Modeling and compensation of nonlinear systems using sensitivity analysis.
Sensitivity analysis application to nonlinear system modeling and compensation noting minimization procedure, parameter determination and performance index
Kohr, R. H.↗
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Computerized symbolic manipulation in nonlinear finite element analysis
The potential of using computerized symbolic manipulation in the development of nonlinear finite elements is discussed. Three tasks which can be efficiently performed using computerized symbolic manipulation are identified: (1) generation of algebraic expressions for the stiffness coefficients of nonlinear finite elements, (2) generation of FORTRAN source code for numerical evaluation of stiffness coefficients, and (3) checking the correctness of the FORTRAN statements for the arrays of coefficients. The symbolic and algebraic manipulation system MACSYMA is used in the present study. Two sample MACSYMA programs are presented for the development of the nonlinear stiffness coefficients of two-dimensional, shear-flexible, doubly-curved deep shell elements. The first program is for displacement models and the second program is for mixed models with discontinuous stress-resultant fields at interelement boundaries.
Noor, A. K.↗
REVISITING EVIDENCE OF CHAOS IN X-RAY LIGHT CURVES: THE CASE OF GRS 1915+105
Nonlinear time series analysis has been widely used to search for signatures of low-dimensional chaos in light curves emanating from astrophysical bodies. A particularly popular example is the microquasar GRS 1915+105, whose irregular but systematic X-ray variability has been well studied using data acquired by the Rossi X-ray Timing Explorer . With a view to building simpler models of X-ray variability, attempts have been made to classify the light curves of GRS 1915+105 as chaotic or stochastic. Contrary to some of the earlier suggestions, after careful analysis, we find no evidence for chaos or determinism in any of the GRS 1915+105 classes. The dearth of long and stationary data sets representing all the different variability classes of GRS 1915+105 makes it a poor candidate for analysis using nonlinear time series techniques. We conclude that either very exhaustive data analysis with sufficiently long and stationary light curves should be performed, keeping all the pitfalls of nonlinear time series analysis in mind, or alternative schemes of classifying the light curves should be adopted. The generic limitations of the techniques that we point out in the context of GRS 1915+105 affect all similar investigations of light curves from other astrophysical sources.
79 ASTRONOMY AND ASTROPHYSICS↗
Computer program for nonlinear static stress analysis of shuttle thermal protection system: User's manual
User documentation is presented for a computer program which considers the nonlinear properties of the strain isolator pad (SIP) in the static stress analysis of the shuttle thermal protection system. This program is generalized to handle an arbitrary SIP footprint including cutouts for instrumentation and filler bar. Multiple SIP surfaces are defined to model tiles in unique locations such as leading edges, intersections, and penetrations. The nonlinearity of the SIP is characterized by experimental stress displacement data for both normal and shear behavior. Stresses in the SIP are calculated using a Newton iteration procedure to determine the six rigid body displacements of the tile which develop reaction forces in the SIP to equilibrate the externally applied loads. This user documentation gives an overview of the analysis capabilities, a detailed description of required input data and an example to illustrate use of the program.
Giles, G. L.↗
Finite element analysis of compressible solids with nonlinear material properties
Finite-element computer program solves for nodal point displacements in an axisymmetric solid. The options in the program include plane stress analysis, axisymmetric solids analysis, nonlinear /plastic/ analysis, and equivalent stress and strain.
Wilson, E. L.↗
High frequency content in nonlinear soil response: A numerical artifact or a reality?
This article probes the reasons for the presence of high frequency components, which are not a part of the input, in the output of nonlinear site response analysis. The nonlinear site response analysis of a single soil element, under a single frequency sinusoidal displacement, is conducted to demonstrate the presence of frequencies higher than the input frequency in the soil element's shear stress and the free surface acceleration. The parameters of this one element problem are chosen carefully to minimize numerical errors. The shape of the stress-strain hysteresis loop is found to be the main cause for the presence of these higher frequencies. A quasi-static problem similar to the direct shear test is then considered to analyze the effect of different hysteresis shapes. Through this analysis, it is numerically and analytically shown that any deviation of the stress-strain hysteresis shape from a perfect ellipse results in output frequencies higher than the input frequency and the number of higher frequencies produced depends on whether the hysteresis shape is smooth or pointed.
42 ENGINEERING↗
Fully Nonlinear Modeling and Analysis of Precision Membranes
High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.
Pai, P. Frank↗
Nonlinear sonic boom analysis including the asymmetric effects
A numerical program is developed which takes into account the nonlinear effects of high Mach number, the entropy change across the shock, the entropy and enthalpy variations in the atmospheric layer and the gravitational effect. The program differs from the existing ones by accounting for non-axisymmetric terms. The asymmetry can be caused by the geometry of the body, the lift and also the fact that the variations in the atmospheric layer are two-dimensional. Numerical results demonstrate that the influence of these asymmetric effects tends to lower the pressure signature.
Ferri, A.↗
Advanced Statistical Methods in Spacecraft Flight Software Cost Estimation: Bayesian Regression and Nonlinear Principal Components Analysis to Support System Engineering in the Early Project Lifecycle
This paper provides an overview of the new features and model updates in the upcoming release of the NASA Analogy Software Cost Tool (ASCoT). ASCoT, hosted within the Online NASA Space Estimation Tools (ONSET) on the One NASA Cost Engineering (ONCE) Database, is a web-based tool that provides a suite of estimation tools to support early lifecycle NASA flight software cost analysis. In addition to the traditional parametric flight software costing method COCOMO II, ASCoT contains a Bayesian linear regression to predict total flight software development cost as a function of total spacecraft cost, as well as four analogic methods: k-Nearest Neighbors (kNN) and Clustering models to predict Effort (in work-months) and total source lines of code (SLOC). These methods are designed to work primarily with system-level inputs such as mission type (orbiter, lander, etc.), mission destination (Earth, Inner Planetary, etc.), and the number of instruments and deployables. Nonlinear principal components analysis (NLPCA) is performed to find the principal features of the data composed of both categorical and numerical variables and is necessary prior to defining our analogic methods. Sensitivity analyses and in- and out-of-sample model performance results are presented for the Bayesian CER and the analogic models.
Johnson, James K.↗
ASCoT 3: Nonlinear Principal Components Analysis and Uncertainty Quantification in Early Concept Spacecraft Flight Software Cost Estimation
For mission planners and evaluators alike, value in cost models comes from a mean or median prediction, an understanding of the uncertainty on that prediction, and an understanding of model performance. Here we apply advanced statistical and machine learning methods to spacecraft flight software cost, effort, and SLOC estimation, and present the results in the latest version of the Analogy Software Cost Tool (ASCoT). We present in- and out-of-sample performance metrics for our models, each of which incorporate some amount of epistemic uncertainty. ASCoT, hosted on the One NASA Cost Engineering (ONCE) database via the Online NASA Space Estimation Tool (ONSET), was first showcased in 2016 as a number of analogy-based models and methods (kNN and Clustering) to support early project formulation. This ASCoT update improves upon the previous analogic methods by incorporating uncertainty in the data transformations. In particular, we use a Nonlinear Principal Components Analysis (NLPCA) to deal with ordinal data.
Robotic Spacecraft↗
Nonlinear global stability analysis of compressor stall phenomena
Compressor stall phenomena are analyzed from the point of view of nonlinear control theory, based on bifurcation-catastrophe techniques. This new approach appears promising and offers insight into such well-known compressor instability problems as surge and rotating stall and suggests strategies for recovery. Three interlocking dynamic nonlinear state space models are developed. It is shown that the problem of rotating stall can be viewed as an induced bifurcation of solution of the unstalled model. Hysteresis effects are shown to exist in the stall/recovery process. Surge cycles are observed for some critical parameter values. The oscillatory behavior is seen to be due to development of limit cycles, generated by Hopf bifurcation of solutions. More specifically, it is observed that at certain critical values of parameters, a family of stable limit cycles with growning and then diminishing amplitudes is generated, then giving rise to an unstable family of limit cycles. This unstable family in turn bifurcates into other unstable families. To further illustrate the utility of the methodology, some partial computation of domains is carried out, and parameter sensitivity analysis is performed.
Razavi, H.↗
Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics
In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.
Atluri, S. N.↗
Nonlinear and Failure Analysis of Composite Structures
The overall goal of this research is to assess the effect of discontinuities and uncertainties on the nonlinear response and failure of stiffened composite panels subjected to combined mechanical and thermal loads. The key elements of the study are: (a) study of the effects of stiffener geometry and of transverse stresses on the response, damage initiation and propagation in stiffened composite panels; (b) use of hierarchical sensitivity coefficients to identify the major parameters that affect the response and damage in each of the different levels in the hierarchy (micromechanical, layer, panel, subcomponent and component levels); and, (c) application of fuzzy set techniques to identify the range and variation of possible responses. The computational models developed are used in conjunction with experiments to understand the physical phenomena associated with the nonlinear response and failure of stiffened composite panels. A toolkit is developed for use in conjunction with deterministic analysis programs to help the designer in assessing the effect of uncertainties in the different computational model parameters on the variability of the response quantities.
Noor, Ahmed K.↗
On P- and S-functions and related classes of n-dimensional nonlinear mappings
Analysis of n-dimensional nonlinear mappings representative of P and S functions
More, J. J.↗
Applications of Automation Methods for Nonlinear Fracture Test Analysis
Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.
Allen, Phillip A.↗
Further development towards a new virtual-pulse time integral methodology for general nonlinear transient thermal analysis
New developments describing the theoretical basis towards an effective virtual-pulse time integral procedure are presented for general nonlinear transient heat transfer problems. To validate the proposed methodology of computation, numerical test examples are given and comparisons are drawn with the implicit second-order accurate Crank-Nicolson technique. The proposed method shows superior or improved accuracy and stability characteristics for the models tested.
Tamma, K. K.↗
Stokes polarimetry using analysis of the nonlinear voltage-retardance relationship for liquid-crystal variable retarders
We present a method for using liquid-crystal variable retarders (LCVR’s) with continually varying voltage to measure the Stokes vector of a light beam. The LCVR's are usually employed with fixed retardance values due to the nonlinear voltage-retardance behavior that they show. The nonlinear voltage-retardance relationship is first measured and then a linear fit of the known retardance terms to the detected signal is performed. We use known waveplates (half-wave and quarter-wave) as devices to provide controlled polarization states to the Stokes polarimeter and we use the measured Stokes parameters as functions of the orientation of the axes of the waveplates as an indication of the quality of the polarimeter. Results are compared to a Fourier analysis method that does not take into account the nonlinear voltage-retardance relationship and also to a Fourier analysis method that uses experimental voltage values to give a linear retardance function with time. Also, we present results of simulations for comparison.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
High Fidelity Failure Analysis for a Composite Fuselage Section
A high fidelity delamination failure analysis was developed by combining a local failure analysis with a global full-scale finite element structural analysis to address strength and delamination failure in a single package. The methodology was demonstrated through a local three-dimensional pull-off failure analysis and a geometrically nonlinear structural analysis of a five-foot composite helicopter fuselage section. Pull-off specimens were used to identify potential debonding failure of co-cured skin-stringer/frame fuselage structures. An investigation of the failed pull-off specimens was performed to determine the location of the failure initiation. Three-dimensional strain energy release rate analysis indicates that the delamination initiation and growth is controlled by Mode 1 opening mode. The bending moment at the delamination tip was identified as the crucial factor controlling the failure. The geometrically nonlinear structural analysis of a five-foot composite fuselage section was performed using a detailed finite element model. Loads were applied along the periphery of the subcomponent using displacement fields generated from solutions of a full-vehicle model.
Li, Jain↗