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NASA NTRS1992

Improved accuracy for finite element structural analysis via a new integrated force method

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

Patnaik, Surya N.↗

NASA NTRS1992

Improved accuracy for finite element structural analysis via an integrated force method

Patnaik, S. N.↗

NASA NTRS1995

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Vanel, Florence O.↗

NASA NTRS1996

Further evaluation of traditional icing scaling methods

This report provides additional evaluations of two methods to scale icing test conditions; it also describes a hybrid technique for use when scaled conditions are outside the operating envelope of the test facility. The first evaluation is of the Olsen method which can be used to scale the liquid-water content in icing tests, and the second is the AEDC (Ruff) method which is used when the test model is less than full size. Equations for both scaling methods are presented in the paper, and the methods were evaluated by performing icing tests in the NASA Lewis Icing Research Tunnel (IRT). The Olsen method was tested using 53 cm diameter NACA 0012 airfoils. Tests covered liquid-water-contents which varied by as much as a factor of 1.8. The Olsen method was generally effective in giving scale ice shapes which matched the reference shapes for these tests. The AEDC method was tested with NACA 0012 airfoils with chords from 18 cm to 53 cm. The 53 cm chord airfoils were used in reference tests, and 1/2 and 1/3 scale tests were made at conditions determined by applying the AEDC scaling method. The scale and reference airspeeds were matched in these tests. The AEDC method was found to provide fairly effective scaling for 1/2 size tests, but for 1/3 size models, scaling was generally less effective. In addition to these two scaling methods, a hybrid approach was also tested in which the Olsen method was used to adjust the LWC after size was scaled using the constant Weber number method. This approach was found to be an effective way to test when scaled conditions would otherwise be outside the capability of the test facility.

Anderson, David N.↗

NASA NTRS1997

Modified Fully Utilized Design (MFUD) Method for Stress and Displacement Constraints

The traditional fully stressed method performs satisfactorily for stress-limited structural design. When this method is extended to include displacement limitations in addition to stress constraints, it is known as the fully utilized design (FUD). Typically, the FUD produces an overdesign, which is the primary limitation of this otherwise elegant method. We have modified FUD in an attempt to alleviate the limitation. This new method, called the modified fully utilized design (MFUD) method, has been tested successfully on a number of designs that were subjected to multiple loads and had both stress and displacement constraints. The solutions obtained with MFUD compare favorably with the optimum results that can be generated by using nonlinear mathematical programming techniques. The MFUD method appears to have alleviated the overdesign condition and offers the simplicity of a direct, fully stressed type of design method that is distinctly different from optimization and optimality criteria formulations. The MFUD method is being developed for practicing engineers who favor traditional design methods rather than methods based on advanced calculus and nonlinear mathematical programming techniques. The Integrated Force Method (IFM) was found to be the appropriate analysis tool in the development of the MFUD method. In this paper, the MFUD method and its optimality are presented along with a number of illustrative examples.

Patnaik, Surya↗

NASA NTRS2019

Bounding Methods for Heterogeneous Lidar-derived Navigational Geofences

Safe Unmanned Aerial Vehicle (UAV) operations near the ground require navigation methods that avoid fixed obstacles such as buildings, power lines and trees. Aerial lidar surveys of ground structures are available with the precision and accuracy to geolocate obstacles, but the high volume of raw survey data can exceed the compute power of onboard processors and the rendering ability of ground-based flight planning maps. Representing ground structures with bounding polyhedra instead of point clouds greatly reduces the data size and can enable effective obstacle avoidance, as long as the bounding geometry envelopes the structures with high spatial fidelity. This report describes in detail four methods to compute bounding geometries of ground obstacles from lidar point clouds. The four methods are: 1) 2.5D Maximum Elevation Box, 2) 2.5D Ground Map Extrusion, 3) 3D Bounding Cylinder, and 4) 3D Bounding Box. The methods are applied to five point cloud datasets from lidar surveys of UAV flight research sites in Georgia and Virginia with an average point spacing that ranges from 0.1m to 0.6m. The methods are assessed using survey areas with geometrically heterogeneous ground structures: buildings, vegetation, power lines, and sub-meter structures such as road signs and guy wires. The 2.5D Maximum Elevation Box method is useful for simple structures. The 2.5D Ground Map Extrusion method efficiently encloses vegetation, but requires handdrawn ground footprints. The 3D Bounding Cylinder method excels at enclosing linear structures such as power lines and fences. The 3D Bounding Box method excels at enclosing planar structures such as buildings. The methods are compared on the basis of data compression and boundary fidelity on selected areas. The 2.5D methods yield the highest data compression but the polyhedra produced by them enclose significant amounts of empty space. Boundary fidelity is superior for the 3D methods, though this fidelity comes at the cost of a roughly thirtyfold lower data compression ratio than the 2.5D Maximum Elevation Box method. A mix of these output geometries is proposed for autonomous UAV navigation with limited on-board computing. Both the accuracy and spatial detail of emerging satellite-based survey technology lower than that of aerial lidar scanning survey technology. Sub-meter structures and thin linear structures are not reliably mapped at present by satellite-based surveys.

Moore, Andrew J.↗

NASA NTRS1973

A study of methods which predict supersonic flow fields from body geometry, distance, and Mach number

A study of seven methods for predicting flow-field pressure signatures from the parameters Mach number, body geometry, and field-path distance has been made. The methods included the method of characteristics, which served as a standard of comparison; a shock-capturing method; three Whitham theory methods; a modified characteristics method; and a bicharacteristics method. Results from each method were also compared with recently obtained wind-tunnel data for a cone-cylinder model at Mach numbers of 2.96 and 4.63 with ratios of radial distance to cone length of 2 and 5. The comparisons at a Mach number of 2.96 showed that signatures from all the methods correlated well with wind-tunnel data and with the signatures predicted by the method of characteristics. At a Mach number of 4.63, however, the agreement between the signatures obtained in the wind tunnel and those predicted by theory varied from good to poor, as did the agreement between the signatures obtained by the method of characteristics and the other six methods. It should be noted that these results and comparisons indicate pressure prediction capabilities only for the near-field flow about bodies of revolution.

Mack, R. J.↗

NASA NTRS1989

High-frequency asymptotic methods for analyzing the EM scattering by open-ended waveguide cavities

Four high-frequency methods are described for analyzing the electromagnetic (EM) scattering by electrically large open-ended cavities. They are: (1) a hybrid combination of waveguide modal analysis and high-frequency asymptotics, (2) geometrical optics (GO) ray shooting, (3) Gaussian beam (GB) shooting, and (4) the generalized ray expansion (GRE) method. The hybrid modal method gives very accurate results but is limited to cavities which are made up of sections of uniform waveguides for which the modal fields are known. The GO ray shooting method can be applied to much more arbitrary cavity geometries and can handle absorber treated interior walls, but it generally only predicts the major trends of the RCS pattern and not the details. Also, a very large number of rays need to be tracked for each new incidence angle. Like the GO ray shooting method, the GB shooting method can handle more arbitrary cavities, but it is much more efficient and generally more accurate than the GO method because it includes the fields diffracted by the rim at the open end which enter the cavity. However, due to beam divergence effects the GB method is limited to cavities which are not very long compared to their width. The GRE method overcomes the length-to-width limitation of the GB method by replacing the GB's with GO ray tubes which are launched in the same manner as the GB's to include the interior rim diffracted field. This method gives good accuracy and is generally more efficient than the GO method, but a large number of ray tubes needs to be tracked.

Burkholder, R. J.↗

NASA NTRS1991

Comparison of advanced reduced-basis methods for transient structural analysis

Two advanced reduced-basis methods for linear, transient structural analysis, the force-derivative method and the Lanczos method, are compared to two widely-used modal methods, the mode-displacement method and the mode-acceleration method. Comparisons are made for two linear example problems: a proportionally-damped cantilevered beam subject to a discrete tip load which varies linearly with time, and a discretely-damped multispan beam subject to a uniformly distributed load which varies as a quintic function of time. Results from the methods are compared in terms of the number of basis vectors required to obtain a desired level of accuracy and the associated computational times. The results are problem dependent, and it is shown that for the cantilevered beam problem, the mode-acceleration and force-derivative methods are the most efficient in terms of the number of basis vectors and computational time. The force-derivative method is shown to be the most effective method for solving the multispan beam problem with closely-spaced frequencies. In general, the force-derivative method is shown to produce an accurate solution using very few basis vectors and to require less computational time as compared to the other methods studied.

Mcgowan, David M.↗

NASA NTRS1994

Spectral Methods for Computational Fluid Dynamics

As a tool for large-scale computations in fluid dynamics, spectral methods were prophesized in 1944, born in 1954, virtually buried in the mid-1960's, resurrected in 1969, evangalized in the 1970's, and catholicized in the 1980's. The use of spectral methods for meteorological problems was proposed by Blinova in 1944 and the first numerical computations were conducted by Silberman (1954). By the early 1960's computers had achieved sufficient power to permit calculations with hundreds of degrees of freedom. For problems of this size the traditional way of computing the nonlinear terms in spectral methods was expensive compared with finite-difference methods. Consequently, spectral methods fell out of favor. The expense of computing nonlinear terms remained a severe drawback until Orszag (1969) and Eliasen, Machenauer, and Rasmussen (1970) developed the transform methods that still form the backbone of many large-scale spectral computations. The original proselytes of spectral methods were meteorologists involved in global weather modeling and fluid dynamicists investigating isotropic turbulence. The converts who were inspired by the successes of these pioneers remained, for the most part, confined to these and closely related fields throughout the 1970's. During that decade spectral methods appeared to be well-suited only for problems governed by ordinary diSerential eqllations or by partial differential equations with periodic boundary conditions. And, of course, the solution itself needed to be smooth. Some of the obstacles to wider application of spectral methods were: (1) poor resolution of discontinuous solutions; (2) inefficient implementation of implicit methods; and (3) drastic geometric constraints. All of these barriers have undergone some erosion during the 1980's, particularly the latter two. As a result, the applicability and appeal of spectral methods for computational fluid dynamics has broadened considerably. The motivation for the use of spectral methods in numerical calculations stems from the attractive approximation properties of orthogonal polynomial expansions.

Zang, T. A.↗

NASA NTRS1996

Multigrid Methods for EHL Problems

In many bearings and contacts, forces are transmitted through thin continuous fluid films which separate two contacting elements. Objects in contact are normally subjected to friction and wear which can be reduced effectively by using lubricants. If the lubricant film is sufficiently thin to prevent the opposing solids from coming into contact and carries the entire load, then we have hydrodynamic lubrication, where the lubricant film is determined by the motion and geometry of the solids. However, for loaded contacts of low geometrical conformity, such as gears, rolling contact bearings and cams, this is not the case due to high pressures and this is referred to as Elasto-Hydrodynamic Lubrication (EHL) In EHL, elastic deformation of the contacting elements and the increase in fluid viscosity with pressure are very significant and cannot be ignored. Since the deformation results in changing the geometry of the lubricating film, which in turn determines the pressure distribution, an EHL mathematical model must simultaneously satisfy the complex elasticity (integral) and the Reynolds lubrication (differential) equations. The nonlinear and coupled nature of the two equations makes numerical calculations computationally intensive. This is especially true for highly loaded problems found in practice. One novel feature of these problems is that the solution may exhibit sharp pressure spikes in the outlet region. To this date both finite element and finite difference methods have been used to solve EHL problems with perhaps greater emphasis on the use of the finite difference approach. In both cases, a major computational difficulty is ensuring convergence of the nonlinear equations solver to a steady state solution. Two successful methods for achieving this are direct iteration and multigrid methods. Direct iteration methods (e.g Gauss Seidel) have long been used in conjunction with finite difference discretizations on regular meshes. Perhaps one of the best examples of the application of such methods is the recent Effective Influence Method of Dowson and Wang. Multigrid methods have also been used with great success by Venner and Venner and Lubrecht with a good summary being given by Venner. As both these finite difference discretization based approaches appear to provide an efficient way of solving EHL problems, it is important to understand their relative merits. This paper is a first attempt at providing such an understanding in the context of EHL point contact problem, (contact of two spheres), in which the contact zone is a point and an ellipse or circle for unloaded and loaded dry contacts respectively. Since the film thickness and the contact width are generally small compared to the local radius of curvature of the two surfaces, the reduced geometry of the surfaces in the contact area can be accurately approximated to the contact between a paraboloid and a flat surface. The layout of the remainder of this paper is as follows. In section 2 we introduce the form of the equations to be solved. The Effective Influence Newton Method is described in Section 3 while Section 4 describes the Multigrid method to be used. Sections 5 and 6 describe the test problems to be used in the comparison between the two methods and compare the performance of the two methods. Section 7 concludes the paper with an argument of the two methods and suggests some future research directions.

Nurgat, Elyas↗

NASA NTRS2001

Multifunctional Collaborative Modeling and Analysis Methods in Engineering Science

Engineers are challenged to produce better designs in less time and for less cost. Hence, to investigate novel and revolutionary design concepts, accurate, high-fidelity results must be assimilated rapidly into the design, analysis, and simulation process. This assimilation should consider diverse mathematical modeling and multi-discipline interactions necessitated by concepts exploiting advanced materials and structures. Integrated high-fidelity methods with diverse engineering applications provide the enabling technologies to assimilate these high-fidelity, multi-disciplinary results rapidly at an early stage in the design. These integrated methods must be multifunctional, collaborative, and applicable to the general field of engineering science and mechanics. Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple-method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized. The multifunctional methodology presented provides an effective mechanism by which domains with diverse idealizations are interfaced. This capability rapidly provides the high-fidelity results needed in the early design phase. Moreover, the capability is applicable to the general field of engineering science and mechanics. Hence, it provides a collaborative capability that accounts for interactions among engineering analysis methods.

Ransom, Jonathan B.↗

NASA NTRS2003

Structural Reliability Using Probability Density Estimation Methods Within NESSUS

A reliability analysis studies a mathematical model of a physical system taking into account uncertainties of design variables and common results are estimations of a response density, which also implies estimations of its parameters. Some common density parameters include the mean value, the standard deviation, and specific percentile(s) of the response, which are measures of central tendency, variation, and probability regions, respectively. Reliability analyses are important since the results can lead to different designs by calculating the probability of observing safe responses in each of the proposed designs. All of this is done at the expense of added computational time as compared to a single deterministic analysis which will result in one value of the response out of many that make up the density of the response. Sampling methods, such as monte carlo (MC) and latin hypercube sampling (LHS), can be used to perform reliability analyses and can compute nonlinear response density parameters even if the response is dependent on many random variables. Hence, both methods are very robust; however, they are computationally expensive to use in the estimation of the response density parameters. Both methods are 2 of 13 stochastic methods that are contained within the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) program. NESSUS is a probabilistic finite element analysis (FEA) program that was developed through funding from NASA Glenn Research Center (GRC). It has the additional capability of being linked to other analysis programs; therefore, probabilistic fluid dynamics, fracture mechanics, and heat transfer are only a few of what is possible with this software. The LHS method is the newest addition to the stochastic methods within NESSUS. Part of this work was to enhance NESSUS with the LHS method. The new LHS module is complete, has been successfully integrated with NESSUS, and been used to study four different test cases that have been proposed by the Society of Automotive Engineers (SAE). The test cases compare different probabilistic methods within NESSUS because it is important that a user can have confidence that estimates of stochastic parameters of a response will be within an acceptable error limit. For each response, the mean, standard deviation, and 0.99 percentile, are repeatedly estimated which allows confidence statements to be made for each parameter estimated, and for each method. Thus, the ability of several stochastic methods to efficiently and accurately estimate density parameters is compared using four valid test cases. While all of the reliability methods used performed quite well, for the new LHS module within NESSUS it was found that it had a lower estimation error than MC when they were used to estimate the mean, standard deviation, and 0.99 percentile of the four different stochastic responses. Also, LHS required a smaller amount of calculations to obtain low error answers with a high amount of confidence than MC. It can therefore be stated that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ and the newest LHS module is a valuable new enhancement of the program.

Chamis, Chrisos C.↗

NASA NTRS2004

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Shu, Chi-Wang↗

NASA NTRS2010

A GPS-Based Pitot-Static Calibration Method Using Global Output-Error Optimization

Pressure-based airspeed and altitude measurements for aircraft typically require calibration of the installed system to account for pressure sensing errors such as those due to local flow field effects. In some cases, calibration is used to meet requirements such as those specified in Federal Aviation Regulation Part 25. Several methods are used for in-flight pitot-static calibration including tower fly-by, pacer aircraft, and trailing cone methods. In the 1990 s, the introduction of satellite-based positioning systems to the civilian market enabled new inflight calibration methods based on accurate ground speed measurements provided by Global Positioning Systems (GPS). Use of GPS for airspeed calibration has many advantages such as accuracy, ease of portability (e.g. hand-held) and the flexibility of operating in airspace without the limitations of test range boundaries or ground telemetry support. The current research was motivated by the need for a rapid and statistically accurate method for in-flight calibration of pitot-static systems for remotely piloted, dynamically-scaled research aircraft. Current calibration methods were deemed not practical for this application because of confined test range size and limited flight time available for each sortie. A method was developed that uses high data rate measurements of static and total pressure, and GPSbased ground speed measurements to compute the pressure errors over a range of airspeed. The novel application of this approach is the use of system identification methods that rapidly compute optimal pressure error models with defined confidence intervals in nearreal time. This method has been demonstrated in flight tests and has shown 2- bounds of approximately 0.2 kts with an order of magnitude reduction in test time over other methods. As part of this experiment, a unique database of wind measurements was acquired concurrently with the flight experiments, for the purpose of experimental validation of the optimization method. This paper describes the GPS-based pitot-static calibration method developed for the AirSTAR research test-bed operated as part of the Integrated Resilient Aircraft Controls (IRAC) project in the NASA Aviation Safety Program (AvSP). A description of the method will be provided and results from recent flight tests will be shown to illustrate the performance and advantages of this approach. Discussion of maneuver requirements and data reduction will be included as well as potential applications.

Foster, John V.↗

NASA NTRS2024

SMAnalytics Automated Shape Memory Test Analysis Software User's Manual: UCFTC, UPER, and DSC Test Methods, Version 1.0.2

Over the course of 60 years of shape memory alloy research and development, the properties of these alloys have been measured using various testing methods, which are often customized by the organization performing the test. However, commercial adoption of shape memory alloys in aeronautic actuator applications requires reducing property uncertainty through standardizing test methods. Historically, differential scanning calorimetry (DSC) has been used to measure transformation temperatures under stress-free conditions. This testing method is well established, and tests are run under the applicable standard, ASTM F2004-17: Standard Test Method for Transformation Temperature of Nickel-Titanium Alloys by Thermal Analysis. Two other test methods for measuring strains and transformation temperatures under constant load or free recovery after prestraining have only recently been standardized—ASTM E3097: Standard Test Method for Mechanical Uniaxial Constant Force Thermal Cycling of SMAs (UCFTC) and ASTM E3098: Standard Test Method for Mechanical Uniaxial Pre-Strain and Thermal Free Recovery of SMAs (UPFR). These standards represent a critical step forward in producing reliable material property data for the use of these alloys in aeronautics and other commercial areas. However, no standard programs or software packages were previously available for postprocessing UCFTC- and UPFR-type test data to extract property data. Each organization that performed the testing analyzed data using its own custom manual methods, such as using a plot and a straight edge, spreadsheet plotting methods, or custom code routines, to extract the required values for strains, stresses, and transformation temperatures. SMAnalytics represents the first publicly available uniform software package for processing data generated using the DSC, UCFTC, and UPFR test methods, as well as many modifications of these methods, including loading in martensite versus austenite and performing multiple thermal cycles at stress. In doing so, it provides a tool for reducing potential error or variability in the measured values due to the precision of the technique used and person-to-person variability. It is also expected that this automated data-parsing tool can accelerate the data analysis phase of the test campaign, especially for large data files. This User’s Manual describes how the SMAnalytics software works and the method for its use.

Shape Memory Alloy↗

NASA NTRS1973

An historical survey of computational methods in optimal control.

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

Polak, E.↗

NASA NTRS1987

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

Three explicit multigrid methods, Ni's method, Jameson's finite-volume method, and a finite-difference method based on Brandt's work, are described and compared for two model problems. All three methods use an explicit multistage Runge-Kutta scheme on the fine grid, and this scheme is also described. Convergence histories for inviscid flow over a bump in a channel for the fine-grid scheme alone show that convergence rate is proportional to Courant number and that implicit residual smoothing can significantly accelerate the scheme. Ni's method was slightly slower than the implicitly-smoothed scheme alone. Brandt's and Jameson's methods are shown to be equivalent in form but differ in their node versus cell-centered implementations. They are about 8.5 times faster than Ni's method in terms of CPU time. Results for an oblique shock/boundary layer interaction problem verify the accuracy of the finite-difference code. All methods slowed considerably on the stretched viscous grid but Brandt's method was still 2.1 times faster than Ni's method.

Chima, Rodrick V.↗