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A new finite element for coupling built-up shell substructures is presented. The present work extends the hybrid variational formulation of the interface element developed by Aminpour and Ransom to permit coupling between two intersecting substructures. Designed for the assembly of independently built-up finite element models, this technique provides a level of modeling flexibility previously unavailable.
We apply the adhesion approximation to study the formation and evolution of voids in the universe. Our simulations-carried out using 128(exp 3) particles in a cubical box with side 128 Mpc-indicate that the void spectrum evolves with time and that the mean void size in the standard Cosmic Background Explorer Satellite (COBE)-normalized cold dark matter (CDM) model with H(sub 50) = 1 scals approximately as bar D(z) = bar D(sub zero)/(1+2)(exp 1/2), where bar D(sub zero) approximately = 10.5 Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way toward reconstructing the form of the primordialpotential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in k-space cutoff we find that the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments erge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitaional potential. A central result of this paper is that voids can be populated by substructure such as mini-sheets and filaments, which run through voids. The number of such mini-pancakes that pass through a given void can be measured by the genus characteristic of an individual void which is an indicator of the topology of a given void in intial (Lagrangian) space. Large voids have on an average a larger measure than smaller voids indicating more substructure within larger voids relative to smaller ones. We find that the topology of individual voids is strongly epoch dependent, with void topologies generally simplifying with time. This means that as voids grow older they become progressively more empty and have less structure within them. We evaluate the genus measure both for individual voids as well as for the entire ensemble of voids predicted by CDM model. As a result we find that the topology of voids when taken together with the void spectrum is a very useful statistical indicator of the evolution of the structure of the universe on large scales.
The analysis aspects of the 23,000-line FORTRAN program VIPASA with constraints and optimization (VICONOPT) are described. Overall stiffness matrices assembled from the earlier exact vibration and instability of plate assemblies including shear and anisotropy (VIPASA) flat plate stiffnesses are optionally coupled by Langrangian multipliers to find critical buckling loads, or natural frequencies of undamped vibration, of prismatic assemblies of anisotropic flat plates with arbitrarily located point supports or simple transverse supporting frames. The longitudunal continuity of typical wing and fuselage panels is closely approximated because the solutions are for the infinitely long structure obtained by repeating a bay and its supports longitudinally. Any longitudinally invariant in-plane plate stresses are permitted, and very rapid solutions are guaranteed by numerous refinements, including multilevel substructuring and a method for repetitive cross sections that is exact for regular polygons used to represent cylinders. Modal displacements and stresses in or between plies of laminated plates are calculated and plotted, with values being recovered at all nodes of substructures. Comparison with usual approximate finite-element methods confirms that, for comparably converged solutions, VICONOPT is typically between 100 and 10(exp 4) times faster.
The cyclic deformation behavior of a wrought cobalt-base superalloy, Haynes 188, has been investigated over a range of temperatures between 25 and 1000 C under isothermal and in-phase thermomechanical fatigue (TMF) conditions. Constant mechanical strain rates (epsilon-dot) of 10(exp -3)/s and 10(exp -4)/s were examined with a fully reversed strain range of 0.8%. Particular attention was given to the effects of dynamic strain aging (DSA) on the stress-strain response and low cycle fatigue life. A correlation between cyclic deformation behavior and microstructural substructure was made through detailed transmission electron microscopy. Although DSA was found to occur over a wide temperature range between approximately 300 and 750 C the microstructural characteristics and the deformation mechanisms responsible for DSA varied considerably and were dependent upon temperature. In general, the operation of DSA processes led to a maximum of the cyclic stress amplitude at 650 C and was accompanied by pronounced planar slip, relatively high dislocation density, and the generation of stacking faults. DSA was evidenced through a combination of phenomena, including serrated yielding, an inverse dependence of the maximum cyclic hardening with epsilon-dot, and an instantaneous inverse epsilon-dot sensitivity verified by specialized epsilon-dot -change tests. The TMF cyclic hardening behavior of the alloy appeared to be dictated by the substructural changes occuring at the maximum temperature in the TMF cycle.
This report describes a methodology which predicts the behavior of ceramic matrix composites and has been incorporated in the computational tool CEMCAN (CEramic Matrix Composite ANalyzer). The approach combines micromechanics with a unique fiber substructuring concept. In this new concept, the conventional unit cell (the smallest representative volume element of the composite) of the micromechanics approach is modified by substructuring it into several slices and developing the micromechanics-based equations at the slice level. The methodology also takes into account nonlinear ceramic matrix composite (CMC) behavior due to temperature and the fracture initiation and progression. Important features of the approach and its effectiveness are described by using selected examples. Comparisons of predictions and limited experimental data are also provided.
Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.
Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.
Current deterministic structural methods are easily applied to substructures and components, and analysts have built great design insights and confidence in them over the years. However, deterministic methods cannot support systems risk analyses, and it was recently reported that deterministic treatment of statistical data is inconsistent with error propagation laws that can result in unevenly conservative structural predictions. Assuming non-nal distributions and using statistical data formats throughout prevailing stress deterministic processes lead to a safety factor in statistical format, which integrated into the safety index, provides a safety factor and first order reliability relationship. The embedded safety factor in the safety index expression allows a historically based risk to be determined and verified over a variety of quasi-static metallic substructures consistent with the traditional safety factor methods and NASA Std. 5001 criteria.
The paper discusses the following: (1) X-ray study of groups of galaxies with Chandra and XMM. (2) X-ray properties of point sources in Chandra deep fields. (3) Study of cluster substructure using wavelet techniques. (4) Combined study of galaxy clusters with X-ray and the S-Z effect. Groups of galaxies are the fundamental building blocks of large scale structure in the Universe. X-ray study of the intragroup medium offers a powerful approach to addressing some of the major questions that still remain about almost all aspects of groups: their ages, origins, importance of composition of various galaxy types, relations to clusters, and origin and enrichment of the intragroup gas. Long exposures with Chandra have opened new opportunities for the study of X-ray background. The presence of substructure within clusters of galaxies has substantial implications for our understanding of cluster evolution as well as fundamental questions in cosmology.
A design of experiments approach has been implemented using computational hypervelocity impact simulations to determine the most effective place to add mass to an existing metallic Thermal Protection System (TPS) to improve hypervelocity impact protection. Simulations were performed using axisymmetric models in CTH, a shock-physics code developed by Sandia National Laboratories, and validated by comparison with existing test data. The axisymmetric models were then used in a statistical sensitivity analysis to determine the influence of five design parameters on degree of hypervelocity particle dispersion. Several damage metrics were identified and evaluated. Damage metrics related to the extent of substructure damage were seen to produce misleading results, however damage metrics related to the degree of dispersion of the hypervelocity particle produced results that corresponded to physical intuition. Based on analysis of variance results it was concluded that the most effective way to increase hypervelocity impact resistance is to increase the thickness of the outer foil layer. Increasing the spacing between the outer surface and the substructure is also very effective at increasing dispersion.
Dislocation dipole substructures formed during metal fatigue are shown to produce a substantial distortion of ultrasonic waves propagating through the fatigued material. A model of ultrasonic wave-dislocation dipole interactions is developed that quantifies the wave distortion by means of a material nonlinearity parameter (beta). Application of the model to AA2024-T4 predicts a value of p approximately 300% larger in material cyclically loaded for 100 kcycles in stress-control at 276 MPa and R=0 than that measured for virgin material. Experimental measurements show a monotonic increase in p as a function of the number of fatigue cycles that closely approaches the predicted increase. The experiments also suggest that the relevant dislocation substructures are localized in the material.
We present the final results of a spectroscopic study of a sample of cD galaxy clusters. The goal of this program has been to study the dynamics of the clusters, with emphasis on determining the nature and frequency of cD galaxies with peculiar velocities. Redshifts measured with the MX Spectrometer have been combined with those obtained from the literature to obtain typically 50 - 150 observed velocities in each of 25 galaxy clusters containing a central cD galaxy. We present a dynamical analysis of the final 11 clusters to be observed in this sample. All 25 clusters are analyzed in a uniform manner to test for the presence of substructure, and to determine peculiar velocities and their statistical significance for the central cD galaxy. These peculiar velocities were used to determine whether or not the central cD galaxy is at rest in the cluster potential well. We find that 30 - 50% of the clusters in our sample possess significant subclustering (depending on the cluster radius used in the analysis), which is in agreement with other studies of non-cD clusters. Hence, the dynamical state of cD clusters is not different than other present-day clusters. After careful study, four of the clusters appear to have a cD galaxy with a significant peculiar velocity. Dressler-Shectman tests indicate that three of these four clusters have statistically significant substructure within 1.5/h(sub 75) Mpc of the cluster center. The dispersion 75 of the cD peculiar velocities is 164 +41/-34 km/s around the mean cluster velocity. This represents a significant detection of peculiar cD velocities, but at a level which is far below the mean velocity dispersion for this sample of clusters. The picture that emerges is one in which cD galaxies are nearly at rest with respect to the cluster potential well, but have small residual velocities due to subcluster mergers.
An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.
A method for the fabrication of active semiconductor and high-temperature superconducting device of the same substrate to form a monolithically integrated semiconductor-superconductor (MISS) structure is disclosed. A common insulating substrate, preferably sapphire or yttria-stabilized zirconia, is used for deposition of semiconductor and high-temperature superconductor substructures. Both substructures are capable of operation at a common temperature of at least 77 K. The separate semiconductor and superconductive regions may be electrically interconnected by normal metals, refractory metal silicides, or superconductors. Circuits and devices formed in the resulting MISS structures display operating characteristics which are equivalent to those of circuits and devices prepared on separate substrates.
A method for the fabrication of active semiconductor and high-temperature perconducting devices on the same substrate to form a monolithically integrated semiconductor-superconductor (MISS) structure is disclosed. A common insulating substrate, preferably sapphire or yttria-stabilized zirconia, is used for deposition of semiconductor and high-temperature superconductor substructures. Both substructures are capable of operation at a common temperature of at least 77 K. The separate semiconductor and superconductive regions may be electrically interconnected by normal metals, refractory metal silicides, or superconductors. Circuits and devices formed in the resulting MISS structures display operating characteristics which are equivalent to those of circuits and devices prepared on separate substrates.
A theory for predicting mechanical, thermal, electrical, and other properties of unidirectional-nanofiber/matrix composite materials is based on the prior theory of micromechanics of composite materials. In the development of the present theory, the prior theory of micromechanics was extended, through progressive substructuring, to the level of detail of a nanoscale slice of a nanofiber. All the governing equations were then formulated at this level. The substructuring and the equations have been programmed in the ICAN/JAVA computer code, which was reported in "ICAN/JAVA: Integrated Composite Analyzer Recoded in Java" (LEW-17247), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 36. In a demonstration, the theory as embodied in the computer code was applied to a graphite-nanofiber/epoxy laminate and used to predict 25 properties. Most of the properties were found to be distributed along the through-the-thickness direction. Matrix-dependent properties were found to have bimodal through-the-thickness distributions with discontinuous changes from mode to mode.
An efficient and computationally robust method for synthesis of component dynamics is developed. The method defines the interface forces/moments as feasible vectors in transformed coordinates to ensure that connectivity requirements of the combined structure are met. The synthesized system is then defined in a transformed set of feasible coordinates. The simplicity of form is exploited to effectively deal with modeling parametric and non-parametric uncertainties at the substructure level. Uncertainty models of reasonable size and complexity are synthesized for the combined structure from those in the substructure models. In particular, we address frequency and damping uncertainties at the component level. The approach first considers the robustness of synthesized flexible systems. It is then extended to deal with non-synthesized dynamic models with component-level uncertainties by projecting uncertainties to the system level. A numerical example is given to demonstrate the feasibility of the proposed approach.
We observe an erupting jet feature in a solar polar coronal hole, using data from Hinode/SOT, EIS, and XRT, with supplemental data from STEREO/EUVI. From EUV and soft X-ray (SXR) images we identify the erupting feature as a blowout coronal jet: in SXRs it is a jet with bright base, and in EUV it appears as an eruption of relatively cool (approximately 50,000 K) material of horizontal size scale approximately 30" originating from the base of the SXR jet. In SOT Ca II H images the most pronounced analog is a pair of thin (approximately 1") ejections, at the locations of either of the two legs of the erupting EUV jet. These Ca II features eventually rise beyond 45", leaving the SOT field of view, and have an appearance similar to standard spicules except that they are much taller. They have velocities similar to that of "type II" spicules, approximately 100 kilometers per second, and they appear to have spicule-like substructures splitting off from them with horizontal velocity approximately 50 kilometers per second, similar to the velocities of splitting spicules measured by Sterling et al. (2010). Motions of splitting features and of other substructures suggest that the macroscopic EUV jet is spinning or unwinding as it is ejected. This and earlier work suggests that a sub-population of Ca II type II spicules are the Ca II manifestation of portions of larger-scale erupting magnetic jets. A different sub-population of type II spicules could be blowout jets occurring on a much smaller horizontal size scale than the event we observe here.