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At least 163 records · Page 9

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NASA NTRS1977

Mixed isoparametric finite element models of laminated composite shells

Mixed shear-flexible isoparametric elements are presented for the stress and free vibration analysis of laminated composite shallow shells. Both triangular and quadrilateral elements are considered. The 'generalized' element stiffness, consistent mass, and consistent load coefficients are obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Group-theoretic techniques are used in conjunction with computerized symbolic integration to obtain analytic expressions for the stiffness, mass and load coefficients. A procedure is outlined for efficiently handling the resulting system of algebraic equations. The accuracy of the mixed isoparametric elements developed is demonstrated by means of numerical examples, and their advantages over commonly used displacement elements are discussed.

Noor, A. K.↗

NASA NTRS1977

A finite element algorithm for sound propagation in axisymmetric ducts containing compressible mean flow

The described investigation is concerned with he development of a finite element scheme which can be used in a study of the acoustics of aircraft-engine ducts. In the absence of suitable variational principles for acoustic fluctuations within an aircraft fan engine, an acoustic analysis must proceed directly from the differential equations which describe compressible flow. The derived equations cannot be solved algebraically. The numerical technique used for solving them makes use of a linear rectangular element of a type considered by Zienkiewicz (1971). Attention is given to aspects of element derivation, the global matrix assembly, the solution of the matrix equation, questions of acoustic attenuation, and illustrations of the potential of the current model in duct optimization.

Abrahamson, A. L.↗

NASA NTRS1978

A mean spherical model for soft potentials: The hard core revealed as a perturbation

The mean spherical approximation for fluids is extended to treat the case of dense systems interacting via soft-potentials. The extension takes the form of a generalized statement concerning the behavior of the direct correlation function c(r) and radial distribution g(r). From a detailed analysis that views the hard core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

Rosenfeld, Y.↗

NASA NTRS1978

Axisymmetric ideal MHD stellar wind flow

The ideal MHD equations are reduced to a single equation under the assumption of axisymmetric flow. A variational principle from which the equation is derivable is given. The characteristics of the equation are briefly discussed. The equation is used to rederive the theorem of Gussenhoven and Carovillano.

Heinemann, M.↗

NASA NTRS1978

Finite elements and finite differences for transonic flow calculations

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Hafez, M. M.↗

NASA NTRS1978

Variationally consistent approximation scheme for charge transfer

The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.

Halpern, A. M.↗

NASA NTRS1979

Acoustic power balance in lined ducts

It is shown that the two common definitions of acoustic energy density and intensity in uniform unlined ducts carrying uniform flow are compatible to the extent that both energy densities can be used in an appropriate variational principle to derive the convected wave equation. When the duct walls are lined both energy densities must be modified to account for the wall energy density. This results in a new energy conservation equation which utilizes a modified definition of axial power and accounts for wall dissipation. Computations in specific cases demonstrate the validity of the modified acoustic energy relation.

Eversman, W.↗

NASA NTRS1979

Variational formulation of Budyko-Sellers climate models

A class of simple climate models including those of the Budyko-Sellers type are formulated from a variational principle. A functional is constructed for the zonally averaged mean annual temperature field such that extrema of the functional occur when the climate satisfies the usual energy-balance equation. Local minima of the functional correspond to stable solutions while saddle points correspond to unstable solutions. The technique can be used to construct approximate solutions from trial functions and to carry out finite-amplitude stability analyses. A spectral example is given in explicit detail.

North, G. R.↗

NASA NTRS1979

Second order nonlinear equations of motion for spinning highly flexible line-elements

A formulation is given for the second order nonlinear equations of motion for spinning line-elements having little or no intrinsic structural stiffness. Such elements have been employed in recent studies of structural concepts for future large space structures such as the Heliogyro solar sailer. The derivation is based on Hamilton's variational principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line-element dynamics. For comparison with previous work, the nonlinear equations are reduced to a linearized form frequently found in the literature. The comparison has revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.

Salama, M.↗

NASA NTRS1980

Modified Iterative Extended Hueckel. 1: Theory

Iterative Extended Huekel is modified by inclusion of explicit effective internuclear and electronic interactions. The one electron energies are shown to obey a variational principle because of the form of the effective electronic interactions. The modifications permit mimicking of aspects of valence bond theory with the additional feature that the energies associated with valence bond type structures are explicitly calculated. In turn, a hybrid molecular, orbital valence, bond scheme is introduced which incorporates variant total molecular electronic density distributions similar to the way that Iterative Extended Hueckel incorporates atoms.

Aronowitz, S.↗

NASA NTRS1980

Solutions of contact problems by the assumed stress hybrid model

A method was developed for contact problems which may be either frictional or frictionless and may involve extensive sliding between deformable bodies. It was based on an assumed stress hybrid approach and on an incremental variational principle for which the Euler's equations of the functional include the equilibrium and compatibility conditions at the contact surface. The tractions at an assumed contact surface were introduced as Lagrangian multipliers in the formulation. It was concluded from the results of several example solutions that the extensive sliding contact between deformable bodies can be solved by the present method.

Kubomura, K.↗

NASA NTRS1979

Mean-spherical model for soft potentials - The hard core revealed as a perturbation

The mean-spherical approximation for fluids is extended to treat the case of dense systems interacting via soft potentials. The extension takes the form of a generalized statement concerning the behavior of the direct-correlation function c(r) and the radial-distribution function g(r). From a detailed analysis that views the hard-core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

Rosenfeld, Y.↗

NASA NTRS1981

Nonlinear magnetohydrodynamic stability

The computer code developed by Bauer et al. (1978) for the study of the magnetohydrodynamic equilibrium and stability of a plasma in toroidal geometry is extended so that the growth rates of instabilities may be estimated more accurately. The original code, which is based on the variational principle of ideal magnetohydrodynamics, is upgraded by the introduction of a nonlinear formula for the growth rate of an unstable mode which acts as a quantitative measure of instability that is important in estimating numerical errors. The revised code has been applied to the determination of the nonlinear saturation, ballooning modes and beta limits for tokamaks, stellarators and torsatrons.

Bauer, F.↗

NASA NTRS1981

Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams

Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.

Noor, A. K.↗

NASA NTRS1982

Improved perfect-fluid energy-momentum tensor with spin in Einstein-Cartan space-time

The description of the spin given here is classical in that it is intrinsic but not quantized. The approach in this matter is similar to, for example, the work of Bailey and Israel (1973, 1975, 1979), where the fluid particles, which have intrinsic spin, may be galaxies or clusters of galaxies. The elementary particles of these objects and the 'ferromagnetic alignment' of their quantum spins are not resorted to in order to describe a fluid with spin. Physically this means that the equation of motion for the spin tensor is a modified Fermi-Walker transport equation (Misner et al., 1973), arising as a direct result of the inclusion of spin as an intrinsic variable in the thermodynamic description of the internal energy. The variables in this description are classical variables throughout and are not microscopic fields. An improved perfect-fluid energy-momentum tensor that includes spin and torsion is presented. Use is made of a Lagrangian variational principle based on the tetrad formalism of Halbwach (1960) and the method od constraints of Ray (1972).

Ray, J. R.↗

NASA NTRS1982

Electrostriction in liquid He-4

The two-fluid model of liquid He-4 is extended to include effects of applied electric fields. New terms that account for electrostriction in equations of motion for superfluid and normal fluid are derived with the aid of a variational principle subject to the assumption that the Clausius-Mossotti relation for the dielectric constant is applicable. Corresponding additions to conservation laws for momentum and energy are presented.

Jackson, H. W.↗

NASA NTRS1982

An investigation of equilibrium concepts

A different approach to modeling of the thermochemistry of rocket engine combustion phenomena is presented. The methodology described is based on the hypothesis of a new variational principle applicable to compressible fluid mechanics. This hypothesis is extended to treat the thermochemical behavior of a reacting (equilibrium) gas in an open system.

Prozan, R. J.↗

NASA NTRS1982

Spinning fluids in general relativity

General relativity field equations are employed to examine a continuous medium with internal spin. A variational principle formerly applied in the special relativity case is extended to the general relativity case, using a tetrad to express the spin density and the four-velocity of the fluid. An energy-momentum tensor is subsequently defined for a spinning fluid. The equations of motion of the fluid are suggested to be useful in analytical studies of galaxies, for anisotropic Bianchi universes, and for turbulent eddies.

Ray, J. R.↗