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NASA NTRS1972

On a stochastic control method for weakly coupled linear systems

The stochastic control of two weakly coupled linear systems with different controllers is considered. Each controller only makes measurements about his own system; no information about the other system is assumed to be available. Based on the noisy measurements, the controllers are to generate independently suitable control policies which minimize a quadratic cost functional. To account for the effects of weak coupling directly, an approximate model, which involves replacing the influence of one system on the other by a white noise process is proposed. Simple suboptimal control problem for calculating the covariances of these noises is solved using the matrix minimum principle. The overall system performance based on this scheme is analyzed as a function of the degree of intersystem coupling.

Kwong, R. H.↗

NASA NTRS1972

The k-space formulation of the n-dimensional scattering problem

The n-dimensional scattering problem is solved by means of a k-space formulation of the field equations, thereby replacing the conventional integral equation formulation by a set of two algebraic equations in two unknowns in two spaces (the constitutive equation being an algebraic equation in x-space). These equations are solved by an iterative method with the aid of the fast Fourier transform (FFT) algorithm connecting the two spaces, requiring very simple initial approximations. Since algebraic and FFT equations are used, the number of arithmetic multiple-add operations and storage allocations required for a numerical solution are reduced from the order of N sq (for solving the matrix equations resulting from the conventional integral equations) to the order of N(log base 2 of N) and N, respectively (where N is the number of data points required for the specification of the problem). The advantage gained in speed and storage is thus of the order of N/log base 2 of N and N, respectively. This method is thus considerably more efficient than the conventional matrix method, and permits exact numerical solutions for much larger problems. Arguments are presented toward the view that the field equations are more fundamental in k-space. The details and some numerical results of the application of this method to the three-dimensional electromagnetic scattering problems are presented as an example.

Bojarski, N. N.↗

NASA NTRS1973

Nonequilibrium chemistry boundary layer integral matrix procedure

The development of an analytic procedure for the calculation of nonequilibrium boundary layer flows over surfaces of arbitrary catalycities is described. An existing equilibrium boundary layer integral matrix code was extended to include nonequilibrium chemistry while retaining all of the general boundary condition features built into the original code. For particular application to the pitch-plane of shuttle type vehicles, an approximate procedure was developed to estimate the nonequilibrium and nonisentropic state at the edge of the boundary layer.

Tong, H.↗

NASA NTRS1978

Fracture and crack growth in orthotropic laminates

Goree, J. G.↗

NASA NTRS1980

Stresses in a three-dimensional unidirectional composite containing broken fibers

An approximate solution is developed for the determination of the interlaminar normal and shear stresses in the vicinity of a crack in a three dimensional composite containing unidirectional linearly elastic fibers in an infinite linearly elastic matrix. In order to reduce the complexity of the formulation, certain assumptions are made as to the physically significant stresses to be retained. These simplifications reduce the partial differential equations of elasticity to differential-difference equations which are tractable using Fourier transform techniques. This 'material modeling' approach is in contrast with solutions developed by considering each lamina as a homogeneous, orthotropic layer. The resulting solution does not contain the classical singular stress field for the fibers and the influence of broken fibers on unbroken fibers is felt by a change in stress concentration factors. The matrix stresses however, are unbounded as the fiber spacing vanishes and an equivalent fiber-matrix geometry is proposed which gives the correct singular behavior. The numerical solution is considered in detail and several specific examples are presented. The potential for damaged or debonded zones to be generated by an embedded crack is discussed, and stress concentration factors for fibers near the crack are given. Detailed comparisons are made between the present solution, the analogous two-dimensional problem, and corresponding shear-lag models.

Goree, J. G.↗

NASA NTRS1991

An improved error assessment for the GEM-T1 gravitational model

Several tests have been designed to estimate the correct error variances for the GEM-T1 gravitational solution that was derived exclusively from satellite tracking data. The basic method uses both independent and dependent subset data solutions and produces a coefficient-by-coefficient estimate of the model uncertainties. The GEM-T1 errors have been further analyzed using a method based on eigenvalue-eigenvector analysis, which calibrates the entire covariance matrix. Dependent satellite data sets and independent altimetric, resonant satellite, and surface gravity data sets all confirm essentially the same error assessment. The calibration test results yield very stable calibration factors, which vary only by approximately 10 percent over the range of tests performed. Based on these calibrated error estimates, GEM-T1 is a significantly improved solution, which to degree and order 8 is twice as accurate as earlier satellite derived models like GEM-L2. Also, by being complete to degree and order 36, GEM-T1 is more complete and has significantly reduced aliasing effects that were present in previous models.

Lerch, F. J.↗

DOE OSTI2023

The Circular Home: Development and Demonstration of a Net Negative Carbon, Reusable Residence

This project started the development of an innovative modular building system intended for residential construction. The project was centered around single-family homes that were carbon-negative cradle-to-grave over a 100 year time frame, which is approximately double the current standard for operational life. The project sought to accomplish this objective by designing the modular home in a manner that ensures circularity, where the main house components can be used over several consecutive 50-year lifespans. To accomplish these objectives, this project utilized integrated design with the inclusion of life-cycle assessment to design the single-family house for architectural, structural, energy, mechanical, thermal, and moisture demands, while ensuring carbon negativity and annual net-zero energy use. The core technology of this project was the use of cross-laminated timber and biogenic materials, such as wood-fiber insulation, in the construction of the modular building units. The robustness and factory manufacturing ability of cross-laminated timber allow for factory construction of most of the home, which minimizes on-site time, saving money and reducing construction waste. During this project, initial milestones were met that delivered the architectural plans for the circular home and an initial structural testing matrix. Compared to current code-built homes, which average 13 kg CO2eq. / ft2 and are demolished at their end of life, the circular home has an estimated -30 kg CO2eq. / ft2 of embodied carbon emissions during its first build iteration. It is estimated that approximately 60%-70% of the total building mass could be reused and/or recycled during subsequent rebuilds. This project was concluded at approximately the 1/3 point and a separate project was established to conclude the remaining milestones. This project promises to benefit the public by delivering another option for single-family, and eventually multi-family, housing using a novel building construction system. The system of reusable modular construction facilitates not only lower emissions during the first building iteration, but also lower emissions during subsequent iterations that drastically reduce waste and help society meet its climate goals. Many other industries, such as clothing and technology sectors, are starting to focus on circularity and this project adds the residential building construction industry to that list.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Printable Fiber Reinforced Cement Composites – Feasibility Study

Additive manufacturing is enabling the manufacturability of structures with previously unattainable complexity or functionality, and there is growing interest in additive manufacturing of “printed” concrete structures. The focus of this Phase 1 Technical Collaboration (TC) project was to evaluate feasibility of printing hybrid cement composite structures reinforced with textile carbon fibers (tCF). This project leverages other (non-IACMI) projects on cement formulation and printing process development, as well as on the production process for tCF. This project’s primary focus was to explore cement composite mix design with textile carbon fibers to be manufactured by MonteFibre (TC partner) and evaluate suitable fiber-matrix interface or sizing for cement composites working with Michelman (TC Partner). This project supports IACMI’s goal of reducing the cost and embodied energy of carbon fiber composites. Cost is one of the fundamental challenges to carbon fiber reinforced cement composites. Cement is an extremely inexpensive material (approximately $\$$0.05/lb). Adding 1 wt% of conventional carbon fiber to cement quadruples its cost. Therefore, the need to use low-cost carbon fiber and ensure that the additional cost of the carbon fiber has a greater cost benefit to the final product. This was the first preliminary evaluation to integrate tCF reinforcement in cement composites, and such potential tCF utilization should significantly reduce materials cost. Cement composite production is energy and emissions intensive, thus by strengthening it less material will be required. Hence, the embodied energy and production time of the resulting structures will be reduced. Additionally, integrating these new materials into additive processes can enable selective use of the material in high load or stress areas. It is noteworthy that past work in this field of fiber reinforced cement composites did not consider the optimization of fiber-matrix interface using suitable sizing. Carbon fiber reinforcement offers potential added benefits of thermal conductivity (which affects cure rate) and flow behavior that could provide opportunities for site specific utilization of carbon fiber on hybrid cement structures (e.g. use the fiber reinforcement on outer surfaces to enhance strength and modulus and then infiltrating the internal structures with conventional concrete). MonteFibre was the industry lead and planned on supplying the tCF for this project. However, during the short Phase-1 duration of this project, MonteFibre was unable to produce tCF for this project due to manufacturing plant being off-line throughout the course of the project. The project team decided to pursue an alternate option which involved demonstrating printable concrete with steel fibers by the ORNL lead, Dr. Brian Post. The University of Tennessee collaboration team focused on evaluating the suitable chemical sizing for carbon fibers working with Michelman and also developed methods for material characterization of cement-based composites to evaluate the material response for compression, shear, flexure, and tension. The two milestones for University of Tennessee, Knoxville were realized related to identification of one sizing suitable for carbon fiber reinforced cement composite and developing data associated with mechanical behavior of unreinforced (neat) and carbon fiber reinforced cement composites. ORNL could not complete the task of carbon fiber reinforced printed cement composites due to the reasons mentioned earlier, but was able to replace tCF with steel fibers to demonstrate the feasibility of printing with fiber reinforced cement composites. The Project team reviewed possible sizing chemistry available in collaboration with Michelman for use on carbon fiber reinforcement in cement composites and concrete applications. Our initial goal was to identify a sizing most promising for formulation with textile carbon fibers (tCF) to deliver excellent mechanical properties in composite material state. Since tCF was not available for this project as originally envisioned, the team continued this task to identify a suitable sizing for carbon fiber applications by applying such sizing to lower cost carbon fibers currently available commercially from Zoltek called Panex fibers. At a future time this can be optimized for textile carbon fibers from Montefibre. The bulk of previous work on carbon fiber reinforced cement has neglected the importance of fiber-matrix adhesion on mechanical properties of the cement composite and identifying this missing link was an important accomplishment for future research. Tensile behavior of fiber reinforced concrete is important to evaluate in order to realize the dream of concrete products that do not need reinforcing steel. Important sample preparation and testing procedures were addressed in this study and it was concluded that substantial improvements in tensile behavior, without compromising compressive strength, and improved ductility can result from the use of carbon fiber reinforcement.

36 MATERIALS SCIENCE↗

NASA NTRS1989

Mesh refinement in finite element analysis by minimization of the stiffness matrix trace

Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.

Kittur, Madan G.↗

DOE OSTI2024

Analysis of static Wilson line correlators from lattice QCD at finite temperature with T -matrix approach

The thermodynamic T-matrix approach is used to study Wilson line correlators (WLCs) for a static quark-antiquark pair in the quark-gluon plasma (QGP). Selfconsistent results that incorporate constraints from the QGP equation of state can approximately reproduce WLCs computed in 2+1-flavor lattice-QCD (lQCD), provided the input potential exhibits less screening than in previous studies. Utilizing the updated potential to calculate pertinent heavylight T-matrices we evaluate thermal relaxation rates of heavy quarks in the QGP. We find a more pronounced temperature dependence for low-momentum quarks than in our previous results (with larger screening), which turns into a weaker temperature dependence of the (temperature-scaled) spatial diffusion coefficient, in fair agreement with the most recent lQCD data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Scalable ab initio fragmentation methods based on a truncated expansion of the non-orthogonal molecular orbital model

An alternative formulation of the non-orthogonal molecular orbital model of electronic structure theory is developed based on the expansion of the inverse molecular orbital overlap matrix. From this model, a hierarchy of ab initio fragment-based quantum chemistry methods, referred to as the nth-order expanded non-orthogonal molecular orbital methods, are developed using a minimal number of approximations, each of which is frequently employed in intermolecular interaction theory. These novel methods are compared to existing fragment-based quantum chemistry methods, and the implications of those significant differences, where they exist, between the methods developed herein and those already existing methods are examined in detail. Computational complexities and theoretical scaling are also analyzed and discussed. Future extensions for the hierarchy of methods, to account for additional intrafragment and interfragment interactions, are outlined.

Westheimer, Bryce M. (ORCID:0000000267645714)↗

NASA NTRS1971

An analysis and comparison of several trajectory optimization methods

The sensitivities of the convergence characteristics of the methods to initially assumed parameters and trial solution, convergence times, computer logic, and storage requirements are discussed. Numerical comparison of the convergence characteristics is made by considering a minimum time, low thrust, Earth-Mars transfer trajectory. A modified quasi-linearization method reduces convergence time by approximately 70% when compared with the generalized Newton-Raphson method and allows the terminal boundary to be specified by a general function of the problem variables. A uniquely specified and easily determined, time dependent weighting matrix for the gradient techniques accelerates the shaping of the optimal control program and improves the convergence characteristics during the terminal iterations. Convergence envelopes, indicating how sensitive the convergence characteristics are to initially assumed parameters, are plotted for the perturbation and quasi-linearization methods. Several iteration schemes are proposed which increase the size of the convergence envelopes and decrease the sensitivity of the method to initially assumed parameters.

Lewallen, J. M.↗

NASA NTRS1972

Filament-wound graphite/epoxy rocket motor case

The fabrication procedures are described for a filament-wound rocket motor case, approximately 56 cm long x 71 cm diameter, utilizing high tensile strength graphite fibers. The process utilized Fiberite Hy-E-1330B prepreg tape which consists of Courtaulds HTS fibers in a temperature-sensitive epoxy matrix. This fabrication effort, with resultant design, material and process recommendations, substantiates the manufacturing feasibility of graphite/epoxy rocket motor cases in the 56 cm x 71 cm size range.

Humphrey, W. D.↗

NASA NTRS1973

The nature of dark-etching rims in meteoritic taenite.

Taenite fields when etched develop a cloudy brown rim with approximate compositional limits of 25 and 40% Ni. In iron meteorites this cloudy zone is only a few microns wide, with a sharp, high-Ni edge about 1 micron from the kamacite interface and a diffuse edge several microns from the central plessite. It is always present in irons unless the meteorite has been cosmically or terrestrially reheated. X-ray and electron diffraction of grains scratched from exceptionally larger areas of cloudy taenite in the mesosiderite Estherville show that this etching zone contains a fine exsolution of kamacite. Detailed electron-probe investigations of taenite in Estherville show that there is a step in the M-shaped Ni profile at the sharp, high-Ni edge of the cloudy region, the Ni dropping suddenly from approximately 45 to 42%. It is proposed that exsolution in the cloudy region effectively froze in the Ni profile at that temperature. On subsequent cooling only the clear outer taenite continued to equilibrate with the kamacite matrix, producing the kink in the M profile. Cloudy taenite is therefore a variety of plessite differing from the usual varieties in that it forms at lower temperatures in areas much richer in Ni, and the morphology is not crystallographically oriented. Its absence can provide a sensitive indication of reheating.

Scott, E. R. D.↗

NASA NTRS1987

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Tiffany, Sherwood H.↗

NASA NTRS1986

Composite tubes for the Space Station truss structure

The reference configuration of NASA's Space Station includes a large truss structure to support the various modules and solar arrays. This truss structure will be constructed from tubular members approximately 2 in. in diameter and up to 23 ft in length. The important design considerations for this structure are light weight, high stiffness, dimensional stability, and long-term durability. Continuous graphite fiber reinforced polymer matrix composite materials can meet the structural requirements, and are leading candidates for the tubular truss members. However, there are concerns regarding the durability of composites during the long-term exposure to atomic oxygen and thermal cycling that will be encountered during the Space Station service life. This paper discusses space environmental factors and their effect on composite materials, and provides estimates of the changes in mechanical and thermal properties of composites exposed to long-term Space Station conditions. The effect of low velocity impact and handling damage on composite tube properties is also discussed.

Bowles, David E.↗

NASA NTRS1988

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

Tiffany, Sherwood H.↗

NASA NTRS1989

Solution of steady-state one-dimensional conservation laws by mathematical programming

Solution techniques for a class of steady-state scalar conservation laws are developed analytically. Discretization by finite-volume formulas is employed to obtain an overdetermined system of algebraic equations, which are then perturbed nonsingularly (with perturbation coefficient = epsilon) and solved using the l(1) mathematical-programming algorithm of Seneta and Steiger (1984); this approach limits the matrix bandwidth to two, so that an explicit solution can be found efficiently. It is shown that, for small values of epsilon, the l(1) solutions exhibit sharp correctly located shocks and are nonoscillatory O(epsilon) approximations of the physically relevant solutions.

Lavery, J. E.↗