SEARCH · Engineering Papers

Results for “Variational methods”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

NASA NTRS1959

Aerodynamic design for supersonic speeds

The aerodynamic phenomena that may profitably be employed by the designer at subsonic speeds seem now to be well understood. At supersonic speeds such phenomena show a greater and more interesting variety. Search for the minimum number of guiding principles of design thus becomes more difficult and more dangerous. Studies which can cover an adequate range of geometrical form are at present limited to the linearized version of aerodynamic theory. Such studies, especially those by variational methods, have disclosed certain basic principles of design for aerodynamic efficiency. In present-day experiments, however, the indicated trends are rather quickly confronted with effects of viscosity and nonlinearities. While the theory indicates that good values of aerodynamic efficiency are possible at supersonic speeds it is not yet clear how closely these expectations may be approached in practice. In the present paper several arrangements of supporting surfaces and bodies are discussed and in some cases comparisons of theory and experiment are made. Finally, certain phenomena connected with lift and drag in a rarefied medium are considered briefly.

Robert T. Jones↗

NASA NTRS1977

Nonlinear flap-lag axial equations of a rotating beam

It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.

Kaza, K. R. V.↗

NASA NTRS1977

Magnetopause shapes - General solutions

The problem of determining the shape of a magnetopause, namely, the tangential discontinuity separating (typically) the magnetic field of a source from external plasma, is reduced to solving an integral equation. No symmetry assumptions whatsoever are used in the derivation, consequently, realistic problems such as model shapes for the earth's magnetosphere (tilted dipole, flowing plasma, etc.) can in principle be treated. Moreover, the magnetic field source itself need not be a simple dipole. A variational method is suggested whereby the optimum parameters for any finite term trial shape are obtained.

Michel, F. C.↗

NASA NTRS1979

Variational description of the positive column with two-stem ionization

The ionization balance in diffusion dominated discharges which depends on both one and two step ionization processes is considered. The Spenke diffusion equation (D sq delta n + neutrino n + sq kn =0) describing such conditions is solved by the Rayleigh-Ritz variational method. Simple analytic approximations to the density profile, and the similarity relation between neutrino,k,D and the discharge dimensions, are derived for planar and cylindrical geometry, and compared with exact computations for certain limiting cases.

Crawford, F. W.↗

NASA NTRS1980

Variational description of the positive column with two-step ionization

The ionization balance in diffusion-dominated discharges may depend on both one- and two-step ionization processes. The Spenke diffusion equation describing such conditions is solved in this paper by the Rayleigh-Ritz variational method. Simple analytic approximations to the density profile, and the similarity relation between the equation parameter, and the discharge dimensions, are derived for planar and cylindrical geometry and compared with exact computations for certain limiting cases.

Crawford, F. W.↗

NASA NTRS1980

Buckling of axially compressed conical shells

The buckling of a truncated elastic conical shell subjected to an axial compression is a classical problem in shell structures. The paper reinvestigates the buckling of an axially compressed truncated conical shell with rigid bulkheads. Two improvements are achieved. First, the condition that the total horizontal displacement must vanish due to rigid bulkhead and axisymmetry is treated as a constraint. This constraint is incorporated into the system through the use of the Lagrange multiplier; then the variational method is used to derive a complete set of boundary conditions for conical shells. Second, the stability is evaluated in the deformed state using the asymptotic solutions of the pair of Donnell-type equations for axisymmetric configuration. The results indicate that the buckling strength of conical shells depends mainly on the condition of the smaller end. In addition to the vertex angle, the distance ratio plays, at least, an equally important role.

Chang, C.-H.↗

NASA NTRS1980

Dynamics and control of a continuum model for a solar power system

An approach for modeling dynamic equations of motion of a plate attached with rigid bodies is presented. The equations of motion are developed using the principle of virtual work. Lagrange multipliers are used as interaction forces and/or moments to maintain prescribed constraints which is the basis of the interconnection between the plate and rigid bodies. The overall approach is unique in the sense that a continuous model described by a family of partial differential equations is established. An approximate formulation by using variational method is established yielding a solution compatible with the assumed degree of approximation. The formulation is useful particularly when parametric study of dynamic response for a satellite power system is desired. As an example, an approximate governing equation of algebraic eigenvalue problem is given for a dual microwave power transmission system. Controller design is discussed.

Juang, J. N.↗

NASA NTRS1980

Simulation studies of a model of high-density metallic hydrogen

Upper bounds for the ground-state energies of liquid and solid phases of metallic hydrogen and metallic deuterium have been calculated with variational methods and Monte Carlo techniques. At four densities (0.8, 1.2, 1.36, and 1.488) crystalline phases are clearly preferred in the sense that the energy difference, when compared to the liquid, is in excess of the errors inherent in the numerical procedures. At a fifth density (1.6), the energy differences between solid and liquid phases are smaller than these errors.

Mon, K. K.↗

NASA NTRS1984

On the magnetic field in the white dwarf Grw + 70.8247 deg

Greenstein (1984) has estimated a 3.5 x 10 to the 8th gauss magnetic field strength for the case of a sharp absorption feature near 1345 A, from the white dwarf Grw + 70.8247 deg that is interpreted as a component of hydrogen Lyman-alpha in a strong magnetic field. A highly accurate multiparameter variational method is the basis of the present deduction of a maximum Lyman-alpha obtainable wavelength of 1342.6 A, with a magnetic field of 5.6 x 10 to the 8th gauss. Alternative explanations of the 1345 A line as H-alpha or H-beta components, or a combination of the two, are given.

Henry, R. J. W.↗

NASA NTRS1984

Modeling of gamma/gamma-prime phase equilibrium in the nickel-aluminum system

A theoretical model is proposed for the determination of phase equilibrium in alloys, taking into consideration dissimilar lattice parameters. Volume-dependent pair interactions are introduced by means of phenomenological Lennard-Jones potentials and the configurational entropy of the system is treated in the tetrahedron approximation of the cluster variation method. The model is applied to the superalloy-relevant, nickel-rich, gamma/gamma-prime phase region of the Ni-Al phase diagram. The model predicts reasonable values for the lattice parameters and the enthalpy of formation as a function of composition, and the calculated phase diagram closely approximates the experimental diagram.

Sanchez, J. M.↗

NASA NTRS1984

VAS data assimilation into a mesoscale model

In numerical weather prediction, one of the arising problems has always been related to insufficient data, especially in cases involving scales smaller than the synoptic rawinsonde network. The Visible Infrared Spin-Scan Radiometer (VISSR) Atmospheric Sounder (VAS) instrument on the Geostationary Operational Environmental Satellite (GOES) can provide mesoscale vertical profiles of temperature and moisture several times over a twelve hour period. However, as this data is only available over a relatively small area at any one time, the VAS data is more suited to data assimilation. A variational method has been developed to assimilate VAS data into a mesoscale model. In the present paper, the assimilation method and VAS data from one case are discussed. It is found that the greatest improvements to the forecast resulted when the VAS data resolved the mesoscale structure of the temperature and relative humidity fields.

Cram, J. M.↗

NASA NTRS1989

Two-phase potential flow

Some features of two recent approaches of two-phase potential flow are presented. The first approach is based on a set of progressive examples that can be analyzed using common techniques, such as conservation laws, and taken together appear to lead in the direction of a general theory. The second approach is based on variational methods, a classical approach to conservative mechanical systems that has a respectable history of application to single phase flows. This latter approach, exemplified by several recent papers by Geurst, appears generally to be consistent with the former approach, at least in those cases for which it is possible to obtain comparable results. Each approach has a justifiable theoretical base and is self-consistent. Moreover, both approaches appear to give the right prediction for several well-defined situations.

Wallis, Graham B.↗

NASA NTRS1990

On the level of skill in predicting maximum sunspot number - A comparative study of single variate and bivariate precursor techniques

The level of skill in predicting the size of the sunspot cycle is investigated for the two types of precursor techniques, single variate and bivariate fits, both applied to cycle 22. The present level of growth in solar activity is compared to the mean level of growth (cycles 10-21) and to the predictions based on the precursor techniques. It is shown that, for cycle 22, both single variate methods (based on geomagnetic data) and bivariate methods suggest a maximum amplitude smaller than that observed for cycle 19, and possibly for cycle 21. Compared to the mean cycle, cycle 22 is presently behaving as if it were a +2.6 sigma cycle (maximum amplitude of about 225), which means that either it will be the first cycle not to be reliably predicted by the combined precursor techniques or its deviation relative to the mean cycle will substantially decrease over the next 18 months.

Wilson, Robert M.↗

NASA NTRS1989

Analytical and computational models of shells; Proceedings of the Symposium, ASME Winter Annual Meeting, San Francisco, CA, Dec. 10-15, 1989

Topics presented include asymptotic analysis and computation for shells, the edge effects in the Reissner-Mindlin plate theory, nonlinear problems of geometrically exact shell theories, and developments in variational methods for high performance plate and shell elements. Also presented are an assumed strain solid element model for geometrically nonlinear shell analysis, shell finite elements with six degrees of freedom per node, hierarchic plate and shell models based on p-extension, and a simple shell element formulation for large-scale elastoplastic analysis. Also discussed are the assessment of computational models for multilayered composite cylinders, shell models for impact analysis, analysis of shell structures subjected to contact-impacts, and the application of shell theory to cardiac mechanics.

Noor, Ahmed K.↗

NASA NTRS1991

Thermal buckling and postbuckling of symmetrically laminated composite plates

The thermal buckling and postbuckling response of symmetrically laminated composite plates are discussed. Using variational methods in conjunction with a Rayleigh-Ritz formulation, thermal buckling and postbuckling are investigated for two laminates, a (+/- 45/0/90) and a (+/- 45/02), under two different simple support conditions, fixed and sliding. These laminates are subjected to the condition of a uniform temperature change. The effects of the principal material axis not being aligned with the edges of the plate, referred to here as material axis skewing, are also investigated. Although differences between buckling temperatures for the two support conditions were small, support conditions can have a large influence on thermal postbuckling response. In general, plates with fixed simple supports deflect more than plates with sliding simple supports. In addition, support conditions can influence modal interaction. Skewing of the material axis decreases the buckling temperatures of both laminates and, like fixed support conditions, causes increased postbuckling deflections. Skewing also influences modal interaction.

Meyers, C. A.↗

NASA NTRS1991

On optimal infinite impulse response edge detection filters

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Sarkar, Sudeep↗

NASA NTRS1992

Importance of parametrizing constraints in quantum-mechanical variational calculations

In variational calculations of quantum mechanics, constraints are sometimes imposed explicitly on the wave function. These constraints, which are deduced by physical arguments, are often not uniquely defined. In this work, the advantage of parametrizing constraints and letting the variational principle determine the best possible constraint for the problem is pointed out. Examples are carried out to show the surprising effectiveness of the variational method if constraints are parameterized. It is also shown that misleading results may be obtained if a constraint is not parameterized.

Chung, Kwong T.↗

NASA NTRS1992

Free-edge effects in laminates under extension, bending and twisting. II - Sublaminate/layer modeling and analysis

The stress-function-based variational method of Yin (1991) is extended and modified into a combined layer/sublaminate approach applicable to a laminated strip composed of a large number of differently orientated, anisotropic elastic plies. Lekhnitskii's (1963) stress functions are introduced into two interior layers adjacent to a particular interface. The remaining layers are grouped into an upper sublaminate and a lower sublaminate. The stress functions are expanded in truncated power series of the thickness coordinate, and the differential equations governing the coefficient functions are derived by using the complementary virtual work principle. The layer/sublaminate approach limits the dimension of the eigenvalue problem to a fixed number irrespective of the number of layers in the sublaminate, so that reasonably accurate solutions of the interlaminar stresses can be computed with extreme ease. For symmetric, four-layer, angle-ply and cross-ply laminates, a comparison of the previous analysis results based on the pure layer model and new results based on two different layer/sublaminate models indicates reasonable over-all agreement in the interlaminar stresses and superior agreement in the total peeling and shearing force.

Yin, Wan-Lee↗