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At least 145 records · Page 8

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NASA NTRS1973

A dual method for optimal control problems with initial and final boundary constraints.

This paper presents two new algorithms belonging to the family of dual methods of centers. The first can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states. The second one can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states and with affine instantaneous inequality constraints on the control. Convergence is established for both algorithms. Qualitative reasoning indicates that the rate of convergence is linear.

Pironneau, O.↗

NASA NTRS1975

Analysis of effect of internal and operating variables on performance of SVDS constraint model (ABIND)

An examination of the factors which modify the simulation of a constraint in the motion of the aft attach points of the orbiter and external tank during separation has been made. The factors considered were both internal (spring and damper constants) and external (friction coefficient and dynamic pressure). The results show that an acceptable choice of spring/damper constant combinations exist over the expected range of the external factors and that the choice is consistent with a practical integration interval. The constraint model is shown to produce about a 10 percent increase in the relative body pitch angles over the unconstrained case whereas the MDC-STL constraint model is shown to produce about a 38 percent increase.

Pendergrass, J. R.↗

NASA NTRS1977

DESAP 2: A structural design program with stress and buckling constraints. Volume 1: Theoretical and user's manual

DESAP 2 is described as a finite element program for computer-automated, minimum weight design of elastic structures with constraints on stresses (including local instability criteria) and buckling loads. No limits are placed on the number of load conditions for stress-constrained design, but only one of these load conditions can be chosen as the potential buckling load. A substantial portion of DESAP 2, particularly the analysis of the prebuckling state, is derived from the SOLID SAP finite element program. The stress-constrained design is based on the classical stress ratio method, which drives the design towards a fully stressed state. The constraints on the buckling load are handled by solving the appropriate optimality criterion by successive iterations. During each iteration, the element sizes determined by the stress ratio method are used as the minimum size constraints. The element subroutines are organized in a manner that permits the user to make additions and changes with a minimal programming effort. Consequently, DESAP 2 can readily be changed into a special-purpose program to handle the user's specific design requirements and failure criteria.

Kiusalaas, J.↗

NASA NTRS1976

General constraints on the Viking biology investigation

The paper discusses some of the constraints pertaining to the Viking mission for detection of life on Mars, within which the Viking experiments were conceived, designed, and developed. The most important limitation to the entire study is the complete information about the nature of Mars, such as the chemical composition of the surface material of Mars and the exact identification of the constituents of that planet. Ways in which celestial mechanics places severe limitations on the Viking biology investigation are discussed. Major engineering constraints are examined relative to the accomodation of biology instrument inside the Viking lander and to the design of the instrument itself. Other constraints discussed concern the operational aspects of the mission and the testing program.

Klein, H. P.↗

NASA NTRS1977

A multilevel approach for minimum weight structural design including local and system buckling constraints

A rational multilevel approach for minimum weight structural design of truss and wing structures including local and system buckling constraints is presented. Overall proportioning of the structure is achieved at the system level subject to strength, displacement and system buckling constraints, while the detailed component designs are carried out separately at the component level satisfying local buckling constraints. Total structural weight is taken to be the objective function at the system level while employing the change in the equivalent system stiffness of the component as the component level objective function. Finite element analysis is used to predict static response while system buckling behavior is handled by incorporating a geometric stiffness matrix capability. Buckling load factors and the corresponding mode shapes are obtained by solving the eigenvalue problem associated with the assembled elastic stiffness and geometric stiffness matrices for the structural system. At the component level various local buckling failure modes are guarded against using semi-empirical formulas. Mathematical programming techniques are employed at both the system and component level.

Schmit, L. A., Jr.↗

NASA NTRS1977

An optimality criterion for sizing members of heated structures with temperature constraints

A thermal optimality criterion is presented for sizing members of heated structures with multiple temperature constraints. The optimality criterion is similar to an existing optimality criterion for design of mechanically loaded structures with displacement constraints. Effectiveness of the thermal optimality criterion is assessed by applying it to one- and two-dimensional thermal problems where temperatures can be controlled by varying the material distribution in the structure. Results obtained from the optimality criterion agree within 2 percent with results from a closed-form solution and with results from a mathematical programming technique. The thermal optimality criterion augments existing optimality criteria for strength and stiffness related constraints and offers the possibility of extension of optimality techniques to sizing structures with combined thermal and mechanical loading.

Rao, G. V.↗

NASA NTRS1978

On the optimization of discrete structures with aeroelastic constraints

The paper deals with the problem of dynamic structural optimization where constraints relating to flutter of a wing (or other dynamic aeroelastic performance) are imposed along with conditions of a more conventional nature such as those relating to stress under load, deflection, minimum dimensions of structural elements, etc. The discussion is limited to a flutter problem for a linear system with a finite number of degrees of freedom and a single constraint involving aeroelastic stability, and the structure motion is assumed to be a simple harmonic time function. Three search schemes are applied to the minimum-weight redesign of a particular wing: the first scheme relies on the method of feasible directions, while the other two are derived from necessary conditions for a local optimum so that they can be referred to as optimality-criteria schemes. The results suggest that a heuristic redesign algorithm involving an optimality criterion may be best suited for treating multiple constraints with large numbers of design variables.

Mcintosh, S. C., Jr.↗

NASA NTRS1979

Investigation and characterization of constraint effects on flaw growth during fatigue loading of composite materials

An investigative program is presented in an attempt to add to the current understanding of constraint effects on the response of composite materials under cyclic loading. The objectives were: (1) to use existing data and to develop additional data in order to establish an understanding and quantitative description of flaw growth in unidirectional lamina under cyclic loading at different load direction to fiber direction angles; (2) to establish a similar understanding and description of flaw growth in lamina which are embedded in laminates between other unflawed lamina; (3) to determine the nature of the influence of constraint on flaw growth by quantitatively comparing the results of the tests; and (4) to develop a model and philosophy of constraints effects based on our investigative results.

Stinchcomb, W. W.↗

NASA NTRS1984

The effect of parking orbit constraints on the optimization of ballistic planetary trajectories

The optimization of ballistic planetary trajectories is developed which includes constraints on departure parking orbit inclination and node. This problem is formulated to result in a minimum total Delta V where the entire constrained injection Delta V is included in the optimization. An additional Delta V is also defined to allow for possible optimization of parking orbit inclination when the launch vehicle orbit capability varies as a function of parking orbit inclination. The optimization problem is formulated using primer vector theory to derive partial derivatives of total Delta V with respect to possible free parameters. Minimization of total Delta V is accomplished using a quasi-Newton gradient search routine. The analysis is applied to an Eros rendezvous mission whose transfer trajectories are characterized by high values of launch asymptote declination during particular launch opportunities. Comparisons in performance are made between trajectories where parking orbit constraints are included in the optimization and trajectories where the constraints are not included.

Sauer, C. G., Jr.↗

NASA NTRS1985

Geomagnetic main field modeling using magnetohydrodynamic constraints

The influence of physical constraints are investigated which may be approximately satisfied by the Earth's liquid core on models of the geomagnetic main field and its secular variation. A previous report describes the methodology used to incorporate nonlinear equations of constraint into the main field model. The application of that methodology to the GSFC 12/83 field model to test the frozen-flux hypothesis and the usefulness of incorporating magnetohydrodynamic constraints for obtaining improved geomagnetic field models is described.

Estes, R. H.↗

NASA NTRS1986

An analytical treatment of discretely varying constraints and inertial properties in multi-body dynamics

A computerized procedure is presented for calculating instantaneous velocity changes due to discrete imposition of constraints, impact or discrete inertial changes. Such discrete changes are impulsive in nature, involve wave propagation and therefore usually require detailed modeling for accurate prediction. It is demonstrated that when modeling is coarse, physically unrealistic results can be produced. The present procedure, which concentrates on finite element analysis, reduces the need for detailed modeling by assuming that only those velocities in the neighborhood of grid points involved in the constraint or those rigidly connected to grid points involved in the constraint need be considered in calculating velocity changes. The procedure utilizes Newton's second law and as such conserves momentum where valid. Sample problems are provided.

Housner, J. M.↗

NASA NTRS1986

Geophysical constraints on the lunar interior

Geophysical constraints relating to the structure, composition, and thermal state of the moon are reviewed in an attempt to evaluate lunar origin models. Particular attention is given to constraints on the bulk composition of the crust and mantle, on the existence and size of a possible metallic core, and on the depth of initial melting and differentiation. It is noted that models such as the binary accretion hypothesis would be capable of producing a bulk moon in accordance with available geophysical constraints.

Hood, L. L.↗

NASA NTRS1987

Order reduction in linear state estimation under performance constraints

The design and analysis of minimal-order state estimators for possibly time-varying linear systems, under constraints on the maximal allowable mean-square error, are considered. A global lower bound on the optimal error is derived, along with a lower bound on the minimal estimator order, needed for meeting the performance constraint. The ideal reduced-order estimator which satisfies the lower bound is derived, along with conditions for its realizability. When the ideal estimator is not realizable, its structure forms a suboptimal estimator, which maintains, in some sense, a local optimality property and is called the pseudoideal estimator. The mean-square error of the pseudoideal estimator defines upper bounds on the optimal error and on the estimator order needed for meeting the performance constraint. The lower and the upper bounds on the order define a reduced search set for the design problem. When the distance between the ideal and the pseudoideal estimators is sufficiently small in a certain numerical sense, the pseudoideal estimator may be considered optimal for practical purposes.

Baram, Yoram↗

NASA NTRS1988

Minimum weight design of rotorcraft blades with multiple frequency and stress constraints

A method is developed for the minimum weight design of helicopter rotor blades having multiple coupled flap-lag natural frequency constraints, in addition to a constraint on the minimum blade autorotation value that will ensure sufficient rotary inertia for autorotation in the event of engine failure. Design variables encompass blade taper ratio, box beam dimensions, and the magnitudes of the nonstructural weights. Optimum designs have been obtained for both rectangular and tapered blades; attention is given to the optimum blade weight effect and the blade mass and stiffness distribution effects of adding constraints on higher frequencies and stresses.

Chattopadhyay, Aditi↗

NASA NTRS1988

Cluster-cluster correlations and constraints on the correlation hierarchy

The hypothesis that galaxies cluster around clusters at least as strongly as they cluster around galaxies imposes constraints on the hierarchy of correlation amplitudes in hierachical clustering models. The distributions which saturate these constraints are the Rayleigh-Levy random walk fractals proposed by Mandelbrot; for these fractal distributions cluster-cluster correlations are all identically equal to galaxy-galaxy correlations. If correlation amplitudes exceed the constraints, as is observed, then cluster-cluster correlations must exceed galaxy-galaxy correlations, as is observed.

Hamilton, A. J. S.↗

NASA NTRS1988

A new constraint on Saturn's zonal gravity harmonics from Voyager observations of an eccentric ringlet

The results obtained by Porco et al. (1984) from an analysis of the kinematics of an eccentric ringlet in Saturn's inner ring are used to add an additional constraint to the gravity solution of Null et al. (1981) and thus to derive the first experimental estimate of the Saturn's J6 gravitational field. On the assumption that the eccentricity of this ringlet is forced by the satellite Titan, the location of the Titan apsidal resonance is determined to an accuracy of + or - 13 km, which in turn provides a strong constraint on Saturn's zonal gravity harmonics. Combining this constraint with the results of Null et all. and adopting a priori values for J8, J10, and J12 based on interior models, new estimates are obtained for the first three zonal gravity coefficients J2, J4, and J6.

Nicholson, Philip D.↗

NASA NTRS1988

Constraints imposed by cosmic evolution towards the development of life

The probability of terrestrial-type life emerging in any other place of the universe will depend on the constraints imposed by cosmic evolution on that particular place. A systematic examination of cosmic constraints, which must have provided the necessary and sufficient conditions for the origin and evolution of life on earth, shows that they are concerned with the nature of the central star, the planetary system, and the specific life-bearing planet, as well as with the chemical and biological evolution processes involved. These constraints or universal requirements for life are briefly described.

Oro, J.↗

NASA NTRS1989

Evidence for an extragalactic component of the far-ultraviolet background and constraints on galaxy evolution for z between 0.1 and 0.6

A sounding rocket experiment that measured the power spectrum of small-scale fluctuations in the far-UV background is described. Evidence is presented that these fluctuations are the integrated light from distant galaxies. If this result is used as an upper limit to the integrated light from galaxies, it provides a constraint on the mean UV luminosity density in the redshift range between 0.1 and 0.6 of L(gal) less than 7 x 10 to the 7th solar luminosities/Mpc. When compared to estimates of the present UV luminosity density, this places a strong constraint on the far-UV evolution of galaxies in the last one-third of a Hubble time. This constraint can be interpreted as a limit on the average past star formation rate relative to the present if dust obscuration was not significantly greater in the past. An upper limit to the average star formation rate is derived.

Martin, Christopher↗