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Research in applied mathematics, numerical analysis, and computer science

Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.

Source record↗

Structural optimization using optimality criteria methods

Optimality criteria methods take advantage of some concepts as those of statically determinate or indeterminate structures, and certain variational principles of structural dynamics, to develop efficient algorithms for the sizing of structures that are subjected to stiffness-related constraints. Some of the methods and iterative strategies developed over the last decade for calculations of the Lagrange multipliers in stressand displacement-limited problems, as well as for satisfying the appropriate optimality criterion, are discussed. The application of these methods are illustrated by solving problems with stress and displacement constraints.

Khot, N. S.↗

Sizing and shape design sensitivity analysis using a hybrid finite element code

The practical (software) implementation of the theoretical FEM-based design sensitivity analysis method of Haug et al. (1986) is described and demonstrated. The fundamental principles of the method are reviewed; the problems involved in applying it to the Engineering Analysis Language (EAL) hybrid FEM code (Whetstone, 1983) are discussed; the formulations for beams, plate bending, and built-up structures are given in detail; programming aspects are considered; and numerical results for sample problems are presented in extensive tables. It is shown that the use of a data-base management system with an FEM such as EAL makes it possible to obtain accurate sizing and shape design sensitivity information using only one program with one data base.

Dopker, Bernhard↗

Maneuvering and vibration control of flexible spacecraft

This paper is concerned with the problem of slewing a large structure in space and suppressing any vibration at the same time. The structure is assumed to undergo large rigid-body motions and small elastic deformations. A perturbation method permits a maneuver strategy independent of the vibration control. Optimal control and pole placement techniques, formulated to include first-order actuator dynamics, are used to suppress the vibration during maneuver. The theory is illustrated by simultaneous maneuvering and vibration control of the Spacecraft Control Laboratory Experiment (SCOLE) model in a space environment.

Meirovitch, L.↗

Ground data systems resource allocation process

The Ground Data Systems Resource Allocation Process at the Jet Propulsion Laboratory provides medium- and long-range planning for the use of Deep Space Network and Mission Control and Computing Center resources in support of NASA's deep space missions and Earth-based science. Resources consist of radio antenna complexes and associated data processing and control computer networks. A semi-automated system was developed that allows operations personnel to interactively generate, edit, and revise allocation plans spanning periods of up to ten years (as opposed to only two or three weeks under the manual system) based on the relative merit of mission events. It also enhances scientific data return. A software system known as the Resource Allocation and Planning Helper (RALPH) merges the conventional methods of operations research, rule-based knowledge engineering, and advanced data base structures. RALPH employs a generic, highly modular architecture capable of solving a wide variety of scheduling and resource sequencing problems. The rule-based RALPH system has saved significant labor in resource allocation. Its successful use affirms the importance of establishing and applying event priorities based on scientific merit, and the benefit of continuity in planning provided by knowledge-based engineering. The RALPH system exhibits a strong potential for minimizing development cycles of resource and payload planning systems throughout NASA and the private sector.

Berner, Carol A.↗

A discourse on sensitivity analysis for discretely-modeled structures

A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.

Adelman, Howard M.↗

Typical testing experience in cryogenic wind tunnels

Airfoil testing as a major activity of many wind tunnels is considered, and emphasis is placed on airfoil testing with sidewall boundary-layer removal, oscillating airfoil testing, and three-dimensional wake topology. Buffeting as the structural response of an aircraft or test model to the aerodynamic excitation produced by separated flows is analyzed, as well as flutter problems and testing techniques. Strain-gage balance studies, optical methods and visualization techniques, and fluid mechanics are examined. Focus is placed on a two-spot laser as a boundary-layer probe, hot-film gages, fluctuating-pressure measurements, skin-friction balance, and nonadiabatic airfoil testing. Boattail afterbody pressure tests are covered, and Space Shuttle Orbiter base drag and launch configuration are discussed.

Kilgore, Robert A.↗

Cryogenic Tank Structure Sizing With Structural Optimization Method

Structural optimization methods in MSC/NASTRAN are used to size substructures and to reduce the weight of a composite sandwich cryogenic tank for future launch vehicles. Because the feasible design space of this problem is non-convex, many local minima are found. This non-convex problem is investigated in detail by conducting a series of' analyses along a design line connecting two feasible designs. Strain constraint violations occur for some design points along the design line. Since MSC/NASTRAN uses gradient based optimization procedures, it does not guarantee that the lowest weight design can be found. In this study, a simple procedure is introduced to create a new starting point based on design variable values from previous optimization analyses. Optimization analysis using this new starting point can produce a lower weight design. Detailed inputs for setting up the MSC/NASTRAN optimization analysis and final tank design results are presented in this paper. Approaches for obtaining further weight reductions are also discussed.

Wang, J. T.↗

Biomimetic Optical Sensor for Real-Time Aircraft Wing Deflection Measurement

Reducing the environmental impact of aviation is a primary goal of NASA aeronautics research. One approach to achieve this goal is to build lighter weight aircraft, which presents complex challenges due to a corresponding increase in structural flexibility. Wing flexibility can adversely affect aircraft performance from the perspective of aerodynamic efficiency and safety. Knowledge of the wing position during flight can aid active control methods designed to mitigate problems due to increased wing flexibility. Current approaches to measuring wing deflection, including strain measurement devices, accelerometers, or GPS solutions, and new technologies such as fiber optic strain sensors, have limitations for their practical application to flexible aircraft control. Hence, it was proposed to use a bio-mimetic optical sensor based on the fly-eye to track wing deflection in real-time. The fly-eye sensor has several advantages over conventional sensors used for this application, including light weight, low power requirements, fast computation, and a small form factor. This paper reports on the fly-eye sensor development and its application to real-time wing deflection measurement.

Frost, Susan A.↗

FEAMAC/CARES Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix Composites

Reported here is a coupling of two NASA developed codes: CARES (Ceramics Analysis and Reliability Evaluation of Structures) with the MAC/GMC (Micromechanics Analysis Code/ Generalized Method of Cells) composite material analysis code. The resulting code is called FEAMAC/CARES and is constructed as an Abaqus finite element analysis UMAT (user defined material). Here we describe the FEAMAC/CARES code and an example problem (taken from the open literature) of a laminated CMC in off-axis loading is shown. FEAMAC/CARES performs stochastic-strength-based damage simulation response of a CMC under multiaxial loading using elastic stiffness reduction of the failed elements.

composite structures↗

A decomposition method for optimization of large-system reliability

This paper considers a decomposition approach for optimization of the reliability of a large system with a general network structure. A 3-level methodology is developed for optimal allocation of available resources among subsystems in order to ensure maximization of system-reliability. The decentralized nature of this methodology greatly reduces the complexity of the large problem and facilitates seeking the optimal solution. Two examples show that the complexity of a large system can be greatly reduced by solving several smaller-dimensional sub-problems iteratively. Sub-problems whose dimensions are small can be efficiently solved by any existing nonlinear programming method. Another important feature of this approach is the possible simplification of the objective function during the solution. This leads in some cases to an analytic solution for the lower-level optimization problems in a 3-level decomposition solution.

Li, Duan↗

Improved Method of Design for Folding Inflatable Shells

An improved method of designing complexly shaped inflatable shells to be assembled from gores was conceived for original application to the inflatable outer shell of a developmental habitable spacecraft module having a cylindrical mid-length section with toroidal end caps. The method is also applicable to inflatable shells of various shapes for terrestrial use. The method addresses problems associated with the assembly, folding, transport, and deployment of inflatable shells that may comprise multiple layers and have complex shapes that can include such doubly curved surfaces as toroids and spheres. One particularly difficult problem is that of mathematically defining fold lines on a gore pattern in a double- curvature region. Moreover, because the fold lines in a double-curvature region tend to be curved, there is a practical problem of how to implement the folds. Another problem is that of modifying the basic gore shapes and sizes for the various layers so that when they are folded as part of the integral structure, they do not mechanically interfere with each other at the fold lines. Heretofore, it has been a common practice to design an inflatable shell to be assembled in the deployed configuration, without regard for the need to fold it into compact form. Typically, the result has been that folding has been a difficult, time-consuming process resulting in a An improved method of designing complexly shaped inflatable shells to be assembled from gores was conceived for original application to the inflatable outer shell of a developmental habitable spacecraft module having a cylindrical mid-length section with toroidal end caps. The method is also applicable to inflatable shells of various shapes for terrestrial use. The method addresses problems associated with the assembly, folding, transport, and deployment of inflatable shells that may comprise multiple layers and have complex shapes that can include such doubly curved surfaces as toroids and spheres. One particularly difficult problem is that of mathematically defining fold lines on a gore pattern in a double- curvature region. Moreover, because the fold lines in a double-curvature region tend to be curved, there is a practical problem of how to implement the folds. Another problem is that of modifying the basic gore shapes and sizes for the various layers so that when they are folded as part of the integral structure, they do not mechanically interfere with each other at the fold lines. Heretofore, it has been a common practice to design an inflatable shell to be assembled in the deployed configuration, without regard for the need to fold it into compact form. Typically, the result has been that folding has been a difficult, time-consuming process resulting in a

Johnson, Christopher J.↗

Multidisciplinary analysis and sensitivity derivatives for isolated helicopter rotors in hover

A new method is presented for using Navier-Stokes results in the system analysis and sensitivity derivative computations for a helicopter rotor in hover. The system coupling includes the interactions between rotor performance, rotor structural properties and aerodynamics (i.e., airfoil shape). Emphasis is placed on the use of high fidelity Navier-Stokes algorithms for the aerodynamic problem. The present formulation is chosen to reduce the number of sensitivity derivative equations and their dimensions as much as possible. In addition, an alternative adjoint formulation is presented which dramatically reduces the computational requirement for disciplines in which there may be a large number of design variables (e.g., aerodynamics). The theoretical method makes use of a combination of derivatives from each discipline; the computation of these derivatives has already been shown to be feasible. Sample computations for the aerodynamic-rotor model coupling and an associated sensitivity derivative are also presented.

Jones, Henry E.↗

Decentralized control of large flexible structures by joint decoupling

This paper presents a novel method to design decentralized controllers for large complex flexible structures by using the idea of joint decoupling. Decoupling of joint degrees of freedom from the interior degrees of freedom is achieved by setting the joint actuator commands to cancel the internal forces exerting on the joint degrees of freedom. By doing so, the interactions between substructures are eliminated. The global structure control design problem is then decomposed into several substructure control design problems. Control commands for interior actuators are set to be localized state feedback using decentralized observers for state estimation. The proposed decentralized controllers can operate successfully at the individual substructure level as well as at the global structure level. Not only control design but also control implementation is decentralized. A two-component mass-spring-damper system is used as an example to demonstrate the proposed method.

LINEAR QUADRATIC REGULATOR MET↗

Time-dependent Structural Analysis of Metal-epoxy Composites

In an effort to reduce structural weight while maintaining structural integrity on the space shuttle and other proposed space vehicles, various composite materials are being evaluated to determine their applicability and reliability in load carrying situations. While most of the composites being considered for structural components are of the metal-metal type, there are some applications for which metal-epoxy composites are proposed. An approximate method is presented to analyze plane stress orthotropic linear viscoelastic problems under isothermal conditions. A computer program which is based on the method was used to solve a simple uniaxial creep problem for a Maxwell type material. This solution is presented and compared with the analytical solution.

Dehoff, P. H.↗

Material and structural studies of metal and polymer matrix composites

Fiber-reinforced composites and design analysis methods for these materials are being developed because of the vast potential of composites for decreasing weight and/or increasing use temperature capability in aerospace systems. These composites have potential for use in airbreathing engine components as well as aeronautical and space vehicle structures. Refractory wire-superalloy composites for use up to 2200 F or more and metal-matrix composites for lower temperature applications such as aerospace structures and turbojet fan and compressor blades are under investigation and are discussed. The development of a number of resin systems, including the polyimides and polyphenylquinoxalines, is described and their potential for use at temperatures approaching 315 C (600 F) is indicated. Various molecular modifications that improve processability and/or increase thermal and oxidative resistance of the resins are also described. Structural analysis methods are discussed for determining the stresses and deformations in complex composite systems. Consideration is also given to residual stresses resulting from the curing process and to the foreign object damage problem in fan blade applications.

Signorelli, R. A.↗

A method for the dynamic and thermal stress analysis of space shuttle surface insulation

The thermal protection system of the space shuttle consists of thousands of separate insulation tiles bonded to the orbiter's surface through a soft strain-isolation layer. The individual tiles are relatively thick and possess nonuniform properties. Therefore, each is idealized by finite-element assemblages containing up to 2500 degrees of freedom. Since the tiles affixed to a given structural panel will, in general, interact with one another, application of the standard direct-stiffness method would require equation systems involving excessive numbers of unknowns. This paper presents a method which overcomes this problem through an efficient iterative procedure which requires treatment of only a single tile at any given time. Results of associated static, dynamic, and thermal stress analyses and sufficient conditions for convergence of the iterative solution method are given.

Ojalvo, I. U.↗