Search NASA⌕ Search

SEARCH · Search NASA

Results for “Spline interpolation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Global/local stress analysis of composite structures

A method for performing a global/local stress analysis is described and its capabilities are demonstrated. The method employs spline interpolation functions which satisfy the linear plate bending equation to determine displacements and rotations from a global model which are used as boundary conditions for the local model. Then, the local model is analyzed independent of the global model of the structure. This approach can be used to determine local, detailed stress states for specific structural regions using independent, refined local models which exploit information from less-refined global models. The method presented is not restricted to having a priori knowledge of the location of the regions requiring local detailed stress analysis. This approach also reduces the computational effort necessary to obtain the detailed stress state. Criteria for applying the method are developed. The effectiveness of the method is demonstrated using a classical stress concentration problem and a graphite-epoxy blade-stiffened panel with a discontinuous stiffener.

Ransom, Jonathan B.↗

Global/local stress analysis of composite panels

A method for performing a global/local stress analysis is described and its capabilities are demonstrated. The method employs spline interpolation functions which satisfy the linear plate bending equation to determine displacements and rotations from a global model which are used as 'boundary conditions' for the local model. Then, the local model is analyzed independently of the global model of the structure. This approach can be used to determine local, detailed stress states for specific structural regions using independent, refined local models which exploit information from less-refined global models. The method presented is not restricted to having a priori knowledge of the location of the regions requiring local detailed stress analysis. This approach also reduces the computational effort necessary to obtain the detailed stress state. Criteria for applying the method are developed. The effectiveness of the method is demonstrated using a classical stress concentration problem and a graphite-epoxy blade-stiffened panel with a discontinuous stiffener.

Ransom, J. B.↗

Static aeroelastic analysis of composite wing

A static aeroelastic analysis capability that can predict aerodynamic loads for the deformed shape of the composite wing has been developed. The finite element method (FEM) was used for composite plate structural analysis, and the linear vortex lattice method (VLM) was used for steady aerodynamic analysis. The final deformed shape of the wing due to applied forces is determined by iterative manner using FEM and VLM. FEM and VLM analysis are related by a surface spline interpolation procedure. The wing with Gr/Ep composite material has been investigated to see the wing deformation effect. Aerodynamic load change due to wing flexibility has been investigated. Also, the effect of fiber orientation and sweep angle on the deformation pattern and aerodynamic coefficients are examined. For a certain fiber orientation, the deflection and aerodynamic loading of the composite wing is very much reduced. The swept forward wing has more significant effect of wing flexibility on aerodynamic coefficient than the swept back wing does.

Lee, IN↗

Bilinear modeling and state estimation of slew-induced deformations of a flexible multibody system

A model of the nonlinear dynamics of a deformable maneuvering multibody system is described, whereby elastic deformations are modeled by restoring forces and dissipative forces at point mass appendages. This model is brought into bilinear form. Estimation of deformations occasioned by rapid slewing maneuvers is carried out by a filter based on a globally equivalent linear model of the bilinear dynamics, and is shown to be an improvement over the extended Kalman filter. To further alleviate the computational burden, the estimated deformation state is propagated between observations by a low dimensional operator spline interpolator of bilinear system Volterra series, which is easily implemented.

Dwyer, Thomas A. W., III↗

Optimal design of geodesically stiffened composite cylindrical shells

An optimization system based on the finite element code Computations Structural Mechanics (CSM) Testbed and the optimization program, Automated Design Synthesis (ADS), is described. The optimization system can be used to obtain minimum-weight designs of composite stiffened structures. Ply thickness, ply orientations, and stiffener heights can be used as design variables. Buckling, displacement, and material failure constraints can be imposed on the design. The system is used to conduct a design study of geodesically stiffened shells. For comparison purposes, optimal designs of unstiffened shells and shells stiffened by rings and stingers are also obtained. Trends in the design of geodesically stiffened shells are identified. An approach to include local stress concentrations during the design optimization process is then presented. The method is based on a global/local analysis technique. It employs spline interpolation functions to determine displacements and rotations from a global model which are used as 'boundary conditions' for the local model. The organization of the strategy in the context of an optimization process is described. The method is validated with an example.

Gendron, G.↗

An independent refinement and integration procedure in multiregion finite element analysis

An independent refinement and integration procedure is developed to couple together independently modeled (global and local) regions in a single analysis. The models can have different levels of refinement and along the interface between them the finite element nodes need not coincide with one another. In the local model all the nodes except the nodes at the interface are statically condensed and the reduced stiffness matrix is obtained. For this static condensation a modified frontal solution technique is employed. A spline interpolation function that satisfies the linear isotropic plate bending differential equation is used to relate the local model interface nodal displacements to the global model interface displacements. The proposed independent refinement and integration procedure is evaluated by applying it to two- and three-dimensional cases involving inplane and out-of-plane deformation. The procedure yielded very accurate results for all the examples studied.

Krishnamurthy, T.↗

Coupled 2D-3D finite element method for analysis of a skin panel with a discontinuous stiffener

This paper describes a computationally efficient analysis method which was used to predict detailed stress states in a typical composite compression panel with a discontinuous hat stiffener. A global-local approach was used. The global model incorporated both 2D shell and 3D brick elements connected by newly developed transition elements. Most of the panel was modeled with 2D elements, while 3D elements were employed to model the stiffener flange and the adjacent skin. Both linear and geometrically nonlinear analyses were performed on the global model. The effect of geometric nonlinearity induced by the eccentric load path due to the discontinuous hat stiffener was significant. The local model used a fine mesh of 3D brick elements to model the region at the end of the stiffener. Boundary conditions of the local 3D model were obtained by spline interpolation of the nodal displacements from the global analysis. Detailed in-plane and through-the-thickness stresses were calculated in the flange-skin interface near the end of the stiffener.

Wang, J. T.↗

Empirical wind model for the middle and lower atmosphere. Part 2: Local time variations

The HWM90 thermospheric wind model was revised in the lower thermosphere and extended into the mesosphere and lower atmosphere to provide a single analytic model for calculating zonal and meridional wind profiles representative of the climatological average for various geophysical conditions. Local time variations in the mesosphere are derived from rocket soundings, incoherent scatter radar, MF radar, and meteor radar. Low-order spherical harmonics and Fourier series are used to describe these variations as a function of latitude and day of year with cubic spline interpolation in altitude. The model represents a smoothed compromise between the original data sources. Although agreement between various data sources is generally good, some systematic differences are noted. Overall root mean square differences between measured and model tidal components are on the order of 5 to 10 m/s.

Hedin, A. E.↗

Liquid Annular Seal Research

This paper highlights the accomplishments on a joint effort between NASA - Marshall Space Flight Center and Texas A and M University to develop accurate seal analysis software for use in rocket turbopump design, design audits and trouble shooting. Results for arbitrary clearance profile, transient simulation, thermal effects solution and flexible seal wall model are presented. A new solution for eccentric seals based on cubic spline interpolation and ordinary differential equation integration is also presented.

Palazzolo, Alan B.↗

Progress Toward Generation of a Navier-Stokes Database for a Harrier in Ground Effect

The Harrier YAV-8B aircraft is capable of vertical and short-field take-off and landing (V/STOL) by directing its four exhaust nozzles toward the ground, or conventional flight by rotating its nozzles into a horizontal position. The British Royal Air Force and the United States Marine Corps have used this aircraft for more than 30 years to provide a quick reaction time for troop support, and reduce the need for long runways. The success of this powered-lift (PL) vehicle has also prompted the more recent design of the Joint Strike Fighter (JSF). However there are significant safety issues that must be addressed when operating a PL vehicle in close proximity to the ground. Hot Gas Ingestion (HGI) by the inlets can result in a rapid loss of powered lift; and high-speed jet flows along the ground plane can induce low pressures underneath the vehicle, causing a 'suck-down' effect. Under these conditions, departure from controlled flight may occur. Moreover, unsteady ground vortices and jet fountains can affect the aircraft,s controllability and its proximity to ground troops. The viscous, time-dependent flow fields of PL vehicles are difficult to accurately and efficiently predict using Computational Fluid Dynamics (CFD). A number of researchers have used the time-dependent Reynolds-averaged Navier-Stokes (RANS) equations to compute flows for single and multiple jets in a cross-flow. A few have added some geometric complexity to the problem by computing flows for jet-augmented delta wings near a ground plane. Smith et.al. computed for the first time a single RANS solution about a simplified Harrier. This geometry included a fuselage, wing, leading edge root extension (LERX), inlets, and exhaust nozzles. All of these investigations cite two practical problems with computing these flows: 1) the need for improved solution accuracy; and, 2) the need for faster solution methods. We view the need for faster solution methods as key to improving the solution accuracy and making this class of computation more routine. One can hardly refine grids, explore the use of advanced turbulence models, and generate databases when it takes weeks of dedicated computer time for a single solution. Chaderjian, Ahmad, Pandya, and Murman have focused on reducing the time-to-solution for this very difficult and complex problem through process automation and exploitation of parallel computing. They began with the Harrier geometry reported, and added a deflected wing flap and empennage for greater realism. To date more than 80 solutions have been carried out. This paper will describe this process and progress made in reducing the time required to generate a simple longitudinal force and moment database for a Harrier in ground effect. It shows a typical snap-shot from an unsteady streakline animation, where fluid particles are colored by temperature. The ground vortex and a jet-fountain vortex are highlighted. It also shows a similar streakline image, where HGI occurs due to the vehicle in close proximity to the ground. It is show the mean lift coefficient as a function of angle of attack and height. The angle of attack range was 4 deg less than or = alpha less than or = 10 deg with an increment of 1 degree, and the height range was 10 ft less than or = h less than or = 30ft with an increment of 5 feet. This 35 solution database was extended to over 2500 cases using a monotone cubic-spline interpolation procedure. The suck-down effect (reduction of lift near the ground) is highlighted in the figure. The "cushion effect," the conventional reduction of lift as the vehicle moves out of ground effect, is also indicated. All 35 RANS solutions were obtained using 952 Silicon Graphics Origin 2000 and 3000 processors in dedicated mode for one week. Typically, 112 processors were assigned to each case. Some other cases used fewer processors to utilize all available CPUS. The final paper will report on the automation of the solution process, including: grid generation, job monitoring, solution completion criteria, and post processing. Moreover, improvements in parallel efficiency for a dual time-step algorithm for the RANS equations will also be presented. Results will be discussed in detail using unsteady streakline flow visualization to correlate unsteady flow structures with dominant aerodynamic frequencies. The stability derivatives, CL, and CL, will also be presented.

Chaderjian, Neal M.↗

Surface structure of an invariant manifold of a Halo Orbit (extended abstract)

We extract the surface structure of the unstable invariant manifold tube projected into position space, of a halo orbit near L2. We do this by using transversal planes to intersect trajectories that approximate the tube. From these intersection points we construct spline-interpolated cross section curves which give a good idea of the structure of the tube. For example, we show that, for the value of (mu) we use, the tube pinches, develops a self-intersection, develops loop-inside-tube structure, pinches some more, and so on. We also construct surfaces made of quadrilaterals and triangles from these cross-sections. The transversal planes are obtained by taking planes orthogonal to a curve that follows the general shape of the tube. One such curve we use, is the unstable invariant manifold of the equilibrium point L2 itself. In another example, we take a circle that follows the tube, as the curve for finding planes transversal to the tube. Our method is complementary to the method of taking cross-sections of constant time (the isochronous method), as used by some other researchers. The isochronous method is good at revealing the temporal structure of trajectories on a tube. However, due to the unequal speeds of different trajectories, it is harder to use for long length surface extraction. In contrast, using our method, we show cross-sections of the tube through an angular extent of nearly (pi) during which the tube becomes extremely convoluted. We also show that tubes of different energies, that start out in certain ordering, do not obey the ordering after a while. Our work is motivated by applications to space mission design.

invariant manifold↗

Aerodynamic Shape Optimization of a Dual-Stream Supersonic Plug Nozzle

Aerodynamic shape optimization was performed on an isolated axisymmetric plug nozzle sized for a supersonic business jet. The dual-stream concept was tailored to attenuate nearfield pressure disturbances without compromising nozzle performance. Adjoint-based anisotropic mesh refinement was applied to resolve nearfield compression and expansion features in the baseline viscous grid. Deformed versions of the adapted grid were used for subsequent adjoint-driven shape optimization. For design, a nonlinear gradient-based optimizer was coupled to the discrete adjoint formulation of the Reynolds-averaged Navier- Stokes equations. All nozzle surfaces were parameterized using 3rd order B-spline interpolants and perturbed axisymmetrically via free-form deformation. Geometry deformations were performed using 20 design variables shared between the outer cowl, shroud and centerbody nozzle surfaces. Interior volume grid deformation during design was accomplished using linear elastic mesh morphing. The nozzle optimization was performed at a design cruise speed of Mach 1.6, assuming core and bypass pressure ratios of 6.19 and 3.24, respectively. Ambient flight conditions at design were commensurate with 45,000-ft standard day atmosphere.

shape optimization↗

Intensity Conserving Spectral Fitting

The detailed shapes of spectral line profiles provide valuable information about the emitting plasma, especially when the plasma contains an unresolved mixture of velocities, temperatures, and densities. As a result of finite spectral resolution, the intensity measured by a spectrometer is the average intensity across a wavelength bin of non-zero size. It is assigned to the wavelength position at the center of the bin. However, the actual intensity at that discrete position will be different if the profile is curved, as it invariably is. Standard fitting routines (spline, Gaussian, etc.) do not account for this difference, and this can result in significant errors when making sensitive measurements. Detection of asymmetries in solar coronal emission lines is one example. Removal of line blends is another. We have developed an iterative procedure that corrects for this effect. It can be used with any fitting function, but we employ a cubic spline in a new analysis routine called Intensity Conserving Spline Interpolation (ICSI). As the name implies, it conserves the observed intensity within each wavelength bin, which ordinary fits do not. Given the rapid convergence, speed of computation, and ease of use, we suggest that ICSI be made a standard component of the processing pipeline for spectroscopic data.

Klimchuk, J. A.↗

Bistable Deployable Composite Booms With Parabolic Cross-Sections

This paper investigates how stable equilibrium states in the extended and coiled configurations can be predicted in thin-shelled composite booms with parabolic cross-sections. These conic shapes potentially offer greater stiffness properties when compared to circular cross-sections, which is critical for improving the load bearing performance of deployed booms. Inducing bistability through the choice of composite shell layups in parabolic booms would allow for controllable self-deployment due to a less energetic coiled state when compared to monostable booms. An inextensional analytical model is used to predict the stable coiled diameters of tape spring and Collapsible Tubular Mast (CTM) booms with parabolic cross-sections. The parabolic section is discretized into circular segments using biarc spline interpolation, which allows them to be integrated into the strain energy minimization procedure used to obtain the equilibrium states. When the parabolic booms are parametrically compared against circular booms with identical layups, flattened height, and mass, the former are found to generally have better stiffness performance while being less efficient in stowed volume as evidenced by larger coiled diameters. Analytical coiled diameters and their strain energy are verified with finite element simulations for optimal parabolic tape spring and CTM booms.

Andrew J. Lee↗

Trajectory Generation with Load Constraints for Robotic Manipulators

Future large spacecraft will utilize robotic manipulators for in-space servicing, assembly, and manufacturing. Due to launch mass constraints, such manipulators will be designed to be as lightweight as possible. Trajectory generation algorithms will need to factor in load constraints to avoid overexerting and damaging manipulators. This paper investigates an approach that combines optimal Rapidly-exploring Random Trees, spline interpolation, and Model Predictive Control to generate a manipulator trajectory which respects load constraints.

Manipulators↗

Development and application of a standardized flow measurement uncertainty analysis framework to various low-head short-converging intake types across the United States federal hydropower fleet

Turbine discharges at low-head short converging intakes are difficult to measure accurately. The proximity of the measurement section to the intake entrance admits large uncertainties related to asymmetry of the velocity profile, swirl, and turbulence. Existing turbine performance codes [10, 24] do not address this special case and published literature is largely silent on rigorous evaluation of uncertainties associated with this measurement context. The American Society of Mechanical Engineers (ASME) Committee investigated the use of Acoustic transit time (ATT), Acoustic scintillation (AS), and Current meter (CM) in a short converging intake at the Kootenay Canal Generating Station in 2009. Based on their findings, a standardized uncertainty analysis (UA) framework for velocity-area method (specifically for CM measurements) is presented in this paper given the fact that CM is still the most fundamental and common type of measurement system. Typical sources of systematic and random errors associated with CM measurements are investigated, and the major sources of uncertainties associated with turbulence and velocity fluctuations, numerical velocity integration technique (bi-cubic spline), and the number and placement of current meters are being considered for an evaluation. Since the velocity measurements in a short converging intake are associated with complex nonlinear and time varying uncertainties (e.g., Reynolds stress in fluid dynamics), simply applying the law of propagation of uncertainty is known to overestimate the measurement variance while the Monte Carlo method does not. Therefore, a pseudo-Monte Carlo simulation method (random flow generation technique [8]) which was initially developed for the purpose of establishing upstream or initial conditions in the Large-Eddy Simulation (LES) and the Direct Numerical Simulation (DNS) is used to statistically determine uncertainties associated with turbulence and velocity fluctuations. This technique is then combined with a bi-cubic spline interpolation method which converts point velocities into a continuous velocity distribution over the measurement domain. Subsequently the number and placement of current meters are simulated to investigate the accuracy of the estimated flow rates using the numerical velocity-area integration method outlined in ISO 3354 [12]. The authors herein consider that statistics on generated flow rates processed with bi-cubic interpolation and sensor simulations are the combined uncertainties which already accounted for the effects of all those three uncertainty sources. A preliminary analysis based on the current meter data obtained through an upgrade acceptance test of a single unit located in a mainstem plant has been presented.

Smith, Brennan T↗

Pulmonary lobe segmentation based on ridge surface sampling and shape model fitting

Purpose: Performing lobe-based quantitative analysis of the lung in computed tomography (CT) scans can assist in efforts to better characterize complex diseases such as chronic obstructive pulmonary disease (COPD). While airways and vessels can help to indicate the location of lobe boundaries, segmentations of these structures are not always available, so methods to define the lobes in the absence of these structures are desirable. Methods: The authors present a fully automatic lung lobe segmentation algorithm that is effective in volumetric inspiratory and expiratory computed tomography (CT) datasets. The authors rely on ridge surface image features indicating fissure locations and a novel approach to modeling shape variation in the surfaces defining the lobe boundaries. The authors employ a particle system that efficiently samples ridge surfaces in the image domain and provides a set of candidate fissure locations based on the Hessian matrix. Following this, lobe boundary shape models generated from principal component analysis (PCA) are fit to the particles data to discriminate between fissure and nonfissure candidates. The resulting set of particle points are used to fit thin plate spline (TPS) interpolating surfaces to form the final boundaries between the lung lobes. Results: The authors tested algorithm performance on 50 inspiratory and 50 expiratory CT scans taken from the COPDGene study. Results indicate that the authors' algorithm performs comparably to pulmonologist-generated lung lobe segmentations and can produce good results in cases with accessory fissures, incomplete fissures, advanced emphysema, and low dose acquisition protocols. Dice scores indicate that only 29 out of 500 (5.85%) lobes showed Dice scores lower than 0.9. Two different approaches for evaluating lobe boundary surface discrepancies were applied and indicate that algorithm boundary identification is most accurate in the vicinity of fissures detectable on CT. Conclusions: The proposed algorithm is effective for lung lobe segmentation in absence of auxiliary structures such as vessels and airways. The most challenging cases are those with mostly incomplete, absent, or near-absent fissures and in cases with poorly revealed fissures due to high image noise. However, the authors observe good performance even in the majority of these cases.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

SU-F-T-315: Comparative Studies of Planar Dose with Different Spatial Resolution for Head and Neck IMRT QA

Purpose: To quantitatively investigate the planar dose difference and the γ value between the reference fluence map with the 1 mm detector-to-detector distance and the other fluence maps with less spatial resolution for head and neck intensity modulated radiation (IMRT) therapy. Methods: For ten head and neck cancer patients, the IMRT quality assurance (QA) beams were generated using by the commercial radiation treatment planning system, Pinnacle3 (ver. 8.0.d Philips Medical System, Madison, WI). For each beam, ten fluence maps (detector-to-detector distance: 1 mm to 10 mm by 1 mm) were generated. The fluence maps with larger than 1 mm detector-todetector distance were interpolated using MATLAB (R2014a, the Math Works,Natick, MA) by four different interpolation Methods: for the bilinear, the cubic spline, the bicubic, and the nearest neighbor interpolation, respectively. These interpolated fluence maps were compared with the reference one using the γ value (criteria: 3%, 3 mm) and the relative dose difference. Results: As the detector-to-detector distance increases, the dose difference between the two maps increases. For the fluence map with the same resolution, the cubic spline interpolation and the bicubic interpolation are almost equally best interpolation methods while the nearest neighbor interpolation is the worst.For example, for 5 mm distance fluence maps, γ≤1 are 98.12±2.28%, 99.48±0.66%, 99.45±0.65% and 82.23±0.48% for the bilinear, the cubic spline, the bicubic, and the nearest neighbor interpolation, respectively. For 7 mm distance fluence maps, γ≤1 are 90.87±5.91%, 90.22±6.95%, 91.79±5.97% and 71.93±4.92 for the bilinear, the cubic spline, the bicubic, and the nearest neighbor interpolation, respectively. Conclusion: We recommend that the 2-dimensional detector array with high spatial resolution should be used as an IMRT QA tool and that the measured fluence maps should be interpolated using by the cubic spline interpolation or the bicubic interpolation for head and neck IMRT delivery. This work was supported by Radiation Technology R&D program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning (No. 2013M2A2A7038291)

60 APPLIED LIFE SCIENCES↗