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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
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NASA NTRS1989

A hybrid perturbation-Galerkin method for differential equations containing a parameter

A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1991

The semi-infinite strip problem in the mechanics of composite materials

Many problems, ranging from interface-fiber fracture to determining the strength of fiber-matrix interfaces in composites, can be greatly assisted by a complete understanding of the boundary value problem of a semi-infinite strip. The specific boundary value problem of a semi-infinite strip with symmetric tractions on the transverse edges and normal loads on the end is investigated in the present study. The nature of the singular behavior in the slope of the end vertical displacement at the corner points is found. An asymptotic analysis of the solution shows that, depending on the nature of the applied stresses in the vicinity of the corner points, the singularity in the slope of the end vertical displacement may either be a power or logarithmic type, both, or not exist at all. Illustrative examples, for which exact or numerical results are known, are given. Numerical procedures are also given. The direct application of the results of the paper are illustrated for several problems in the mechanics of composite materials.

Kaw, Autar K.↗
NASA NTRS1973

Numerical integration of shell equations using the field method.

The 'field method' for the numerical solution of even-order linear boundary-value problems in ordinary differential equations is formulated. This method converts the boundary-value problem into two successive initial-value problems, which may be solved by standard forward integration techniques. The method has been implemented in a computer program to calculate the static response of ring-stiffened branched shells of revolution to asymmetric loads. For such problems the field method eliminates the well-known numerical problem of 'long subintervals' and also executes operations significantly faster than other numerical integration methods.

Cohen, G. A.↗
NASA NTRS1989

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.↗
NASA NTRS1972

A reciprocal theorem for a mixture theory

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Martin, C. J.↗
NASA NTRS1987

A global time-dependent model of thunderstorm electricity. I - Mathematical properties of the physical and numerical models

A time-dependent model is introduced that can be used to simulate the interaction of a thunderstorm with its global electrical environment. The model solves the continuity equation of the Maxwell current, which is assumed to be composed of the conduction, displacement, and source currents. Boundary conditions which can be used in conjunction with the continuity equation to form a well-posed initial-boundary value problem are determined. Properties of various components of solutions of the initial-boundary value problem are analytically determined. The results indicate that the problem has two time scales, one determined by the background electrical conductivity and the other by the time variation of the source function. A numerical method for obtaining quantitative results is introduced, and its properties are studied. Some simulation results on the evolution of the displacement and conduction currents during the electrification of a storm are presented.

Browning, G. L.↗
NASA NTRS1987

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.↗
NASA NTRS1983

Inelastic stress analyses at finite deformation through complementary energy approaches

A new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is based upon a generalization of de Veubeke's (1972) complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and the resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a boundary value problem (for stress rate and velocity) and an initial value problem (for total stress and deformation). A discussion of the numerical treatment of the boundary value problem is followed by a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability, and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.

Atluri, S. N.↗
NASA NTRS1990

Optimal trajectories based on linear equations

The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.

Carter, Thomas E.↗
NASA NTRS1983

Numerical computations on one-dimensional inverse scattering problems

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

Dunn, M. H.↗
NASA NTRS1984

Numerical computations on one-dimensional inverse scattering problems

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

Dunn, M. H.↗
NASA NTRS2010

Optimal Low Energy Earth-Moon Transfers

The optimality of a low-energy Earth-Moon transfer is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the ballistic lunar capture trajectory is examined to determine whether one or more additional impulses may improve on the cost of the transfer.

Griesemer, Paul Ricord↗
NASA NTRS1957

Torsional stiffness of thin-walled shells having reinforcing cores and rectangular, triangular, or diamond cross section

A theoretical investigation has been made of the Saint-Venant torsion of certain composite bars. These bars are composed of two materials -- one material in the form of a thin-walled cylindrical shell and the other material in the form of a core which fills the interior of the shell and is bonded to it. An approximate boundary-value problem is formulated on assumptions similar to those of the theory of torsion of hollow thin-walled shells (Bredt theory). This boundary-value problem is solved exactly for a rectangular cross section and approximately for slender triangular and diamond cross sections. Results for the torsional stiffness constants are presented graphically.

Mccomb, Harvey G , Jr↗