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NASA NTRS1996

Coupled Structural, Thermal, Phase-Change and Electromagnetic Analysis for Superconductors

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermal and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. This volume, Volume 1, describes mostly formulations for specific problems. Volume 2 describes generalization of those formulations.

Felippa, C. A.↗

NASA NTRS1989

Global sensitivity analysis in control-augmented structural synthesis

In this paper, an integrated approach to structural/control design is proposed in which variables in both the passive (structural) and active (control) disciplines of an optimization process are changed simultaneously. The global sensitivity equation (GSE) method of Sobieszczanski-Sobieski (1988) is used to obtain the behavior sensitivity derivatives necessary for the linear approximations used in the parallel multidisciplinary synthesis problem. The GSE allows for the decoupling of large systems into smaller subsystems and thus makes it possible to determine the local sensitivities of each subsystem's outputs to its inputs and parameters. The advantages in using the GSE method are demonstrated using a finite-element representation of a truss structure equipped with active lateral displacement controllers, which is undergoing forced vibration.

Bloebaum, Christina L.↗

NASA NTRS1983

Assessment of current state of the art in modeling techniques and analysis methods for large space structures

Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.

Noor, A. K.↗

NASA NTRS1939

A method of estimating the critical buckling load for structural members

The relations between load on the structure and rotation of a joint can be used to estimate the lowest critical load after the equation for neutral stability has been tested for three assumed critical loads, each of which is less than the lowest critical load. The solutions of six simple problems are included to illustrate the application of the method of estimating critical loads and to reveal certain characteristics of the method that should be known by the practical engineer using it. Four of these problems are concerned with members that lie in the elastic, or long-column, range. The other two problems are concerned with members that lie in the short-column range.

Lundquist, Eugene E↗

NASA NTRS1986

On the electromagnetic scattering from infinite rectangular grids with finite conductivity

A variety of methods can be used in constructing solutions to the problem of mesh scattering. However, each of these methods has certain drawbacks. The present paper is concerned with a new technique which is valid for all spacings. The new method involved, called the fast Fourier transform-conjugate gradient method (FFT-CGM), represents an iterative technique which employs the conjugate gradient method to improve upon each iterate, utilizing the fast Fourier transform. The FFT-CGM method provides a new accurate model which can be extended and applied to the more difficult problems of woven mesh surfaces. The formulation of the FFT-conjugate gradient method for aperture fields and current densities for a planar periodic structure is considered along with singular operators, the formulation of the FFT-CG method for thin wires with finite conductivity, and reflection coefficients.

Christodoulou, C. G.↗

NASA NTRS1987

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Yao, Tse-Min↗

NASA NTRS1986

Kinematic observers for active control of helicopter rotor vibration

A simple scheme for estimating the state variables of a helicopter rotor is presented. The method incorporates the use of blade-mounted accelerometers and/or position transducers to reconstruct modal displacements and velocities. The design of the observer structure and feedback gains is simplified by the fact that the method requires only knowledge of basic kinematic relationships between the various modal quantities. The observer structure described is particularly well-suited to control problems where the use of a traditional Kalman Filter approach would be too complex or costly. The technique can be viewed as decreasing the requirements on observer complexity while increasing the need for an enhanced sensor complement.

Mckillip, Robert M., Jr.↗

NASA NTRS1989

Efficient optimization of integrated aerodynamic-structural design

Techniques for reducing the computational complexity of multidisciplinary design optimization (DO) of aerodynamic structures are described and demonstrated. The basic principles of aerodynamic and structural DO are reviewed; the formulation of the combined DO problem is outlined; and particular attention is given to (1) the application of perturbation methods to cross-sensitivity computations and (2) numerical approximation procedures. Trial DOs of a simple sailplane design are presented in tables and graphs and discussed in detail. The IBM 3090 CPU time for the entire integrated DO was reduced from an estimated 10 h to about 6 min.

Haftka, R. T.↗

NASA NTRS1990

Computation of maximum gust loads in nonlinear aircraft using a new method based on the matched filter approach and numerical optimization

Time-correlated gust loads are time histories of two or more load quantities due to the same disturbance time history. Time correlation provides knowledge of the value (magnitude and sign) of one load when another is maximum. At least two analysis methods have been identified that are capable of computing maximized time-correlated gust loads for linear aircraft. Both methods solve for the unit-energy gust profile (gust velocity as a function of time) that produces the maximum load at a given location on a linear airplane. Time-correlated gust loads are obtained by re-applying this gust profile to the airplane and computing multiple simultaneous load responses. Such time histories are physically realizable and may be applied to aircraft structures. Within the past several years there has been much interest in obtaining a practical analysis method which is capable of solving the analogous problem for nonlinear aircraft. Such an analysis method has been the focus of an international committee of gust loads specialists formed by the U.S. Federal Aviation Administration and was the topic of a panel discussion at the Gust and Buffet Loads session at the 1989 SDM Conference in Mobile, Alabama. The kinds of nonlinearities common on modern transport aircraft are indicated. The Statical Discrete Gust method is capable of being, but so far has not been, applied to nonlinear aircraft. To make the method practical for nonlinear applications, a search procedure is essential. Another method is based on Matched Filter Theory and, in its current form, is applicable to linear systems only. The purpose here is to present the status of an attempt to extend the matched filter approach to nonlinear systems. The extension uses Matched Filter Theory as a starting point and then employs a constrained optimization algorithm to attack the nonlinear problem.

Pototzky, Anthony S.↗

NASA NTRS1991

Application of multidisciplinary optimization methods to the design of a supersonic transport

An optimization design method is discussed. This method is based on integrating existing disciplinary analysis and sensitivity analysis techniques by means of generalized sensitivity equations. A generic design system implementing this method is described. The system is being used to design the configuration and internal structure of a supersonic transport wing for optimum performance. This problem combines the disciplines of linear aerodynamics, structures, and performance. Initial results which include the disciplines of aerodynamics and structures in a conventional minimum weight design under static aeroelastic constraints are presented.

Barthelemy, J.-F. M.↗

NASA NTRS1992

Application of multidisciplinary optimization methods to the design of a supersonic transport

A new optimization based design method is discussed. This method is based on integrating existing disciplinary analysis and sensitivity analysis techniques by means of generalized sensitivity equations. A generic design system implementing this method is described. The system is being used to design the configuration and internal structure of a supersonic transport wing for optimum performance. This problem combines the disciplines of linear aerodynamics, structures, and performance. Initial results which include the disciplines of aerodynamics and structures in a conventional minimum weight design under static aeroelastic constraints are presented.

Barthelemy, J.-F. M.↗

NASA NTRS1988

An adaptive identification and control scheme for large space structures

A unified identification and control scheme capable of achieving space at form performance objectives under nominal or failure conditions is described. Preliminary results are also presented, showing that the methodology offers much promise for effective robust control of large space structures. The control method is a multivariable, adaptive, output predictive controller called Model Predictive Control (MPC). MPC uses a state space model and input reference trajectories of set or tracking points to adaptively generate optimum commands. For a fixed model, MPC processes commands with great efficiency, and is also highly robust. A key feature of MPC is its ability to control either nonminimum phase or open loop unstable systems. As an output controller, MPC does not explicitly require full state feedback, as do most multivariable (e.g., Linear Quadratic) methods. Its features are very useful in LSS operations, as they allow non-collocated actuators and sensors. The identification scheme is based on canonical variate analysis (CVA) of input and output data. The CVA technique is particularly suited for the measurement and identification of structural dynamic processes - that is, unsteady transient or dynamically interacting processes such as between aerodynamics and structural deformation - from short, noisy data. CVA is structured so that the identification can be done in real or near real time, using computationally stable algorithms. Modeling LSS dynamics in 1-g laboratories has always been a major impediment not only to understanding their behavior in orbit, but also to controlling it. In cases where the theoretical model is not confirmed, current methods provide few clues concerning additional dynamical relationships that are not included in the theoretical models. CVA needs no a priori model data, or structure; all statistically significant dynamical states are determined using natural, entropy-based methods. Heretofore, a major limitation in applying adaptive controllers to LSS problems has been the requirement for accurate models. We feel that MPC coupled with the CVA identification scheme will resolve this limitation. The results are based on research performed under an SBIR grant, administered by the Air Force Office of Scientific Research.

Carroll, J. V.↗

NASA NTRS1990

An application of compound scaling to wind tunnel model design

An approach was developed for the stiffness design of aeroelastically scaled wind tunnel models. The object of designing such models is to make a structure whose stiffness matches a desired stiffness distribution. This design problem is cast as a formal constrained optimization problem and worked with two different optimization methods. A previous effort used the modified method of feasible directions (MFD) as implemented in a general purpose finite element based optimization code. In this effort, a special purpose finite element based optimization program was written and run using both MFD and compound scaling optimization methods. Results are presented comparing the final designs obtained using MFD and compound scaling.

French, Mark↗

NASA NTRS1999

A New Stochastic Equivalent Linearization Implementation for Prediction of Geometrically Nonlinear Vibrations

In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.

Muravyov, Alexander A.↗

NASA NTRS2004

Progressive Response Surfaces

Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. Progressive response surfaces are ones that are built up progressively as global information is added from new sample points in the parameter space. As the response surfaces are globally upgraded based on new information, heuristic indications of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured fashion, or in an unstructured fashion. Whatever the approach, at least in early stages of sampling it is usually desirable to sample the entire parameter space uniformly. At later stages of sampling, depending on the nature of the quantity being resolved, it may be desirable to continue sampling uniformly over the entire parameter space (Progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in early stages of sampling (Adaptive response surfaces). Here we consider Progressive response surfaces where a balanced indication of global response over the parameter space is desired.We use a variant of Moving Least Squares to fit and interpolate structured and unstructured point sets over the parameter space. On a 2-D test problem we compare response surface accuracy for three incremental sampling methods: Progressive Lattice Sampling; Simple-Random Monte Carlo; and Halton Quasi-Monte-Carlo sequences. We are ultimately after a system for constructing efficiently upgradable response surface approximations with reliable error estimates.

Romero, V. J.↗

NASA NTRS2006

A LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR (LASSO) FOR NONLINEAR SYSTEM IDENTIFICATION

Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. The LASSO minimises the residual sum of squares by the addition of a 1 penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. The performance of this LASSO structure detection method was evaluated by using it to estimate the structure of a nonlinear polynomial model. Applicability of the method to more complex systems such as those encountered in aerospace applications was shown by identifying a parsimonious system description of the F/A-18 Active Aeroelastic Wing using flight test data.

Kukreja, Sunil L.↗

NASA NTRS1990

Automated assembly of large space structures

A research program to evaluate telerobotic methods for inspace assembly of large truss structures has been initiated at the NASA Langley Research Center. A commercial robot is mounted on a carriage positioning system and a tetrahedral truss, which is composed of 102 members each 2 m long, is assembled on a rotating motion-base. The facility system is described including details of characterization tests on the truss structure. The current status of the assembly tests is discussed and observations from these tests indicate that no problems have been encountered that would prohibit automated telerobotic assembly from being a viable inspace construction method.

Rhodes, Marvin D.↗

NASA NTRS1977

Linear systems with structure group and their feedback invariants

A general method described by Hermann and Martin (1976) for the study of the feedback invariants of linear systems is considered. It is shown that this method, which makes use of ideas of topology and algebraic geometry, is very useful in the investigation of feedback problems for which the classical methods are not suitable. The transfer function as a curve in the Grassmanian is examined. The general concepts studied in the context of specific systems and applications are organized in terms of the theory of Lie groups and algebraic geometry. Attention is given to linear systems which have a structure group, linear mechanical systems, and feedback invariants. The investigation shows that Lie group techniques are powerful and useful tools for analysis of the feedback structure of linear systems.

Martin, C.↗