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At least 451 records · Page 25

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NASA NTRS1983

Robust penalty method for structural synthesis

The Sequential Unconstrained Minimization Technique (SUMT) offers an easy way of solving nonlinearly constrained problems. However, this algorithm frequently suffers from the need to minimize an ill-conditioned penalty function. An ill-conditioned minimization problem can be solved very effectively by posing the problem as one of integrating a system of stiff differential equations utilizing concepts from singular perturbation theory. This paper evaluates the robustness and the reliability of such a singular perturbation based SUMT algorithm on two different problems of structural optimization of widely separated scales. The report concludes that whereas conventional SUMT can be bogged down by frequent ill-conditioning, especially in large scale problems, the singular perturbation SUMT has no such difficulty in converging to very accurate solutions.

Kamat, M. P.↗

NASA NTRS1983

Hybrid perturbation/Bubnov-Galerkin technique for nonlinear thermal analysis

A two step hybrid analysis technique to predict the nonlinear steady state temperature distribution in structures and solids is presented. The technique is based on the regular perturbation expansion and the classical Bubnov-Galerkin approximation. The functions are obtained by using the regular perturbation method. These functions are selected as coordinate functions and the classical Bubnov-Galerkin technique is used to compute their amplitudes. The potential of the proposed hybrid technique for the solution of nonlinear thermal problems is discussed. The effectiveness of this technique is demonstrated by the effects of conduction, convection, and radiation modes of heat transfer. It is indicated that the hybrid technique overcomes the two major drawbacks of the classical techniques: (1) the requirement of using a small parameter in the regular perturbation method; and (2) the arbitrariness in the choice of the coordinate functions in the Bubnov-Galerkin technique. The proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of the Bubnov-Galerkin technique.

Noor, A. K.↗

NASA NTRS1982

The CMC/3DPNS computer program for prediction of three-dimension, subsonic, turbulent aerodynamic juncture region flow. Volume 2: Users' manual

The CMC fluid mechanics program system was developed to transmit the theoretical solution of finite element numerical solution methodology, applied to nonlinear field problems into a versatile computer code for comprehensive flow field analysis. Data procedures for the CMC 3 dimensional Parabolic Navier-Stokes (PNS) algorithm are presented. General data procedures a juncture corner flow standard test case data deck is described. A listing of the data deck and an explanation of grid generation methodology are presented. Tabulations of all commands and variables available to the user are described. These are in alphabetical order with cross reference numbers which refer to storage addresses.

Manhardt, P. D.↗

NASA NTRS1984

Theoretical analyses of baroclinic flows

Completed and ongoing research activities are discussed briefly, including a three-dimensional, linear stability analysis of the baroclinic Hadley cell and a numerical model of the baroclinic flow between two rotating concentric spheres. This model simulates axisymmetric flow in the Atmospheric General Circulation Experiment configuration. A computer code designed to solve the strongly nonlinear stability problem for the Eady basic state is mentioned.

Antar, B. N.↗

NASA NTRS1983

Equivalent source modeling of the core magnetic field using magsat data

Experiments are carried out on fitting the main field using different numbers of equivalent sources arranged in equal area at fixed radii at and inside the core-mantle boundary. In fixing the radius for a given series of runs, the convergence problems that result from the extreme nonlinearity of the problem when dipole positions are allowed to vary are avoided. Results are presented from a comparison between this approach and the standard spherical harmonic approach for modeling the main field in terms of accuracy and computational efficiency. The modeling of the main field with an equivalent dipole representation is found to be comparable to the standard spherical harmonic approach in accuracy. The 32 deg dipole density (42 dipoles) corresponds approximately to an eleventh degree/order spherical harmonic expansion (143 parameters), whereas the 21 dipole density (92 dipoles) corresponds to approximately a seventeenth degree and order expansion (323 parameters). It is pointed out that fixing the dipole positions results in rapid convergence of the dipole solutions for single-epoch models.

Mayhew, M. A.↗

NASA NTRS1982

Dynamic effects of combustion

The dynamic effects of combustion are due to the evolution of exothermic energy and its deposition in the compressible medium where the process takes place. The paper examines the dynamics of combustion phenomena, including ignition, turbulent flame propagation (inflammation), explosion, and detonation, with emphasis on their exothermic characteristics. Ignition and explosion are treated as problems of nonlinear mechanics, and their dynamic behavior is described in terms of phase space models and cinematographic laser shear interferograms. The results of a numerical random vortex model of turbulent flame propagation are confirmed in a combustion tunnel experiment, where it was observed that a fresh mixture of burnt and unburnt gases can sustain combustion with a relatively small expenditure of overall mass flow, due to the increasing specific volume of burnt gases inside the flame front. An isentropic pressure wave is found to precede the accelerating flame in the process of detonation, and components of this presssure wave are shown to propagate at local sonic velocities.

Oppenheim, A. K.↗

NASA NTRS1984

Differential eigenvalue problems in which the parameter appears nonlinearly

Several methods are examined for determining the eigenvalues of a system of equations in which the parameter appears nonlinearly. The equations are the result of the discretization of differential eigenvalue problems using a finite Chebyshev series. Two global methods are considered which determine the spectrum of eigenvalues without an initial estimate. A local iteration scheme with cubic convergence is presented. Calculations are performed for a model second order differential problem and the Orr-Sommerfeld problem for plane Poiseuille flow.

Bridges, T. J.↗

NASA NTRS1986

Three-Dimensional, Subsonic, Turbulent Juncture Region Flow

CMC3DPNS predicts three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Versatile program for comprehensive flow-field analysis applies finite-element methodology to nonlinear field problems. Order-ofmagnitude analysis of subsonic, three-dimensional, steady time-averaged NavierStokes equations for semibounded aerodynamic juncture geometries yields para bolic Navier-Stokes equations. CMC3DPNS solves these equations to predict juncture-region flow.

Baker, A. J.↗

NASA NTRS1982

The CMC/3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 3: Programmers' manual

The CMC fluid mechanics program system was developed to transmit the theoretical evolution of finite element numerical solution methodology, applied to nonlinear field problems into a versatile computer code for comprehensive flow field analysis. A detailed view of the code from the standpoint of a computer programmer's use is presented. A system macroflow chart and detailed flow charts of several routines necessary to interact with a theoretican/user to modify the operation of this program are presented. All subroutines and details of usage, primarily for input and output routines are described. Integer and real scalars and a cross reference list denoting subroutine usage for these scalars are outlined. Entry points in dynamic storage vector IZ; the lengths of each vector accompanying the scalar definitions are described. A listing of the routines peculiar to the standard test case and a listing of the input deck and printout for this case are included.

Orzechowski, J. A.↗

NASA NTRS1985

Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations

Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.

Hodges, D. H.↗

NASA NTRS1985

Long-time asymptotics of a system for plasma diffusion

A system of parabolic nonlinear equations that describe the diffusion of a fully collisional plasma across a strong magnetic field is discussed. It is demonstrated that the solution to this system tends to a time asymptotic state which is of space-time separable form, theta(t)f(x). Furthermore, f(x) is independent of the initial conditions and theta(t) depends slightly on the initial conditions. The rate of decay of the temporal part is governed by a nonlinear eigenvalue problem. Since the equations are considered in a bounded domain we are able to analyze the effect of boundary conditions on the evolution of the system. Additional effects on radiation, heating, and particle injection can also be accounted for. Essential differences between the behavior of a fully-coupled system and a scalar equation are observed.

Rosenau, P.↗

NASA NTRS1985

Some recent advances in computational aerodynamics for helicopter applications

The growing application of computational aerodynamics to nonlinear helicopter problems is outlined, with particular emphasis on several recent quasi-two-dimensional examples that used the thin-layer Navier-Stokes equations and an eddy-viscosity model to approximate turbulence. Rotor blade section characteristics can now be calculated accurately over a wide range of transonic flow conditions. However, a finite-difference simulation of the complete flow field about a helicopter in forward flight is not currently feasible, despite the impressive progress that is being made in both two and three dimensions. The principal limitations are today's computer speeds and memories, algorithm and solution methods, grid generation, vortex modeling, structural and aerodynamic coupling, and a shortage of engineers who are skilled in both computational fluid dynamics and helicopter aerodynamics and dynamics.

Mccroskey, W. J.↗

NASA NTRS1986

Theoretical studies of Resonance Enhanced Stimulated Raman Scattering (RESRS) of frequency doubled Alexandrite laser wavelengths in cesium vapor

This work focused on understanding the effects of arbitrary transverse and longitudinal relaxation rates on the susceptibilities of coherently driven three-level systems. The approximation of a single relaxation rate often made in previous work is strongly invalidated by the variation in the spontaneous emission lifetime between various atomic level pairs in systems such as cesium. It is of great importance to the problem of nonlinear infrared generation to determine the dependence of both real and imaginary susceptibility on relaxation rates. The imaginary susceptibility on the pump transition determines the absorption of pump photons and the imaginary susceptibility on the laser transition determines the spectral dependence of the gain. This is of particular importance for pure Raman emission (i.e., absorption at linecenter of the gain transition) as it determines the tunability characteristics we are aiming to predict. The real susceptibility is important when cavities are used at the signal field as this will determine the loaded resonance of the Raman oscillator. Researchers show that in some cases which result from having different relaxation rates mode splitting may result, allowing more than one frequency to have the same Raman wavelength, possibly resulting in a temporal instability.

Lawandy, N. M.↗

NASA NTRS1985

Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and nonlinear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of /y(dot) = f(y) for t greater than 0, y(0) given/ is typically reduced to the mth order (m is much less than n) problem of /z(dot) = g(z) for t greater than 0, z(0) given/ by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e-i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian and of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e., the columns of P.

Utku, S.↗

NASA NTRS1987

Evaluation of on-line pulse control for vibration suppression in flexible spacecraft

On-line pulse control for vibration suppression in a flexible spacecraft was evaluated. A continuous beam vs. a truss was modeled. A linear finite element model was used to determine the truss characteristics. Control issues outlined are ED pulse actuator development, pseudo pulse algorithm development, and large nonlinear simulation problems.

Bekey, G. A.↗

NASA NTRS1987

Computable optimal value bounds for generalized convex programs

It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimal value function. The approach is attractive because it involves manipulation of information normally required to characterize solution optimality. A procedure is briefly described for calculating and improving the bounds as well as its extensions to generalized convex and concave functions. Several areas of applications are also indicated.

Fiacco, Anthony V.↗

NASA NTRS1987

Stability of streamwise vortices

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

Khorrami, M. K.↗

NASA NTRS1987

Optimal placement of critical speeds in rotor-bearing systems

The design of a rotor-bearing system is an iterative process in which the parameters that influence the design are modified until the desired design objectives are achieved. Primary among the design objectives is the minimization of the response amplitude within the operating range of the rotor system. An automated design procedure for the optimal placement of the critical speeds of a rotor is presented. The desired design objective is cast as a nonlinear programming problem that minimizes an objective function subject to constraints. The optimization program interacts with an analysis program to search for the feasible optimal design.

Rajan, M.↗