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NASA NTRS1989

Input-output oriented computation algorithms for the control of large flexible structures

An overview is given of work in progress aimed at developing computational algorithms addressing two important aspects in the control of large flexible space structures; namely, the selection and placement of sensors and actuators, and the resulting multivariable control law design problem. The issue of sensor/actuator set selection is particularly crucial to obtaining a satisfactory control design, as clearly a poor choice will inherently limit the degree to which good control can be achieved. With regard to control law design, the researchers are driven by concerns stemming from the practical issues associated with eventual implementation of multivariable control laws, such as reliability, limit protection, multimode operation, sampling rate selection, processor throughput, etc. Naturally, the burden imposed by dealing with these aspects of the problem can be reduced by ensuring that the complexity of the compensator is minimized. Our approach to these problems is based on extensions to input/output oriented techniques that have proven useful in the design of multivariable control systems for aircraft engines. In particular, researchers are exploring the use of relative gain analysis and the condition number as a means of quantifying the process of sensor/actuator selection and placement for shape control of a large space platform.

Minto, K. D.↗

NASA NTRS1982

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame tst article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described.

Adelman, H. M.↗

NASA NTRS2012

Deterministic Design Optimization of Structures in OpenMDAO Framework

Nonlinear programming algorithms play an important role in structural design optimization. Several such algorithms have been implemented in OpenMDAO framework developed at NASA Glenn Research Center (GRC). OpenMDAO is an open source engineering analysis framework, written in Python, for analyzing and solving Multi-Disciplinary Analysis and Optimization (MDAO) problems. It provides a number of solvers and optimizers, referred to as components and drivers, which users can leverage to build new tools and processes quickly and efficiently. Users may download, use, modify, and distribute the OpenMDAO software at no cost. This paper summarizes the process involved in analyzing and optimizing structural components by utilizing the framework s structural solvers and several gradient based optimizers along with a multi-objective genetic algorithm. For comparison purposes, the same structural components were analyzed and optimized using CometBoards, a NASA GRC developed code. The reliability and efficiency of the OpenMDAO framework was compared and reported in this report.

Coroneos, Rula M.↗

NASA NTRS2012

Deterministic Design Optimization of Structures in OpenMDAO Framework

Coroneos, Rula M.↗

NASA NTRS1988

Development of a block Lanczos algorithm for free vibration analysis of spinning structures

This paper is concerned with the development of an efficient eigenproblem solution algorithm and an associated computer program for the economical solution of the free vibration problem of complex practical spinning structural systems. Thus, a detailed description of a newly developed block Lanczos procedure is presented in this paper that employs only real numbers in all relevant computations and also fully exploits sparsity of associated matrices. The procedure is capable of computing multiple roots and proves to be most efficient compared to other existing similar techniques.

Gupta, K. K.↗

NASA NTRS1990

Application of a finite element algorithm for high speed viscous flows using structured and unstructured meshes

A higher-order streamline upwinding Petrov-Galerkin finite element method is employed for high speed viscous flow analysis using structured and unstructured meshes. For a Mach 8.03 shock interference problem, successive mesh adaptation was performed using an adaptive remeshing method. Results from the finite element algorithm compare well with both experimental data and results from an upwind cell-centered method. Finite element results for a Mach 14.1 flow over a 24 degree compression corner compare well with experimental data and two other numerical algorithms for both structured and unstructured meshes.

Vemaganti, Gururaja R.↗

NASA NTRS2000

Sensitivity of Latent Heating Profiles to Environmental Conditions: Implications for TRMM and Climate Research

The Tropical Rainfall Measuring Mission (TRMM) as a part of NASA's Earth System Enterprise is the first mission dedicated to measuring tropical rainfall through microwave and visible sensors, and includes the first spaceborne rain radar. Tropical rainfall comprises two-thirds of global rainfall. It is also the primary distributor of heat through the atmosphere's circulation. It is this circulation that defines Earth's weather and climate. Understanding rainfall and its variability is crucial to understanding and predicting global climate change. Weather and climate models need an accurate assessment of the latent heating released as tropical rainfall occurs. Currently, cloud model-based algorithms are used to derive latent heating based on rainfall structure. Ultimately, these algorithms can be applied to actual data from TRMM. This study investigates key underlying assumptions used in developing the latent heating algorithms. For example, the standard algorithm is highly dependent on a system's rainfall amount and structure. It also depends on an a priori database of model-derived latent heating profiles based on the aforementioned rainfall characteristics. Unanswered questions remain concerning the sensitivity of latent heating profiles to environmental conditions (both thermodynamic and kinematic), regionality, and seasonality. This study investigates and quantifies such sensitivities and seeks to determine the optimal latent heating profile database based on the results. Ultimately, the study seeks to produce an optimized latent heating algorithm based not only on rainfall structure but also hydrometeor profiles.

Shepherd, J. Marshall↗

NASA NTRS1993

A Darwinian approach to control-structure design

Genetic algorithms (GA's), as introduced by Holland (1975), are one form of directed random search. The form of direction is based on Darwin's 'survival of the fittest' theories. GA's are radically different from the more traditional design optimization techniques. GA's work with a coding of the design variables, as opposed to working with the design variables directly. The search is conducted from a population of designs (i.e., from a large number of points in the design space), unlike the traditional algorithms which search from a single design point. The GA requires only objective function information, as opposed to gradient or other auxiliary information. Finally, the GA is based on probabilistic transition rules, as opposed to deterministic rules. These features allow the GA to attack problems with local-global minima, discontinuous design spaces and mixed variable problems, all in a single, consistent framework.

Zimmerman, David C.↗

NASA NTRS1993

Analysis of the anisotropic viscoplastic-damage response of composite laminates - Continuum basis and computational algorithms

The mathematical structure underlying the rate equations of a recently-developed constitutive model for the coupled viscoplastic-damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully-implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three-dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time-step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.

Saleeb, A. F.↗

NASA NTRS1995

Adaptive Mesh Refinement in Curvilinear Body-Fitted Grid Systems

To be truly compatible with structured grids, an AMR algorithm should employ a block structure for the refined grids to allow flow solvers to take advantage of the strengths of unstructured grid systems, such as efficient solution algorithms for implicit discretizations and multigrid schemes. One such algorithm, the AMR algorithm of Berger and Colella, has been applied to and adapted for use with body-fitted structured grid systems. Results are presented for a transonic flow over a NACA0012 airfoil (AGARD-03 test case) and a reflection of a shock over a double wedge.

Steinthorsson, Erlendur↗

NASA NTRS1981

Some aspects of algorithm performance and modeling in transient analysis of structures

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit algorithms with variable time steps, known as the GEAR package, is described. Four test problems, used for evaluating and comparing various algorithms, were selected and finite-element models of the configurations are described. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system, and a model of the wing of the space shuttle orbiter. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures).

Adelman, H. M.↗

NASA NTRS1990

Highly parallel sparse Cholesky factorization

Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms.

Gilbert, John R.↗

NASA NTRS1991

Transform methods for precision continuum and control models of flexible space structures

An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality.

Lupi, Victor D.↗

NASA NTRS2001

A Bell-Curved Based Algorithm for Mixed Continuous and Discrete Structural Optimization

An evolutionary based strategy utilizing two normal distributions to generate children is developed to solve mixed integer nonlinear programming problems. This Bell-Curve Based (BCB) evolutionary algorithm is similar in spirit to (mu + mu) evolutionary strategies and evolutionary programs but with fewer parameters to adjust and no mechanism for self adaptation. First, a new version of BCB to solve purely discrete optimization problems is described and its performance tested against a tabu search code for an actuator placement problem. Next, the performance of a combined version of discrete and continuous BCB is tested on 2-dimensional shape problems and on a minimum weight hub design problem. In the latter case the discrete portion is the choice of the underlying beam shape (I, triangular, circular, rectangular, or U).

Kincaid, Rex K.↗

NASA NTRS1989

NASA Workshop on Computational Structural Mechanics 1987, part 3

Computational Structural Mechanics (CSM) topics are explored. Algorithms and software for nonlinear structural dynamics, concurrent algorithms for transient finite element analysis, computational methods and software systems for dynamics and control of large space structures, and the use of multi-grid for structural analysis are discussed.

Sykes, Nancy P.↗

NASA NTRS1999

Implementation of Interaction Algorithm to Non-Matching Discrete Interfaces Between Structure and Fluid Mesh

This paper presents software for solving the non-conforming fluid structure interfaces in aeroelastic simulation. It reviews the algorithm of interpolation and integration, highlights the flexibility and the user-friendly feature that allows the user to select the existing structure and fluid package, like NASTRAN and CLF3D, to perform the simulation. The presented software is validated by computing the High Speed Civil Transport model.

Chen, Shu-Po↗

NASA NTRS1981

Recent developments in quasi-Newton methods for structural analysis and synthesis

Unlike the Newton-Raphson method, quasi-Newton methods by virture of the updates and step length control procedures are globally convergent and hence better suited for the solution of nonlinear problems of structural analysis and synthesis. Extension of quasi-Newton algorithms to large scale problems has led to the development of sparse update algorithms and to economical strategies for evaluating sparse Hessians. Ill-conditioning problems have led to the development of self-scaled variable metric and conjugate gradient algorithms, as well as the use of the singular perturbation theory. This paper emphasizes the effectiveness of such quasi-Newton algorithms for nonlinear structural analysis and synthesis.

Kamat, M. P.↗

NASA NTRS1993

A novel VLSI processor architecture for supercomputing arrays

Design of the processor element for general purpose massively parallel supercomputing arrays is highly complex and cost ineffective. To overcome this, the architecture and organization of the functional units of the processor element should be such as to suit the diverse computational structures and simplify mapping of complex communication structures of different classes of algorithms. This demands that the computation and communication structures of different class of algorithms be unified. While unifying the different communication structures is a difficult process, analysis of a wide class of algorithms reveals that their computation structures can be expressed in terms of basic IP,IP,OP,CM,R,SM, and MAA operations. The execution of these operations is unified on the PAcube macro-cell array. Based on this PAcube macro-cell array, we present a novel processor element called the GIPOP processor, which has dedicated functional units to perform the above operations. The architecture and organization of these functional units are such to satisfy the two important criteria mentioned above. The structure of the macro-cell and the unification process has led to a very regular and simpler design of the GIPOP processor. The production cost of the GIPOP processor is drastically reduced as it is designed on high performance mask programmable PAcube arrays.

Venkateswaran, N.↗