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NASA NTRS1991

Solution of geometrically nonlinear statics problems by the p-version of the finite element method

This project is concerned with the possibility of using computers for the simulation of structural systems with the same degree of reliability as full scale physical experiments. Reliable numerical simulation will make it possible to reduce the costs of engineering and improve the quality of engineering decisions based on computed information. An error of idealization is an error between the actual physical quantities on which engineering decisions are based (e.g., maximum principal stress, first natural frequency, etc.) and the same data corresponding to the exact solution of the mathematical model. An error of discretization is an error between the quantities of interest corresponding to the exact and approximate solutions of a mathematical model. A high degree of reliability can be achieved in numerical simulation only if both the errors of idealization and errors of discretization can be shown to be small.

Szabo, Barna A.↗

NASA NTRS1994

Optimal active control for Burgers equations

A method for active fluid flow control based on control theory is discussed. Dynamic programming and fixed point successive approximations are used to accommodate the nonlinear control problem. The long-term goal of this project is to establish an effective method applicable to complex flows such as turbulence and jets. However, in this report, the method is applied to stochastic Burgers equation as an intermediate step towards this goal. Numerical results are compared with those obtained by gradient search methods.

Ikeda, Yutaka↗

NASA NTRS2003

Linear optics and projective measurements for fun and profit

The technique of projective measurements in linear optics can provide an apparent, efficient nonlinear interaction between photons, which is technically problematic otherwise. We present an application of such a technique to prepare large photon-number path entanglement.

linear↗

NASA NTRS2014

Nonlinear Development and Secondary Instability of Traveling Crossflow Vortices

Transition research under NASA's Aeronautical Sciences Project seeks to develop a validated set of variable fidelity prediction tools with known strengths and limitations, so as to enable "sufficiently" accurate transition prediction and practical transition control for future vehicle concepts. This paper builds upon prior effort targeting the laminar breakdown mechanisms associated with stationary crossflow instability over a swept-wing configuration relevant to subsonic aircraft with laminar flow technology. Specifically, transition via secondary instability of traveling crossflow modes is investigated as an alternate scenario for transition. Results show that, for the parameter range investigated herein, secondary instability of traveling crossflow modes becomes insignificant in relation to the secondary instability of the stationary modes when the relative initial amplitudes of the traveling crossflow instability are lower than those of the stationary modes by approximately two orders of magnitudes or more. Linear growth predictions based on the secondary instability theory are found to agree well with those based on PSE and DNS, with the most significant discrepancies being limited to spatial regions of relatively weak secondary growth, i.e., regions where the primary disturbance amplitudes are smaller in comparison to its peak amplitude. Nonlinear effects on secondary instability evolution is also investigated and found to be initially stabilizing, prior to breakdown.

Li, Fei↗

NASA NTRS1987

Highly Non-Linear Optical (NLO) organic crystals

This research project involves the synthesis and characterization of organic materials having powerful nonlinear optical (NLO) properties and the growth of highly ordered crystals and monomolecular films of these materials. Research in four areas is discussed: theoretical design of new materials, characterization of NLO materials, synthesis of new materials and development of coupling procedures for forming layered films, and improvement of the techniques for vapor phase and solution phase growth of high quality organic crystals. Knowledge gained from these experiments will form the basis for experiments in the growth of these crystals.

Harris, J. Milton↗

NASA NTRS2019

Optimal Control within the Context of Multidisciplinary Design, Analysis, and Optimization

Multidisciplinary design, analysis and optimization involves modeling the interactions of complex systems across a variety of disciplines. The optimization of such systems can be a computationally expensive exercise with multiple levels of nested nonlinear solvers running under an optimizer.The application of optimal control in project development often involves performing trajectory optimization for fixed vehicle designs or parametric sweeps across some key vehicle properties.This information is then relayed to the subsystem design teams who update their designs and relay some bulk characteristics back to the trajectory optimization procedure.This iteration is then repeated until the design closes.However, with increasing interest in more tightly coupled systems, such as electric and hybrid-electric aircraft propulsion and boundary layer ingestion, this process is prone to ignore subtle coupling between vehicle subsystem designs and vehicle operation on a given mission.Integrating trajectory optimization into a tightly coupled multidisciplinary design procedure can be computationally prohibitive, depending on the complexity of the subsystem analyses and the optimal control technique applied.To address these issues a new optimal control software tool, Dymos, has been developed.Dymos is built upon NASA's OpenMDAO software and can leverage its capabilities to efficiently compute gradients for the optimization and optimize complex models in parallel on distributed memory systems.This report provides some explanation into the numerical methods employed in Dymos and provides several use cases that demonstrate its performance on traditional optimal control problems and improvements ino techniques have been used extensively in recent decades to solve a variety of optimal control problems, typically in the form of aerospace vehicle trajectory optimization.

pseudospectral↗

NASA NTRS2014

Nonlinear Finite Element Analysis of a Composite Non-Cylindrical Pressurized Aircraft Fuselage Structure

The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously published preliminary linear analysis, it is demonstrated in the present paper that neglecting nonlinear effects for the structure and loads of interest can lead to appreciable loss in analysis fidelity.

Przekop, Adam↗

NASA NTRS2003

A Nonlinear Model for Fuel Atomization in Spray Combustion

Most gas turbine combustion codes rely on ad-hoc statistical assumptions regarding the outcome of fuel atomization processes. The modeling effort proposed in this project is aimed at developing a realistic model to produce accurate predictions of fuel atomization parameters. The model involves application of the nonlinear stability theory to analyze the instability and subsequent disintegration of the liquid fuel sheet that is produced by fuel injection nozzles in gas turbine combustors. The fuel sheet is atomized into a multiplicity of small drops of large surface area to volume ratio to enhance the evaporation rate and combustion performance. The proposed model will effect predictions of fuel sheet atomization parameters such as drop size, velocity, and orientation as well as sheet penetration depth, breakup time and thickness. These parameters are essential for combustion simulation codes to perform a controlled and optimized design of gas turbine fuel injectors. Optimizing fuel injection processes is crucial to improving combustion efficiency and hence reducing fuel consumption and pollutants emissions.

Liu, Nan-Suey↗

NASA NTRS1990

An expert system based software sizing tool, phase 2

A software tool was developed for predicting the size of a future computer program at an early stage in its development. The system is intended to enable a user who is not expert in Software Engineering to estimate software size in lines of source code with an accuracy similar to that of an expert, based on the program's functional specifications. The project was planned as a knowledge based system with a field prototype as the goal of Phase 2 and a commercial system planned for Phase 3. The researchers used techniques from Artificial Intelligence and knowledge from human experts and existing software from NASA's COSMIC database. They devised a classification scheme for the software specifications, and a small set of generic software components that represent complexity and apply to large classes of programs. The specifications are converted to generic components by a set of rules and the generic components are input to a nonlinear sizing function which makes the final prediction. The system developed for this project predicted code sizes from the database with a bias factor of 1.06 and a fluctuation factor of 1.77, an accuracy similar to that of human experts but without their significant optimistic bias.

Friedlander, David↗

NASA NTRS2011

Project Management Using Modern Guidance, Navigation and Control Theory

Implementing guidance, navigation, and control (GN&C) theory principles and applying them to the human element of project management and control is not a new concept. As both the literature on the subject and the real-world applications are neither readily available nor comprehensive with regard to how such principles might be applied, this paper has been written to educate the project manager on the "laws of physics" of his or her project (not to teach a GN&C engineer how to become a project manager) and to provide an intuitive, mathematical explanation as to the control and behavior of projects. This paper will also address how the fundamental principles of modern GN&C were applied to the National Aeronautics and Space Administration's (NASA) Constellation Program (CxP) space suit project, ensuring the project was managed within cost, schedule, and budget. A project that is akin to a physical system can be modeled and managed using the same over arching principles of GN&C that would be used if that project were a complex vehicle, a complex system(s), or complex software with time-varying processes (at times nonlinear) containing multiple data inputs of varying accuracy and a range of operating points. The classic GN&C theory approach could thus be applied to small, well-defined projects; yet when working with larger, multiyear projects necessitating multiple organizational structures, numerous external influences, and a multitude of diverse resources, modern GN&C principles are required to model and manage the project. The fundamental principles of a GN&C system incorporate these basic concepts: State, Behavior, Feedback Control, Navigation, Guidance and Planning Logic systems. The State of a system defines the aspects of the system that can change over time; e.g., position, velocity, acceleration, coordinate-based attitude, and temperature, etc. The Behavior of the system focuses more on what changes are possible within the system; this is denoted in the state of the system. The behavior of a system, as captured in the system modeling, when properly done will aid in accurately predicting future system performance. The Feedback Control system understands the state and behavior of the system and uses feedback to adjust control inputs into the system. The feedback, which is the right arm of the Control system, allows change to be affected in the overall system; it therefore is important to not only correctly identify the system feedback inputs, but also the system response to the feedback inputs. The Navigation system takes multiple data inputs and based on a priori knowledge of the inputs, develops a statistically based weighting of the inputs and measurements to determine the system's state. Guidance and Planning Logic of the system, complete with an understanding of where the system is (provided by the Navigation system), will in turn determine where the system needs to be and how to get it there. With any system/project, it is critical that the objective of the system/project be clearly defined -- not only to plan but to measure performance and to aid in guiding the system or the project. The system principles discussed above, which can be and have been applied to the current CxP space suit development project, can also be mapped to real-world constituents, thus allowing project managers to apply systems theories that are well defined in engineering and mathematics to a discipline (i.e., Project Management) that historically has been based in personal experience and intuition. This mapping of GN&C theory to Project Management will, in turn, permit a direct, methodical approach to Project Management, planning and control providing a tool to help predict (and guide) performance and an understanding of the project constraints, how the project can be controlled, and the impacts to external influences and inputs. This approach, to a project manager, flows down to the three bottom-line variables of cost, schedule, and scope ando the needed control of these three variables to successfully perform and complete a project.

Hill, Terry R.↗

NASA NTRS1989

Analytical modeling of structure-soil systems for lunar bases

The study of the behavior of granular materials in a reduced gravity environment and under low effective stresses became a subject of great interest in the mid 1960's when NASA's Surveyor missions to the Moon began the first extraterrestrial investigation and it was found that Lunar soils exhibited properties quite unlike those on Earth. This subject gained interest during the years of the Apollo missions and more recently due to NASA's plans for future exploration and colonization of Moon and Mars. It has since been clear that a good understanding of the mechanical properties of granular materials under reduced gravity and at low effective stress levels is of paramount importance for the design and construction of surface and buried structures on these bodies. In order to achieve such an understanding it is desirable to develop a set of constitutive equations that describes the response of such materials as they are subjected to tractions and displacements. This presentation examines issues associated with conducting experiments on highly nonlinear granular materials under high and low effective stresses. The friction and dilatancy properties which affect the behavior of granular soils with low cohesion values are assessed. In order to simulate the highly nonlinear strength and stress-strain behavior of soils at low as well as high effective stresses, a versatile isotropic, pressure sensitive, third stress invariant dependent, cone-cap elasto-plastic constitutive model was proposed. The integration of the constitutive relations is performed via a fully implicit Backward Euler technique known as the Closest Point Projection Method. The model was implemented into a finite element code in order to study nonlinear boundary value problems associated with homogeneous as well as nonhomogeneous deformations at low as well as high effective stresses. The effect of gravity (self-weight) on the stress-strain-strength response of these materials is evaluated. The calibration of the model is performed via three techniques: (1) physical identification, (2) optimized calibration at the constitutive level, and (3) optimized calibration at the finite element level (Inverse Identification). Activities are summarized in graphic and outline form.

Macari-Pasqualino, Jose Emir↗

NASA NTRS2005

Biaxial Stress Limit for ULDB Film

The current ULDB design applies stress to the shell film biaxially to control creep in the latitudinal direction. The recent change in design paradigm, from a uniaxial to biaxial stress state basis, arose from a new perspective that the biaxial loading can control strain in both principal surface dimensions as discussed below. The current ULDB project path was thus enabled by a more thorough understanding of the nonlinear viscoelastic properties of the shell film material, linear low-density polyethylene (LLDPE). Although a very similar material is also used in NASA zero-pressure (ZPB) and long-duration balloons (LDB), the different stress state requires a new approach to shell material qualification.

Sterling, W. J.↗

NASA NTRS1997

An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics

This project is motivated by the desire to develop numerical methods that will be useful in the study of compressible flows that exhibit aeroacoustic phenomena. Solutions to linear problems have been investigated through the development of a computer code based on the recent dispersion-relation-preserving (DRP) methodology. In regard to nonlinear problems, the class of essentially nonoscillatory (ENO) schemes have been considered as the primary candidates for solving aeroacoustic problems in which discontinuities are involved. Discontinuities in the solution itself (e.g. shocks) as well as in the geometry on which the problem is defined have been studied. Two-dimensional nonlinear problems were considered in order to determine if the one-dimensional results obtained in the first phase of this project were extendable to more realistic problems. Conclusions have been drawn in regard to the ability to numerically predict solutions of nonlinear problems with shocks to high-order accuracy.

Casper, Jay↗

NASA NTRS1992

Reconstruction of internal density distributions in porous bodies from laser ultrasonic data

It is presently shown that, for density-reconstruction problems in which information about the inhomogeneity is known a priori, the nonlinear least-squares algorithm yields satisfactory results on the basis of limited projection data. The back-projection algorithm, which obviates assumptions about the objective function to be reconstructed, does not recover the boundary of the inhomogeneity when the number of projections is limited and ray-bending is ignored.

Lu, Yichi↗

NASA NTRS2000

Application of a Reduced Order Kalman Filter to Initialize a Coupled Atmosphere-Ocean Model: Impact on the Prediction of El Nino

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model of Zebiak and Cane. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Ballabrera-Poy, J.↗

NASA NTRS1997

Inverting the Pendulum Using Fuzzy Control (Center Director's Discretionary Fund (Project 93-02)

A single pendulum was simulated in software and then built on a rotary base. A fuzzy controller was used to show its advantages as a nonlinear controller since bringing the pendulum inverted is extremely nonlinear. The controller was implemented in a Motorola 6811 microcontroller. A double pendulum was simulated and fuzzy control was used to hold it in a vertical position. The double pendulum was not built into hardware for lack of time. This project was for training and to show advantages of fuzzy control.

Kissel, R. R.↗

NASA NTRS2022

Alternative regularizations for Outer-Approximation algorithms for convex MINLP

In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance metrics and Lagrangean approximations, used in the projection problem for finding new integer combinations to be used within the Outer-Approximation (OA) method. The new approach, called Regularized Outer-Approximation (ROA), has been implemented as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo—MindtPy. We compare the OA method with seven regularization function alternatives for ROA. Moreover, we extend the LP/NLP Branch and Bound method proposed by Quesada and Grossmann (Comput Chem Eng 16(10–11):937–947, 1992) to include regularization in an algorithm denoted RLP/NLP. We provide convergence guarantees for both ROA and RLP/NLP. Finally, we perform an extensive computational experiment considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization combined with the OA method.

Convex Mixed-integer nonlinear programming↗

NASA NTRS1970

Luminescent screen composition and apparatus

Ultraviolet light projects photographically produced images on a screen composed of a mixture of linear and nonlinear phosphors whose spectral emissions are different. This allows the display of polychromatic luminescent images, which gives better discrimination of the objects being viewed.

Hilborn, E. H.↗