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NASA NTRS1979

Evaluation of improved algorithms for nonlinear transient structural heat transfer

The paper presents the evaluation of algorithms having potential for reducing computer time to integrate large systems of equations governing nonlinear transient heat transfer in complex structures. A series of test problems is being developed to test two algorithms. The Shuttle Orbiter frame model having 190 nodes was the subject of an analytical/experimental study. Plans are to perform calculations for the complete wing model having about 4000 nodes as well as a regional (plug) model having about 200 nodes.

Adelman, H. M.↗

NASA NTRS1980

Progress in passive microwave remote sensing - Nonlinear retrieval techniques

A variety of nonlinear retrieval methods have been applied to passive microwave remote sensing problems. These problems can be characterized in part by the degree to which their underlying physics and statistics can be understood and characterized in a simple way. Four examples of varying complexity are considered here; the simplest problem requires only analytic expressions for retrievals, whereas the most complex problem has been handled only with pattern classification techniques. The four examples are: (1) Doppler measurements of winds at 70 to 100 km, (2) retrieval of atmospheric water vapor profiles using the opaque 183-GHz water vapor resonance, (3) retrieval of snow accumulation rate by means of combined theoretical and empirical procedures, and (4) classification of diverse polar terrain by means of pattern recognition techniques.

Staelin, D. H.↗

NASA NTRS1983

A multigrid method for the Euler equations

A multigrid algorithm has been developed for the numerical solution of the steady two-dimensional Euler equations. Flux vector splitting and one-sided differencing are employed to define the spatial discretization. Newton's method is used to solve the nonlinear equations, and a multigrid solver is used on each linear problem. The relaxation scheme for the linear problems is symmetric Gauss-Seidel. Standard restriction and interpolation operators are employed. Local mode analysis is used to predict the convergence rate of the multigrid process on the linear problems. Computed results for transonic flows over airfoils are presented.

Jespersen, D. C.↗

NASA NTRS1984

Vibration characteristics of the HPOTP (High-Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Engine)

Attention is given to rotor dynamic problems that have been encountered and eliminated in the course of Space Shuttle Main Engine (SSME) development, as well as continuing, subsynchronous problems which are being encountered in the development of a 109-percent power level engine. The basic model for the SSME's High Pressure Oxygen Turbopump (HPOTP) encompasses a structural dynamic model for the rotor and housing, and component models for the liquid and gas seals, turbine clearance excitation forces, and impeller diffuser forces. Linear model results are used to examine the synchronous response and stability characteristics of the HPOTP, with attention to bearing load and stability problems associated with the second critical speed. Differences between linear and nonlinear model results are discussed and explained in terms of simple models. Simulation results indicate that while synchronous bearing loads can be reduced, subsynchronous motion is not eliminated by seal modifications.

Childs, D. W.↗

NASA NTRS1984

Estimation of regions of attraction and ultimate boundedness for multiloop LQ regulators

Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.

Joshi, S. M.↗

NASA NTRS1987

An Exponential Finite Difference Technique for Solving Partial Differential Equations

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

Handschuh, Robert F.↗

NASA NTRS1987

Nonlinear/linear unified thermal stress formulations - Transfinite element approach

A new unified computational approach for applicability to nonlinear/linear thermal-structural problems is presented. Basic concepts of the approach including applicability to nonlinear and linear thermal structural mechanics are first described via general formulations. Therein, the approach is demonstrated for thermal stress and thermal-structural dynamic applications. The proposed transfinite element approach focuses on providing a viable hybrid computational methodology by combining the modeling versatility of contemporary finite element schemes in conjunction with transform techniques and the classical Bubnov-Galerkin schemes. Comparative samples of numerical test cases highlight the capabilities of the proposed concepts.

Tamma, Kumar K.↗

NASA NTRS1990

Efficient Implementation of Minimal Polynomial and Reduced Rank Extrapolation Methods

The minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equation. Their definitions involve some linear least squares problems, and this causes difficulties in their numerical implementation. Timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems.

Sidi, Avram↗

NASA NTRS1991

On computing the global time-optimal motions of robotic manipulators in the presence of obstacles

A method for computing the time-optimal motions of robotic manipulators is presented that considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacles. The optimization problem is reduced to a search for the time-optimal path in the n-dimensional position space. A small set of near-optimal paths is first efficiently selected from a grid, using a branch and bound search and a series of lower bound estimates on the traveling time along a given path. These paths are further optimized with a local path optimization to yield the global optimal solution. Obstacles are considered by eliminating the collision points from the tessellated space and by adding a penalty function to the motion time in the local optimization. The computational efficiency of the method stems from the reduced dimensionality of the searched spaced and from combining the grid search with a local optimization. The method is demonstrated in several examples for two- and six-degree-of-freedom manipulators with obstacles.

Shiller, Zvi↗

NASA NTRS1992

Asteroid proper elements and secular resonances

In a series of papers (e.g., Knezevic, 1991; Milani and Knezevic, 1990; 1991) we reported on the progress we were making in computing asteroid proper elements, both as regards their accuracy and long-term stability. Additionally, we reported on the efficiency and 'intelligence' of our software. At the same time, we studied the associated problems of resonance effects, and we introduced the new class of 'nonlinear' secular resonances; we determined the locations of these secular resonances in proper-element phase space and analyzed their impact on the asteroid family classification. Here we would like to summarize the current status of our work and possible further developments.

Knezevic, Zoran↗

NASA NTRS1944

Applicability of Similarity Principles to Structural Models

A systematic account is given in part I of the use of dimensional analysis in constructing similarity conditions for models and structures. The analysis covers large deflections, buckling, plastic behavior, and materials with nonlinear stress-strain characteristics, as well as the simpler structural problems. (author)

Goodier, J N↗

NASA NTRS1993

Active control of acoustic pressure fields using smart material technologies

An overview describing the use of piezoceramic patches in reducing noise in a structural acoustics setting is presented. The passive and active contributions due to patches which are bonded to an Euler-Bernoulli beam or thin shell are briefly discussed and the results are incorporated into a 2-D structural acoustics model. In this model, an exterior noise source causes structural vibrations which in turn lead to interior noise as a result of nonlinear fluid/structure coupling mechanism. Interior sound pressure levels are reduced via patches bonded to the flexible boundary (a beam in this case) which generate pure bending moments when an out-of-phase voltage is applied. Well-posedness results for the infinite dimensional system are discussed and a Galerkin scheme for approximating the system dynamics is outlined. Control is implemented by using linear quadratic regulator (LQR) optimal control theory to calculate gains for the linearized system and then feeding these gains back into the nonlinear system of interest. The effectiveness of this strategy for this problem is illustrated in an example.

Banks, H. T.↗

NASA NTRS1996

Parallelization of a Parabolized Navier-Stokes Solver with a Design Optimizer

The design of future supersonic aircraft, such as the High Speed Civil Transport (HSCT), will rely heavily on computational methods for aircraft design and the prediction of the complex aerodynamics encountered in flight. Parabolized Navier-Stokes (PNS) equation flow solvers are recognized as efficient and accurate computational tools for the solution of supersonic and hypersonic flow-fields, while design optimizers have the potential to be valuable tools within the overall design process. Presently, however, the execution of the flow solver in conjunction with a design optimizer presents a computationally intensive and formidable problem. To meet the challenges and increasing demand for multidisciplinary numerical tools which are faster, more robust and provide greater functionality, alternative strategies are explored to increase computational throughput by coupling a design optimizer and flow solver in a parallel processing environment. To address this problem the parallel processing of a PNS flow solver with a nonlinear constraint design optimizer is investigated as an alternative computational method.

Pallis, J. M.↗

NASA NTRS2003

Binary-Phase Fourier Gratings for Nonuniform Array Generation

We describe a design method for a binary-phase Fourier grating that generates an array of spots with nonuniform, user-defined intensities symmetric about the zeroth order. Like the Dammann fanout grating approach, the binary-phase Fourier grating uses only two phase levels in its grating surface profile to generate the final spot array. Unlike the Dammann fanout grating approach, this method allows for the generation of nonuniform, user-defined intensities within the final fanout pattern. Restrictions governing the specification and realization of the array's individual spot intensities are discussed. Design methods used to realize the grating employ both simulated annealing and nonlinear optimization approaches to locate optimal solutions to the grating design problem. The end-use application driving this development operates in the near- to mid-infrared spectrum - allowing for higher resolution in grating specification and fabrication with respect to wavelength than may be available in visible spectrum applications. Fabrication of a grating generating a user-defined nine spot pattern is accomplished in GaAs for the near-infrared. Characterization of the grating is provided through the measurement of individual spot intensities, array uniformity, and overall efficiency. Final measurements are compared to calculated values with a discussion of the results.

Keys, Andrew S.↗

NASA NTRS2004

Computation of Sensitivity Derivatives of Navier-Stokes Equations using Complex Variables

Accurate computation of sensitivity derivatives is becoming an important item in Computational Fluid Dynamics (CFD) because of recent emphasis on using nonlinear CFD methods in aerodynamic design, optimization, stability and control related problems. Several techniques are available to compute gradients or sensitivity derivatives of desired flow quantities or cost functions with respect to selected independent (design) variables. Perhaps the most common and oldest method is to use straightforward finite-differences for the evaluation of sensitivity derivatives. Although very simple, this method is prone to errors associated with choice of step sizes and can be cumbersome for geometric variables. The cost per design variable for computing sensitivity derivatives with central differencing is at least equal to the cost of three full analyses, but is usually much larger in practice due to difficulty in choosing step sizes. Another approach gaining popularity is the use of Automatic Differentiation software (such as ADIFOR) to process the source code, which in turn can be used to evaluate the sensitivity derivatives of preselected functions with respect to chosen design variables. In principle, this approach is also very straightforward and quite promising. The main drawback is the large memory requirement because memory use increases linearly with the number of design variables. ADIFOR software can also be cumber-some for large CFD codes and has not yet reached a full maturity level for production codes, especially in parallel computing environments.

Vatsa, Veer N.↗

NASA NTRS2007

Comparison of Fixed and Variable Time Step Trajectory Integration Methods for Cislunar Trajectories

Due to the nonlinear nature of the Earth-Moon-Sun three-body problem and non-spherical gravity, CEV cislunar targeting algorithms will require many propagations in their search for a desired trajectory. For on-board targeting especially, the algorithm must have a simple, fast, and accurate propagator to calculate a trajectory with reasonable computation time, and still be robust enough to remain stable in the various flight regimes that the CEV will experience. This paper compares Cowell s method with a fourth-order Runge- Kutta integrator (RK4), Encke s method with a fourth-order Runge-Kutta- Nystr m integrator (RKN4), and a method known as Multi-Conic. Additionally, the study includes the Bond-Gottlieb 14-element method (BG14) and extends the investigation of Encke-Nystrom methods to integrators of higher order and with variable step size.

Weeks, ichael W.↗

NASA NTRS2007

An Aeroelastic Analysis of a Thin Flexible Membrane

Studies have shown that significant vehicle mass and cost savings are possible with the use of ballutes for aero-capture. Through NASA's In-Space Propulsion program, a preliminary examination of ballute sensitivity to geometry and Reynolds number was conducted, and a single-pass coupling between an aero code and a finite element solver was used to assess the static aeroelastic effects. There remain, however, a variety of open questions regarding the dynamic aeroelastic stability of membrane structures for aero-capture, with the primary challenge being the prediction of the membrane flutter onset. The purpose of this paper is to describe and begin addressing these issues. The paper includes a review of the literature associated with the structural analysis of membranes and membrane utter. Flow/structure analysis coupling and hypersonic flow solver options are also discussed. An approach is proposed for tackling this problem that starts with a relatively simple geometry and develops and evaluates analysis methods and procedures. This preliminary study considers a computationally manageable 2-dimensional problem. The membrane structural models used in the paper include a nonlinear finite-difference model for static and dynamic analysis and a NASTRAN finite element membrane model for nonlinear static and linear normal modes analysis. Both structural models are coupled with a structured compressible flow solver for static aeroelastic analysis. For dynamic aeroelastic analyses, the NASTRAN normal modes are used in the structured compressible flow solver and 3rd order piston theories were used with the finite difference membrane model to simulate utter onset. Results from the various static and dynamic aeroelastic analyses are compared.

Scott, Robert C.↗

NASA NTRS2008

Aircraft Loss-of-Control Accident Prevention: Switching Control of the GTM Aircraft with Elevator Jam Failures

Switching control, servomechanism, and H2 control theory are used to provide a practical and easy-to-implement solution for the actuator jam problem. A jammed actuator not only causes a reduction of control authority, but also creates a persistent disturbance with uncertain amplitude. The longitudinal dynamics model of the NASA GTM UAV is employed to demonstrate that a single fixed reconfigured controller design based on the proposed approach is capable of accommodating an elevator jam failure with arbitrary jam position as long as the thrust control has enough control authority. This paper is a first step towards solving a more comprehensive in-flight loss-of-control accident prevention problem that involves multiple actuator failures, structure damages, unanticipated faults, and nonlinear upset regime recovery, etc.

Chang, Bor-Chin↗

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