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NASA NTRS1990

Mathematical theory of a relaxed design problem in structural optimization

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Kikuchi, Noboru↗

NASA NTRS1972

Computer analysis of two-dimensional fatigue flaw-growth problems

A description is given of a computer program for analyzing the crack propagation in cyclic loaded structures. By using equations for the stress intensity factors for surface and embedded flaws, the capability of ascertaining lengthwise crack growth as well as crack growth through the thickness of the structure was determined. Equations used are written in general form so that many other types of crack growth problems, such as through the thickness type cracks, can be analyzed. Provisions have been made in the computer program to analyze crack growth for repeated blocks of variable-amplitude fatigue load spectra. Additional features of the computer program include a variable print interval and a variable integration interval to minimize computer printout and computer run time. A source listing and instructions for using the computer program are included.

Forman, R. G.↗

NASA NTRS1970

New Jacobi-type necessary and sufficient conditions for singular optimization problems

Jacobi conditions for singular optimization problems by transforming singular accessory minimum problem into nonclassical nonsingular form, considering optimal control theory applicability

Mcdanell, J. P.↗

NASA NTRS2009

Direct Multiple Shooting Optimization with Variable Problem Parameters

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

Whitley, Ryan J.↗

NASA NTRS1992

A comparison of chromic acid and sulfuric acid anodizing

Because of federal and state mandates restricting the use of hexavalent chromium, it was deemed worthwhile to compare the corrosion protection afforded 2219-T87 aluminum alloy by both Type I chromic acid and Type II sulfuric acid anodizing per MIL-A-8625. Corrosion measurements were made on large, flat 2219-T87 aluminum alloy sheet material with an area of 1 cm(exp 2) exposed to a corrosive medium of 3.5-percent sodium chloride at pH 5.5. Both ac electrochemical impedance spectroscopy and the dc polarization resistance techniques were employed. The results clearly indicate that the corrosion protection obtained by Type II sulfuric acid anodizing is superior, and no problems should result by substituting Type II sulfuric acid anodizing for Type I chromic acid anodizing.

Danford, M. D.↗

NASA NTRS1993

Classification of simple vegetation types using POLSAR image data

Mapping basic vegetation or land cover types is a fairly common problem in remote sensing. Knowledge of the land cover type is a key input to algorithms which estimate geophysical parameters, such as soil moisture, surface roughness, leaf area index or biomass from remotely sensed data. In an earlier paper, an algorithm for fitting a simple three-component scattering model to POLSAR data was presented. The algorithm yielded estimates for surface scatter, double-bounce scatter and volume scatter for each pixel in a POLSAR image data set. In this paper, we show how the relative levels of each of the three components can be used as inputs to simple classifier for vegetation type. Vegetation classes include no vegetation cover (e.g. bare soil or desert), low vegetation cover (e.g. grassland), moderate vegetation cover (e.g. fully developed crops), forest and urban areas. Implementation of the approach requires estimates for the three components from all three frequencies available using the NASA/JPL AIRSAR, i.e. C-, L- and P-bands. The research described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration.

Freeman, A.↗

NASA NTRS1993

Classification of Simple Vegetation Types Using POLSAR Image Data

Freeman, A.↗

NASA NTRS1975

Adiabatic invariants and phase equilibria for first-order orbital resonances

In the planar circular restricted three-body problem, the evolution of near-commensurable orbits is studied under change in the mass ratio, mu. The evolution involves preservation of two adiabatic invariants. Transition from circulation to libration may occur; such transitions are of two types. Type I transition occurs when the evolutionary track in phase space passes through near-zero eccentricity; as in the ordinary case (no transition), pre- and post-evolutionary states are linked by solution of a two-point boundary-value problem. Type II transition occurs when the evolutionary track encounters an unstable phase equilibrium or periodic orbit. There is then a discontinuous change in one adiabatic invariant, and pre- and post-evolutionary states are linked by solution of a three-point boundary-value problem. No evolutionary track can encounter a stable phase equilibrium, but the class of all stable phase equilibria is mapped into itself under mu change.

Heppenheimer, T. A.↗

NASA NTRS2002

Partnership and the Revitalization of Aviation: A Study of the Advanced General Aviation Transport Experiments Program, 1994-2001

As the Advanced General Aviation Transport Experiments (AGATE) program completes its eight-year plan, the outcomes and industry effects reveal its successes and problems. AGATE engaged several different types of institutions, including federal agencies, business and industry, universities, and non-profit organizations. By examining the perceptions of those intimately involved as well as periphery members, this study shows the powerful consequences of this type of combination both now and in the future. The problems are a particularly useful illustration of the interworking of a jointly funded research and development initiative. By learning how these problems are addressed, the study reveals lessons that may be applied to future government-industry partnerships.

Metz, Nanette Scarpellini↗

NASA NTRS2009

Kurtosis Approach to Solution of a Nonlinear ICA Problem

An algorithm for solving a particular nonlinear independent-component-analysis (ICA) problem, that differs from prior algorithms for solving the same problem, has been devised. The problem in question of a type known in the art as a post nonlinear mixing problem is a useful approximation of the problem posed by the mixing and subsequent nonlinear distortion of sensory signals that occur in diverse scientific and engineering instrumentation systems.

Duong, Vu↗

NASA NTRS1963

Vehicle Design for Mars Landing and Return to Mars Orbit

This paper briefly describes three modes for accomplishing the Mars landing mission and compares them on a gross basis to indicate their probable order of merit and to identify design requirements placed on the Mars-excursion module (MEM) by the choice of mode. The paper shows that a flyby-rendezvous mode requiring low weight in earth orbit requires the MEM to enter the Mars atmosphere at velocities ranging from 20,000 to 30,000 ft/sec. The MEM for the flyby-rendezvous mode is not covered in this paper but merits further study. The MEM for the other modes of mission accomplishment begins its active operational sequence in Mars orbit and need not be greatly influenced by the method of delivery to Mars orbit. Parametric studies of the entry problem for two vehicles typifying a ballistic-type and a lifting-body-type were conducted to identify the problems associated with design of a MEM to accommodate the extremes of Mars atmospheric density presently predicted. This brief study indicates that: (a) the presently predicted density extremes of the Mars atmosphere present no serious design problems for a MEM which can operate across the entire band of predicted densities; (b) details of operational requirements and mission objectives will control the choice of configuration rather than entry requirements; and (c) the ballistic-type MEM is lighter and simpler but has less operational flexibility than a high L/D MEM.

Hammock, D. M.↗

NASA NTRS2003

Enhancing and Archiving the APS Catalog of the POSS I

We have worked on two different projects: 1) Archiving the APS Catalog of the POSS I for distribution to NASA's NED at IPAC, SIMBAD in France, and individual astronomers and 2) The automated morphological classification of galaxies. We have completed archiving the Catalog into easily readable binary files. The database together with the software to read it has been distributed on DVD's to the national and international data centers and to individual astronomers. The archived Catalog contains more than 89 million objects in 632 fields in the first epoch Palomar Observatory Sky Survey. Additional image parameters not available in the original on-line version are also included in the archived version. The archived Catalog is also available and can be queried at the APS web site (URL: http://aps.umn.edu) which has been improved with a much faster and more efficient querying system. The Catalog can be downloaded as binary datafiles with the source code for reading it. It is also being integrated into the SkyQuery system which includes the Sloan Digital Sky Survey, 2MASS, and the FIRST radio sky survey. We experimented with different classification algorithms to automate the morphological classification of galaxies. This is an especially difficult problem because there are not only a large number of attributes or parameters and measurement uncertainties, but also the added complication of human disagreement about the adopted types. To solve this problem we used 837 galaxy images from nine POSS I fields at the North Galactic Pole classified by two independent astronomers for which they agree on the morphological types. The initial goal was to separate the galaxies into the three broad classes relevant to issues of large scale structure and galaxy formation and evolution: early (ellipticals and lenticulars), spirals, and late (irregulars) with an accuracy or success rate that rivals the best astronomer classifiers. We also needed to identify a set of parameters derived from the digitized images that separate the galaxies by type. The human eye can easily recognize complicated patterns in images such as spiral arms which can be spotty, blotchy affairs that are difficult for automated techniques. A galaxy image can potentially be described by hundreds of parameters, all of which may have some relation to the morphological type. In the set of initial experiments we used 624 such parameters, in two colors, blue and red. These parameters include the surface brightness and color measured at different radii, ratios of these parameters at different radii, concentration indices, Fourier transforms and wavelet decomposition coefficients. We experimented with three different classes of classification algorithms; decision trees, k-nearest neighbors, and support vector machines (SVM). A range of experiments were conducted and we eventually narrowed the parameters to 23 selected parameters. SVM consistently outperformed the other algorithms with both sets of features. By combining the results from the different algorithms in a weighted scheme we achieved an overall classification success of 86%.

Humphreys, Roberta M.↗

NASA NTRS1986

An isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry

High-order (p-type) finite element methods combine the geometric flexibility of standard low-order finite element (or finite volume) techniques with the rapid convergence properties of spectral methods. Various p-type schemes have been proposed for elliptic problems. However, an application of p-type methods to more complex equations, in particular the passive scalar or Navier-Stokes equations, is complicated by the nature of the equations and by efficiency considerations as regards the solution procedure. Patera (1984) has proposed a p-type method for the Navier-Stokes equations, taking into account the arising additional complications. The present study is concerned with an isoparametric spectral element discretization for the solution of flow problems in fully general, curvy geometries. Attention is given to the isoparametric formulation for elliptic equations and a time-splitting scheme for the Navier-Stokes equations.

Korczak, K. Z.↗

NASA NTRS1972

Time-dependent Structural Analysis of Metal-epoxy Composites

In an effort to reduce structural weight while maintaining structural integrity on the space shuttle and other proposed space vehicles, various composite materials are being evaluated to determine their applicability and reliability in load carrying situations. While most of the composites being considered for structural components are of the metal-metal type, there are some applications for which metal-epoxy composites are proposed. An approximate method is presented to analyze plane stress orthotropic linear viscoelastic problems under isothermal conditions. A computer program which is based on the method was used to solve a simple uniaxial creep problem for a Maxwell type material. This solution is presented and compared with the analytical solution.

Dehoff, P. H.↗

NASA NTRS1986

Some design constraints required for the use of generic software in embedded systems: Packages which manage abstract dynamic structures without the need for garbage collection

The embedded systems running real-time applications, for which Ada was designed, require their own mechanisms for the management of dynamically allocated storage. There is a need for packages which manage their own internalo structures to control their deallocation as well, due to the performance implications of garbage collection by the KAPSE. This places a requirement upon the design of generic packages which manage generically structured private types built-up from application-defined input types. These kinds of generic packages should figure greatly in the development of lower-level software such as operating systems, schedulers, controllers, and device driver; and will manage structures such as queues, stacks, link-lists, files, and binary multary (hierarchical) trees. Controlled to prevent inadvertent de-designation of dynamic elements, which is implicit in the assignment operation A study was made of the use of limited private type, in solving the problems of controlling the accumulation of anonymous, detached objects in running systems. The use of deallocator prodecures for run-down of application-defined input types during deallocation operations during satellites.

Johnson, Charles S.↗

NASA NTRS1989

A review of some problems in global-local stress analysis

The various types of local-global finite-element problems point out the need to develop a new generation of software. First, this new software needs to have a complete analysis capability, encompassing linear and nonlinear analysis of 1-, 2-, and 3-dimensional finite-element models, as well as mixed dimensional models. The software must be capable of treating static and dynamic (vibration and transient response) problems, including the stability effects of initial stress, and the software should be able to treat both elastic and elasto-plastic materials. The software should carry a set of optional diagnostics to assist the program user during model generation in order to help avoid obvious structural modeling errors. In addition, the program software should be well documented so the user has a complete technical reference for each type of element contained in the program library, including information on such topics as the type of numerical integration, use of underintegration, and inclusion of incompatible modes, etc. Some packaged information should also be available to assist the user in building mixed-dimensional models. An important advancement in finite-element software should be in the development of program modularity, so that the user can select from a menu various basic operations in matrix structural analysis.

Nelson, Richard B.↗

NASA NTRS1995

Completed Beltrami-Michell formulation for analyzing mixed boundary value problems in elasticity

In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation (BMF). The existing BMF can only solve stress boundary value problems; it cannot handle the more prevalent displacement of mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier's displacement method, which can solve all three types of boundary value problems. The restrictions in the BMF have been alleviated by augmenting the classical formulation with a novel set of conditions identified as the boundary compatibility conditions. This new method, which completes the classical force formulation, has been termed the completed Beltrami-Michell formulation (CBMF). The CBMF can solve general elasticity problems with stress, displacement, and mixed boundary conditions in terms of stresses as the primary unknowns. The CBMF is derived from the stationary condition of the variational functional of the integrated force method. In the CBMF, stresses for kinematically stable structures can be obtained without any reference to the displacements either in the field or on the boundary. This paper presents the CBMF and its derivation from the variational functional of the integrated force method. Several examples are presented to demonstrate the applicability of the completed formulation for analyzing mixed boundary value problems under thermomechanical loads. Selected example problems include a cylindrical shell wherein membrane and bending responses are coupled, and a composite circular plate.

Patnaik, Surya N.↗

NASA NTRS2014

Phase Transitions in Planning Problems: Design and Analysis of Parameterized Families of Hard Planning Problems

There are two common ways to evaluate algorithms: performance on benchmark problems derived from real applications and analysis of performance on parametrized families of problems. The two approaches complement each other, each having its advantages and disadvantages. The planning community has concentrated on the first approach, with few ways of generating parametrized families of hard problems known prior to this work. Our group's main interest is in comparing approaches to solving planning problems using a novel type of computational device - a quantum annealer - to existing state-of-the-art planning algorithms. Because only small-scale quantum annealers are available, we must compare on small problem sizes. Small problems are primarily useful for comparison only if they are instances of parametrized families of problems for which scaling analysis can be done. In this technical report, we discuss our approach to the generation of hard planning problems from classes of well-studied NP-complete problems that map naturally to planning problems or to aspects of planning problems that many practical planning problems share. These problem classes exhibit a phase transition between easy-to-solve and easy-to-show-unsolvable planning problems. The parametrized families of hard planning problems lie at the phase transition. The exponential scaling of hardness with problem size is apparent in these families even at very small problem sizes, thus enabling us to characterize even very small problems as hard. The families we developed will prove generally useful to the planning community in analyzing the performance of planning algorithms, providing a complementary approach to existing evaluation methods. We illustrate the hardness of these problems and their scaling with results on four state-of-the-art planners, observing significant differences between these planners on these problem families. Finally, we describe two general, and quite different, mappings of planning problems to QUBOs, the form of input required for a quantum annealing machine such as the D-Wave II.

Problems↗