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At least 235 records · Page 13

Chebyshev Polynomials Are Not Always Optimal

The authors are concerned with the problem of finding among all polynomials of degree at most n and normalized to be 1 at c the one with minimal uniform norm on Epsilon. Here, Epsilon is a given ellipse with both foci on the real axis and c is a given real point not contained in Epsilon. Problems of this type arise in certain iterative matrix computations, and, in this context, it is generally believed and widely referenced that suitably normalized Chebyshev polynomials are optimal for such constrained approximation problems. In this note, the authors show that this is not true in general. Moreover, the authors derive sufficient conditions which guarantee that Chebyshev polynomials are optimal. Also, some numerical examples are presented.

CHEBYSHEV APPROXIMATION↗

An Overview of NASA Glenn Research Center's Antenna R&D and Technology Efforts

This viewgraph presentation provides an overview of antenna research and design efforts being performed at NASA's Glenn Research Center. The following type of antenna research projects are discussed: phased array antennas, thin film ferroelectric reflectarray antenna, microelectromechanical systems (MEMs) based antennas and multi-beam antennas. Project overviews, design issues and research problems for each type of antenna system are covered. Additional topics reviewed included: communication systems of the future and a facility description.

Miranda, Felix A.↗

Shape Memory Composite Hybrid Hinge

There are two conventional types of hinges for in-space deployment applications. The first type is mechanically deploying hinges. A typical mechanically deploying hinge is usually composed of several tens of components. It is complicated, heavy, and bulky. More components imply higher deployment failure probability. Due to the existence of relatively moving components among a mechanically deploying hinge, it unavoidably has microdynamic problems. The second type of conventional hinge relies on strain energy for deployment. A tape-spring hinge is a typical strain energy hinge. A fundamental problem of a strain energy hinge is that its deployment dynamic is uncontrollable. Usually, its deployment is associated with a large impact, which is unacceptable for many space applications. Some damping technologies have been experimented with to reduce the impact, but they increased the risks of an unsuccessful deployment. Coalescing strain energy components with shape memory composite (SMC) components to form a hybrid hinge is the solution. SMCs are well suited for deployable structures. A SMC is created from a high-performance fiber and a shape memory polymer resin. When the resin is heated to above its glass transition temperature, the composite becomes flexible and can be folded or packed. Once cooled to below the glass transition temperature, the composite remains in the packed state. When the structure is ready to be deployed, the SMC component is reheated to above the glass transition temperature, and it returns to its as-fabricated shape. A hybrid hinge is composed of two strain energy flanges (also called tape-springs) and one SMC tube. Two folding lines are placed on the SMC tube to avoid excessive strain on the SMC during folding. Two adapters are used to connect the hybrid hinge to its adjacent structural components. While the SMC tube is heated to above its glass transition temperature, a hybrid hinge can be folded and stays at folded status after the temperature is reduced to below its glass transition temperature. After the deployable structure is launched in space, the SMC tube is reheated and the hinge is unfolded to deploy the structure. Based on test results, the hybrid hinge can achieve higher than 99.999% shape recovery. The hybrid hinge inherits all of the good characteristics of a tape-spring hinge such as simplicity, light weight, high deployment reliability, and high deployment precision. Conversely, it eliminates the deployment impact that has significantly limited the applications of a tape-spring hinge. The deployment dynamics of a hybrid hinge are in a slow and controllable fashion. The SMC tube of a hybrid hinge is a multifunctional component. It serves as a deployment mechanism during the deployment process, and also serves as a structural component after the hinge is fully deployed, which makes a hybrid hinge much stronger and stiffer than a tape-spring hinge. Unlike a mechanically deploying hinge that uses relatively moving components, a hybrid hinge depends on material deformation for its packing and deployment. It naturally eliminates the microdynamic phenomenon.

Fang, Houfei↗

On polynomial preconditioning for indefinite Hermitian matrices

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Freund, Roland W.↗

Local strain redistribution corrections for a simplified inelastic analysis procedure based on an elastic finite-element analysis

Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction proposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite-element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure predicts stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load-cycled problems. Neuber-type corrections were derived and incorporated in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was used on a mechanically load-cycled benchmark notched-plate problem. The predicted material response agrees well with the nonlinear finite-element solutions for the problem. The simplified analysis computer program was 0.3% of the central processor unit time required for a nonlinear finite-element analysis.

Kaufman, A.↗

The Initial Orbit Determination (IOD) Problem With Range, Range-Rate and Angles

The Initial Orbit Determination (IOD) problem has been tacked since Laplace, Euler and Gauss in the service of determining the orbits of planets, asteroids, and comets. The measurements that established the orbit characteristics were angles over long arcs.1 The Space Age brought two new measurement types to bear: range and range-rate.2, 3 Initially these measurements were provided by radars through skin-tracking. Soon, however, transponders allowed better measurement accuracy and availability. To date, there are three types of IOD problems: angles only, range and angles, and range and range-rate. The Orion program exposed the need for an additional capability in the case of an extended loss of communication: when the measurements included antenna angles (azimuth and elevation or right-ascension and declination), range and range-rate. This paper contains the details of this new methodology. We will begin with state determination with range, range-rate and angle measurements. First the state estimate, given a sequence of these four time-synchronized measurements, will be analytically developed. Next the covariance matrix associated with this state estimate will be analytically developed. Finally, these will be verified by Monte Carlo simulations.

Christopher D’Souza↗

A unified approach for the application of general perturbation theories to the artificial satellite problem

An Encke-type method is developed as well as a variation of parameters method, both of which use a non-Keplerian reference orbit. The regularized time is used in the numerical integration and the optimum value of n is found for each type of orbit investigated. Accuracy and computation time comparisons are made with a classical Cowell method. It should be noted that the element formulations developed and tested were found to be exceptionally numerically stable in the sense that it was possible to achieve numerical consistency order of very long integration periods - a property not available with the Cowell formulation - and therefore these formulations may be helpful for high precision calculations.

Alfriend, K. T.↗

Fracture of composite orthotropic plates for materials type 2

The fracture problem of laminated plates which consist of orthotropic layers is considered. Symmetrical cracks are located normal to the bimaterial interfaces. The external loads are applied away from the crack region. Three cases are considered: (a) the case of internal cracks; (b) the case of broken laminates; and (c) case of a crack crossing the interface. A general formulation of the problem is given for plane strain and generalized plane stress cases. The singular behavior of stresses at the crack tips and at the interfaces is studied. In each case the stress intensity factors are computed for various crack geometries.

Delale, F.↗

CSM solutions of rotating blade dynamics using integrating matrices

The dynamic behavior of flexible rotating beams continues to receive considerable research attention as it constitutes a fundamental problem in applied mechanics. Further, beams comprise parts of many rotating structures of engineering significance. A topic of particular interest at the present time involves the development of techniques for obtaining the behavior in both space and time of a rotor acted upon by a simple airload loading. Most current work on problems of this type use solution techniques based on normal modes. It is certainly true that normal modes cannot be disregarded, as knowledge of natural blade frequencies is always important. However, the present work has considered a computational structural mechanics (CSM) approach to rotor blade dynamics problems in which the physical properties of the rotor blade provide input for a direct numerical solution of the relevant boundary-and-initial-value problem. Analysis of the dynamics of a given rotor system may require solution of the governing equations over a long time interval corresponding to many revolutions of the loaded flexible blade. For this reason, most of the common techniques in computational mechanics, which treat the space-time behavior concurrently, cannot be applied to the rotor dynamics problem without a large expenditure of computational resources. By contrast, the integrating matrix technique of computational mechanics has the ability to consistently incorporate boundary conditions and 'remove' dependence on a space variable. For problems involving both space and time, this feature of the integrating matrix approach thus can generate a 'splitting' which forms the basis of an efficient CSM method for numerical solution of rotor dynamics problems.

Lakin, William D.↗

Exploring Network-Related Optimization Problems Using Quantum Heuristics

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics.One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.

Wang, Zhihui↗

Study network-related optimization problems using quantum alternating optimization ansatz

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics. One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.

Zhihui Wang↗

Use of the NLPQLP Sequential Quadratic Programming Algorithm to Solve Rotorcraft Aeromechanical Constrained Optimisation Problems

Optimization of the control vector, configuration and aerodynamic surface design potentially offers significant performance enhancement to rotorcraft systems. These analyses indicated that non-linear programming methods that solve a sequence of related quadratic-programming sub-problems could be used successfully to solve these problems. Accordingly, a license for one of the latest versions of Professor Schittkowski's very successful Sequential Quadratic Programming NLPQLP software was obtained and used to experiment and analyze typical optimization problems of the type encountered in various rotorcraft wind tunnel and flight tests. Emphasis was directed toward obtaining efficiency, robustness and speed in computation.

Use of the NLPQLP↗

Structural Model Tuning Capability in an Object-Oriented Multidisciplinary Design, Analysis, and Optimization Tool

Updating the finite element model using measured data is a challenging problem in the area of structural dynamics. The model updating process requires not only satisfactory correlations between analytical and experimental results, but also the retention of dynamic properties of structures. Accurate rigid body dynamics are important for flight control system design and aeroelastic trim analysis. Minimizing the difference between analytical and experimental results is a type of optimization problem. In this research, a multidisciplinary design, analysis, and optimization [MDAO] tool is introduced to optimize the objective function and constraints such that the mass properties, the natural frequencies, and the mode shapes are matched to the target data as well as the mass matrix being orthogonalized.

Lung, Shun-fat↗

Structural Model Tuning Capability in an Object-Oriented Multidisciplinary Design, Analysis, and Optimization Tool

Updating the finite element model using measured data is a challenging problem in the area of structural dynamics. The model updating process requires not only satisfactory correlations between analytical and experimental results, but also the retention of dynamic properties of structures. Accurate rigid body dynamics are important for flight control system design and aeroelastic trim analysis. Minimizing the difference between analytical and experimental results is a type of optimization problem. In this research, a multidisciplinary design, analysis, and optimization (MDAO) tool is introduced to optimize the objective function and constraints such that the mass properties, the natural frequencies, and the mode shapes are matched to the target data as well as the mass matrix being orthogonalized.

Lung, Shun-fat↗

Control of Spacecraft Control Laboratory Experiment (SCOLE) slew maneuvers

This is the second report of a set of two reports on the dynamics and control of slewing maneuvers of NASA Spacecraft Control Laboratory Experiment (SCOLE). The control problem of slewing maneuvers of SCOLE is developed in terms of an arbitrary maneuver about any given axis. The control system is developed for the combined problem of rigid-body slew maneuver and vibration suppression of flexible appendage. The control problem is formulated by incorporating the nonlinear equations derived in the previous report and is expressed in terms of a two-point boundary value problem utilizing a quadratic type of performance index. The two-point boundary value problem is solved as a hierarchical control problem with the overall system being split in terms of two subsystems, namely the slewing of the entire assembly and the vibration suppression of the flexible antenna. The coupling variables between the two dynamical subsystems are identified and these two subsystems for control purposes are treated independently in parallel at the first level. Then the state-space trajectory of the combined problem is optimized at the second level.

Kakad, Y. P.↗

Dynamics and control of flexible spacecraft during and after slewing maneuvers

The dynamics and control of slewing maneuvers of NASA Spacecraft COntrol Laboratory Experiment (SCOLE) are analyzed. The control problem of slewing maneuvers of SCOLE is formulated in terms of an arbitrary maneuver about any given axis. The control system is developed for the combined problem of rigid-body slew maneuver and vibration suppression of the flexible appendage. The control problem formulation incorporates the nonlinear dynamical equations derived previously, and is expressed in terms of a two-point boundary value problem utilizing a quadratic type of performance index. The two-point boundary value problem is solved as a hierarchical control problem with the overall system being split in terms of two subsystems, namely the slewing of the entire assembly and the vibration suppression of the flexible antenna. The coupling variables between the two dynamical subsystems are identified and these two subsystems for control purposes are treated independently in parallel at the first level. Then the state-space trajectory of the combined problem is optimized at the second level.

Kakad, Yogendra P.↗

Torsion Tests of Stiffened Circular Cylinders

The design of curved sheet panels to resist shear involves a consideration of several factors: the buckling resistance of the sheet, the stress at which buckling becomes permanent, and the strength which may be developed beyond the buckling limit by tension-field action. Although some experimental as well as theoretical work has been done on the buckling and tension-field phases of this problem, neither of these types of action appears to be very well understood. The problem is of sufficient importance from the standpoint of aircraft design, it is believed, to warrant further experimental investigation. This report presents the results of the first series of torsion tests of stiffened circular cylinders to be completed in connection with this study at Aluminum Research Laboratories. (author)

Moore, R L↗