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At least 757 records · Page 42

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NASA NTRS1975

A triangular thin shell finite element: Nonlinear analysis

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Thomas, G. R.↗

NASA NTRS1975

Estimation and Analysis of Nonlinear Stochastic Systems

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Marcus, S. I.↗

NASA NTRS1974

Nonlinear theory of electron neutralization waves in ions beams with dissipation

An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.

Wilhelm, H. E.↗

NASA NTRS1975

Stability analysis of nonlinear autonomous systems - General theory and application to flutter

The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

Smith, L. L.↗

NASA NTRS1975

Empirical comparison of a linear and a nonlinear washout for motion simulators

The subjective opinions gathered from seven pilots in the process of comparing a linear and a nonlinear washout for motion simulators reveal an important advance in motion cue presentation. The advance is not in the increased cue provided by the nonlinear filter over a linear filter for the same amount of motion base travel, but rather in the elimination of false rotational rate cues presented by linear filters.

Parrish, R. V.↗

NASA NTRS1974

Nonlinear finite-element analysis of laminated composite shells

Two aspects of the geometrically nonlinear analysis of laminated composite shells are considered in this paper. The first pertains to the simplifications and computational advantages resulting from the use of group-theoretic methods in conjunction with computerized symbolic (algebraic) manipulation in the element development. The second aspect pertains to the combined effects of shear deformation and nonlinearity on the accuracy and convergence of two-dimensional, shear-flexible stiffness finite element models.

Noor, A. K.↗

NASA NTRS1975

Nonlinear transient neutralization theory of ion beams with dissipation

An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions. The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave. This periodic wave structure is damped out by intercomponent momentum transfer, i.e., after a few relaxation lengths a quasi-neutral beam results. The relaxation scale in space agrees with neutralization experiments of rarefied ion beams, if the collective momentum transfer between the electron and ion streams is assumed to be of the Buneman type.

Wilhelm, H. E.↗

NASA NTRS1975

Nonlinear hyperbolic theory of thermal waves in metals

A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.

Wilhelm, H. E.↗

NASA NTRS1975

Nonlinear vibration of cylindrical shells

The large amplitude vibration of a thin-walled cylindrical shell is analyzed. A perturbation method is used to solve the steady-state forced vibration problem. The simply-supported boundary conditions and the circumferential periodicity condition are satisfied. The resulting solution indicates that in addition to the fundamental mode, the response contains asymmetric modes as well as axisymmetric modes with the frequency twice that of the fundamental mode. Vibrations involving a single driven mode response are investigated. The results indicate that the nonlinearity is either softening or hardening depending on the mode. The vibrations involving both a driven mode and a companion mode are also investigated. An experimental investigation is conducted, and the results are in qualitative agreement with the theory. 'Nonstationary' response is detected at some frequencies for large amplitude response in which the amplitude drifts from one value to another. Various nonlinear phenomena are observed and comparisons with the theoretical results are made.

Chen, J. C.↗

NASA NTRS1975

Application of multivariable search techniques to the optimization of airfoils in a low speed nonlinear inviscid flow field

Multivariable search techniques are applied to a particular class of airfoil optimization problems. These are the maximization of lift and the minimization of disturbance pressure magnitude in an inviscid nonlinear flow field. A variety of multivariable search techniques contained in an existing nonlinear optimization code, AESOP, are applied to this design problem. These techniques include elementary single parameter perturbation methods, organized search such as steepest-descent, quadratic, and Davidon methods, randomized procedures, and a generalized search acceleration technique. Airfoil design variables are seven in number and define perturbations to the profile of an existing NACA airfoil. The relative efficiency of the techniques are compared. It is shown that elementary one parameter at a time and random techniques compare favorably with organized searches in the class of problems considered. It is also shown that significant reductions in disturbance pressure magnitude can be made while retaining reasonable lift coefficient values at low free stream Mach numbers.

Hague, D. S.↗

NASA NTRS1975

An in-flight simulation of lateral control nonlinearities

An in-flight simulation program was conducted to explore, in a generalized way, the influence of spoiler-type roll-control nonlinearities on handling qualities. The roll responses studied typically featured a dead zone or very small effectiveness for small control inputs, a very high effectiveness for mid-range deflections, and low effectiveness again for large inputs. A linear force gradient with no detectable breakout force was provided. Given otherwise good handling characteristics, it was found that moderate nonlinearities of the types tested might yield acceptable roll control, but the best level of handling qualities is obtained with linear, aileron-like control.

Ellis, D. R.↗

NASA NTRS1975

PLANS: A finite element program for nonlinear analysis of structures. Volume 1: Theoretical manual

The PLANS system is described which is a finite element program for nonlinear analysis. The system represents a collection of special purpose computer programs each associated with a distinct physical problem class. Modules of PLANS specifically referenced and described in detail include: (1) REVBY, for the plastic analysis of bodies of revolution; (2) OUT-OF-PLANE, for the plastic analysis of 3-D built-up structures where membrane effects are predominant; (3) BEND, for the plastic analysis of built-up structures where bending and membrane effects are significant; (4) HEX, for the 3-D elastic-plastic analysis of general solids; and (5) OUT-OF-PLANE-MG, for material and geometrically nonlinear analysis of built-up structures. The SATELLITE program for data debugging and plotting of input geometries is also described. The theoretical foundations upon which the analysis is based are presented. Discussed are the form of the governing equations, the methods of solution, plasticity theories available, a general system description and flow of the programs, and the elements available for use.

Pifko, A.↗

NASA NTRS1976

A technique using a nonlinear helicopter model for determining trims and derivatives

A technique is described for determining the trims and quasi-static derivatives of a flight vehicle for use in a linear perturbation model; both the coupled and uncoupled forms of the linear perturbation model are included. Since this technique requires a nonlinear vehicle model, detailed equations with constants and nonlinear functions for the CH-47B tandem rotor helicopter are presented. Tables of trims and derivatives are included for airspeeds between -40 and 160 knots and rates of descent between + or - 10.16 m/sec (+ or - 200 ft/min). As a verification, the calculated and referenced values of comparable trims, derivatives, and linear model poles are shown to have acceptable agreement.

Ostroff, A. J.↗

NASA NTRS1976

Nonlinear Equations of Motion for Cantilever Rotor Blades in Hover with Pitch Link Flexibility, Twist, Precone, Droop, Sweep, Torque Offset, and Blade Root Offset

Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.

Hodges, D. H.↗

NASA NTRS1976

Comparison of a linear and a nonlinear washout for motion simulators utilizing objective and subjective data from CTOL transport landing approaches

Objective and subjective data gathered in the processes of comparing a linear and a nonlinear washout for motion simulators reveal that there is no difference in the pilot performance measurements used during instrument landing system (ILS) approaches with a Boeing 737 conventional takeoff and landing (CTOL) airplane between fixed base, linear washout, and nonlinear washout operations. However, the subjective opinions of the pilots reveal an important advance in motion cue presentation. The advance is not in the increased cue available over a linear filter for the same amount of motion base travel but rather in the elimination of false rotational rate cues presented by linear filters.

Parrish, R. V.↗

NASA NTRS1976

Nonlinear analysis of laminated fibrous composites

A computerized analysis of the nonlinear behavior of fibrous composite laminates including axial loading, thermal loading, temperature dependent properties, and edge effects is presented. Ramberg-Osgood approximations are used to represent lamina stress-strain behavior and percent retention curves are employed to model the variation of properties with temperature. Balanced, symmetric laminates comprised of either boron/epoxy, graphite/epoxy, or borsic-aluminum are analyzed using a quasi-three-dimensional finite element analysis. Results are presented for the interlaminar stress distributions in cross-ply, angle-ply, and more complex laminates. Nonlinear stress-strain curves for a variety of composite laminates in tension and compression are obtained and compared to other existing theories and experimental results.

Renieri, G. D.↗

NASA NTRS1975

An approximation technique for predicting the transient response of a second order nonlinear equation

An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.

Laurenson, R. M.↗

NASA NTRS1975

Controllability in nonlinear systems

An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.

Hirschorn, R. M.↗