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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Modification of basic stress-ratio algorithm enhances convergence. In conjunction with reliable stress-analysis algorithm, stress-ratio algorithm used to compute fully stressed state to obtain efficient distribution of materials in structure.
Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.
A second derivative frequency modification procedure is developed to iteratively change analysis modeling parameters for the more rapid convergence of analytically determined frequencies to those obtained by structural dynamic testing. A nonlinear system of algebraic equations in the modeling parameters is derived and a rapidly converging iterative method for their solution is presented. Numerical results obtained show that the higher order formulation and nonlinear predictor-corrector solution procedure yields results which are more rapidly convergent than those obtained using only the usual linear first-order parameter modification procedure. The proposed higher order theory also connverges in some cases when the ordinary linear theory does not.
The local buckling and the associated postbuckling response of stiffened composite shells are studied using an asymptotic approach. Both the classical (Kirchhoff) theory (CPT) and a first-order shear deformation theory (SDT) are employed in the study. SDT analysis was carried out using p-version type finite strips, whereas CPT analysis employed h-version based strips. Convergence studies confirm the superiority of the p-version approach. A panel width-to-thickness ratio of 50 was chosen to investigate the influence of shear deformation for stiffened and isolated panels fabricated out of isotropic and composite layered materials. The shear deformation effects were significant for composite stiffened shell panels with CPT giving a noticeably stiffer response. In comparison with isotropic shell panels, orthotropic layered panels buckle at lower nondimensional buckling loads but are appreciably less sensitive to imperfection.
An iterative, simulation-based design procedure for a neural network chip is introduced. For this design procedure, the goal is to produce a chip layout for a neural network in which the weights are determined by transistor gate width-to-length ratios. In a given iteration, the current layout is simulated using the circuit simulator SPICE, and layout adjustments are made based on conventional gradient-decent methods. After the iteration converges, the chip is fabricated. Monte Carlo analysis is used to predict the effect of statistical fabrication process variations on the overall performance of the neural network chip.
A time series of coastal zone color scanner (CZCS) derived chlorophyll (CZCS-chl) and sea surface temperature (SST) satellite imagery was developed for the Mid-Atlantic Bight (MAB). Warm-core rings (WCR) were identified by both the warmer SST signal as well as the low pigment concentrations of their cores. The variation in pigment concentrations and SST observed in satellite imagery over the geographic range and life span of four WCRs is investigated. The hypotheses are that pigment concentration increase during the lifetime of the WCR is a response to processes such as convective overturn, upwelling, edge enhancement due to increased vertical mixing, active convergence, or lateral exchange. Empirical orthogonal function analysis (EOF) is used to investigate the relationship between SST and pigment patterns observed in the presence of a WCR. The first two EOF modes explain more than 80% of the variability observed in all four WCRs and in both (SST and pigment) data sets. The results of this study show that, at the synoptic scales of staellite data, the variability observed in the WCRs is greater at the periphery of the rings. These results show that advective entrainment, rather than processes at ring center (e.g., shoaling of the pycnocline/nutricline in response to frictional decay) or at the periphery due to other processes such as vertical mixing, is the mechanism responsible for the observed variability.
Precision Formation Flying is an enabling technology for a variety of proposed space-based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), the associated MAXIM pathfinder mission, and the Stellar Imager. An essential element of the technology is the control algorithm. This paper discusses the development of a nonlinear, six-degree of freedom (6DOF) control algorithm for maintaining the relative position and attitude of a spacecraft within a formation. The translation dynamics are based on the equations of motion for the restricted three body problem. The control law guarantees the tracking error convergences to zero, based on a Lyapunov analysis. The simulation, modelled after the MAXIM Pathfinder mission, maintains the relative position and attitude of a Follower spacecraft with respect to a Leader spacecraft, stationed near the L2 libration point in the Sun-Earth system.
Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.
The practical benefits of the hyper-accuracy properties of the discontinuous Galerkin method are examined. In particular, we demonstrate that some flow attributes exhibit super-convergence even in the absence of any post-processing technique. Theoretical analysis suggest that flow features that are dominated by global propagation speeds and decay or growth rates should be super-convergent. Several discrete forms of the discontinuous Galerkin method are applied to the simulation of unsteady viscous flow over a two-dimensional cylinder. Convergence of the period of the naturally occurring oscillation is examined and shown to converge at 2p+1, where p is the polynomial degree of the discontinuous Galerkin basis. Comparisons are made between the different discretizations and with theoretical analysis.
Rapid warming over the Tibetan Plateau (TP) has been associated with a wetting trend in atmospheric water vapor content, which is critical for recharging the Asian water tower. However, the mechanism associated with the wetting phenomenon remains unclear. Long-term changes in moisture balance and precipitation recycling processes are investigated using the ERA5 reanalysis from 1979 to 2019. The wetting trend over TP is mainly due to the summer water vapor trend with signi?cantly increases over the western TP. Based on the moisture balance analysis, it is found that precipitation, evaporation, and the convergence of moisture are all increasing over the western TP but decreasing over the eastern TP. Based on the dynamical precipitation recycling model, the results suggest that both internal and external cycles contributes to the wetting over TP, with 63.87% and 36.13% contributions respectively. Further analysis found that the atmospheric heating source is also increasing over the western TP, which could shift the moisture transportation from east to west at the southern boundary of TP. The increasing moisture convergence could enhance precipitation, and the enhanced latent heating in the mid-atmosphere can further induced moisture convergence, which forms a positive feedback. However, an opposite situation occurred over the eastern TP. The internal and external cycle of the recycling process can stimulate (suppress) each other through precipitation over the western (eastern) TP. This mechanism linked the changes in the precipitation recycling and atmospheric circulation, and induced the wetting trend over TP in summer.
This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.
This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.
Asymptotic modal analysis, a method that has recently been developed for structural dynamical systems, has been applied to a rectangular acoustic cavity. The cavity had a flexible vibrating portion on one wall, and the other five walls were rigid. Banded white noise was transmitted through the flexible portion (plate) only. Both the location along the wall and the size of the plate were varied. The mean square pressure levels of the cavity interior were computed as a ratio of the result obtained from classical modal analysis to that obtained from asymptotic modal analysis for the various plate configurations. In general, this ratio converged to 1.0 as the number of responding modes increased. Intensification effects were found due to both the excitation location and the response location. The asymptotic modal analysis method was both efficient and accurate in solving the given problem. The method has advantages over the traditional methods that are used for solving dynamics problems with a large number of responding modes.
Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are presented to show how surface wrinkle progress with increasing tension loads. Antenna reflector surface accuracies were found to be very much dependent on the type and size of the antenna, the reflector surface curvature, reflector membrane supports in terms of spacing of catenaries, as well as the amount of applied load.
This slide presentation reviews a method for the assessment of three-dimensional conduction effects during test in a Aerothermal Wind Tunnel. The test objectives were to duplicate and extend tests that were performed during the 1960's on thermal conduction on proturberance on a flat plate. Slides review the 1D versus 3D conduction data reduction error, the analysis process, CFD-based analysis, loose coupling method that simulates a wind tunnel test run, verification of the CFD solution, Grid convergence, Mach number trend, size trends, and a Sumary of the CFD conduction analysis. Other slides show comparisons to pretest CFD at Mach 1.5 and 2.16 and the geometries of the models and grids.
We consider asynchronous versions of the first- and second-order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values are chosen a priori. We explore the parameter values that can be proven to give convergence of the asynchronous methods. This is the first such analysis for asynchronous second-order methods. We find that for the first-order method, the optimal parameter value for the synchronous case also gives an asynchronously convergent method. For the second-order method, the parameter ranges for which we can prove asynchronous convergence do not contain the optimal parameter values for the synchronous iteration. In practice, however, the asynchronous second-order iterations may still converge using the optimal parameter values, or parameter values close to the optimal ones, despite this result. We explore this behavior with a multithreaded parallel implementation of the asynchronous methods.
A number of non-standard finite element methods have been proposed in recent years, each of which derives from a specific class of PDE-constrained norm minimization problems. The most notable examples are LL* methods. In this work, we argue that all high-order methods in this class should be expected to deliver substandard uniform h-refinement convergence rates. In fact, one may not even see rates proportional to the polynomial order p > 1 when the exact solution is a constant function. Here, we show that the convergence rate is limited by the regularity of an extraneous Lagrange multiplier variable which naturally appears via a saddle-point analysis. In turn, limited convergence rates appear because the regularity of this Lagrange multiplier is determined, in part, by the geometry of the domain. Numerical experiments support our conclusions.
By comparing to the most recent experimental data and spectra of the SO2 628 ν1/ν3 bands (see Ulenikov et al., JQSRT 168 (2016) 29-39), this study illustrates the reliability and accuracy of the Ames-296K SO2 line list, which is accurate enough to facilitate such high-resolution spectroscopic analysis. The SO2 628 IR line list is computed on a recently improved potential energy surface (PES) refinement, denoted Ames-Pre2, and the published purely ab initio CCSD(T)/aug-cc-pVQZ dipole moment surface. Progress has been made in both energy level convergence and rovibrational quantum number assignments agreeing with laboratory analysis models. The accuracy of the computed 628 energy levels and line list is similar to what has been achieved and reported for SO2 626 and 646, i.e. 0.01-0.03 cm(exp −1) for bands up to 5500 cm(exp −1). During the comparison, we found some discrepancies in addition to overall good agreements. The three-IR-list based feature-by-feature analysis in a 0.25 cm(exp −1) spectral window clearly demonstrates the power of the current Ames line lists with new assignments, correction of some errors, and intensity contributions from varied sources including other isotopologues. We are inclined to attribute part of detected discrepancies to an incomplete experimental analysis and missing intensity in the model. With complete line position, intensity, and rovibrational quantum numbers determined at 296 K, spectroscopic analysis is significantly facilitated especially for a spectral range exhibiting such an unusually high density of lines. The computed 628 rovibrational levels and line list are accurate enough to provide alternatives for the missing bands or suspicious assignments, as well as helpful to identify these isotopologues in various celestial environments. The next step will be to revisit the SO2 828 and 646 spectral analyses.