC) major element composition and compilation are presented, together with rare earth element (REE) redeterminations obtained by high precision analytical methods. The major element composition of the NASC compares closely with other average shale compositions, and significant portions of the REE and some other trace elements are contained in minor phases. The uneven REE distribution in NASC powder appears to yield the heterogeneity in analyzed aliquants. REE distributions of detrital sediments may to some extent be dependent on their minor mineral assemblages and the sedimentological factors controlling these assemblages.

Gromet, L. P.↗

NASA NTRS1985

An analysis of cross-coupling of a multicomponent jet engine test stand using finite element modeling techniques

A two axis thrust measuring system was analyzed by using a finite a element computer program to determine the sensitivities of the thrust vectoring nozzle system to misalignment of the load cells and applied loads, and the stiffness of the structural members. Three models were evaluated: (1) the basic measuring element and its internal calibration load cells; (2) the basic measuring element and its external load calibration equipment; and (3) the basic measuring element, external calibration load frame and the altitude facility support structure. Alignment of calibration loads was the greatest source of error for multiaxis thrust measuring systems. Uniform increases or decreases in stiffness of the members, which might be caused by the selection of the materials, have little effect on the accuracy of the measurements. It is found that the POLO-FINITE program is a viable tool for designing and analyzing multiaxis thrust measurement systems. The response of the test stand to step inputs that might be encountered with thrust vectoring tests was determined. The dynamic analysis show a potential problem for measuring the dynamic response characteristics of thrust vectoring systems because of the inherently light damping of the test stand.

Schweikhard, W. G.↗