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NASA NTRS1988

A nonlinear history-dependent damage model for low cycle fatigue

A nonlinear damage postulate that embodies the dependence of the damage rate on cycle-dependent changes in the bulk microstructure and the surface topography is examined. The postulate is analytically formulated in terms of the deformation history dependence of the bulk behavior. This formulation is used in conjunction with baseline data in accordance with the damage postulate to predict the low cycle fatigue resistance of OFE copper. Close comparison of the predictions with experimentally observed behavior suggests that the postulate offers a viable basis for nonlinear damage analysis.

Leis, B. N.↗

NASA NTRS1988

Nonlinear stability of the dayside cometary ionopause

The MHD stability of the cometary ionopause is investigated by nonlinear analysis, describing that stability in terms of the finite perturbation amplitude of both Kelvin-Helmholtz and Rayleigh-Taylor modes. The evolution of the unstable modes is examined, determining the conditions under which finite amplitude effects are expected to stabilize a growing wave disturbance. The analysis is applied to the ionopause at Comet Halley and Comet Giacobini-Zinner, showing that the theoretical prediction concerning the stability of this interface based on an earlier linear analysis remains valid in both cases despite the nonlinear stabilization effects.

Ershkovich, A. I.↗

NASA NTRS1988

Wavenumber selection for single-wave steady states in a nonlinear baroclinic system

The principles involved in the selection of a wavenumber for single-wave steady states are examined numerically and analytically in the framework of an Eady-type model with uneven Ekman dissipation. The process of selection involves the determination of the preferred wavenumber for a given parameter setting in the nonlinear system by testing the stability of steady single-wave states in a triad with wavenumbers n(0) - 1, n(0), and n(0) + 1, where n(0) may change successively in the selection procedure. In a given triad for a given parameter setting, the preferred wave is the wave with the nonlinear Eady angle that is last to vanish.

Weng, H.-Y.↗

NASA NTRS1988

Nonlinear vortex trail dynamics

The nonlinear evolution of periodic disturbances on vortex trails is considered. In addition to following small initial perturbations, large amplitude initial disturbances of the vortex trails are also studied. It is shown that the equations support a rich variety of essentially nonlinear solutions including unbounded and quasisteady ones. These solutions are found to correspond to various modes of vortex clustering in the physical plane. At the close of the paper, comparisons of these results with recent numerical and experimental findings on the wakes behind stationary cylinders, and also transversely oscillating bluff objects, are made.

Lim, Chjan C.↗

NASA NTRS1988

Application of dynamical systems theory to nonlinear aircraft dynamics

Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.

Culick, Fred E. C.↗

NASA NTRS1988

The nonlinear development of Goertler vortices in growing boundary layers

The development of Goertler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion while the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflectional character as the flow moves downstream. The latter result suggests that the major effect of Goertler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.

Hall, Philip↗

NASA NTRS1987

A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.

Shay, R. M., Jr.↗

NASA NTRS1987

Hierarchically partitioned nonlinear equation solvers

By partitioning solution space into a number of subspaces, a new multiply constrained partitioned Newton-Raphson nonlinear equation solver is developed. Specifically, for a given iteration, each of the various separate partitions are individually and simultaneously controlled. Due to the generality of the scheme, a hierarchy of partition levels can be employed. For finite-element-type applications, this includes the possibility of degree-of-freedom, nodal, elemental, geometric substructural, material and kinematically nonlinear group controls. It is noted that such partitioning can be continuously updated, depending on solution conditioning. In this context, convergence is ascertained at the individual partition level.

Padovan, Joseph↗

NASA NTRS1988

Nonlinearities in spacecraft structural dynamics

In considering nonlinearities in spacecraft structural dynamics, the following are examined: (1) SCOLE Configuration-Equations of Motion; (2) Modeling Error Sources; (3) Approximate Solutions; (4) Comparison of Model Accuracy; (5) Linear and Nonlinear Damping; (6) Experimental Results; and, (7) Future Work.

Taylor, Larry↗

NASA NTRS1988

Modifying PASVART to solve singular nonlinear 2-point boundary problems

To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.

Fulton, James P.↗

NASA NTRS1989

Equivalent linearization for fatigue life estimates of a nonlinear structure

An analysis is presented of the suitability of the method of equivalent linearization for estimating the fatigue life of a nonlinear structure. Comparisons are made of the fatigue life of a nonlinear plate as predicted using conventional equivalent linearization and three other more accurate methods. The excitation of the plate is assumed to be Gaussian white noise and the plate response is modeled using a single resonant mode. The methods used for comparison consist of numerical simulation, a probabalistic formulation, and a modification of equivalent linearization which avoids the usual assumption that the response process is Gaussian. Remarkably close agreement is obtained between all four methods, even for cases where the response is significantly linear.

Miles, R. N.↗

NASA NTRS1989

A simple nonlinear model for the return to isotropy in turbulence

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable non-trivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable non-trivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Sarkar, Sutanu↗

NASA NTRS1989

Nonlinear hierarchical substructural parallelism and computer architecture

Computer architecture is investigated in conjunction with the algorithmic structures of nonlinear finite-element analysis. To help set the stage for this goal, the development is undertaken by considering the wide-ranging needs associated with the analysis of rolling tires which possess the full range of kinematic, material and boundary condition induced nonlinearity in addition to gross and local cord-matrix material properties.

Padovan, Joe↗

NASA NTRS1989

Nonlinear characteristics of joints as elements of multi-body dynamic systems

As the connecting elements in multi-body structures, joints play a pivotal role in the overall dynamic response of these systems. Obviously, the linear stiffness of the joint strongly influences the system frequencies, but the joints are also likely to be the dominant sources of damping and nonlinearities, especially in aircraft and space structures. The general characteristics of such joints will be discussed. Then the state of the art in nonlinear joint characterization techniques will be surveyed. Finally, the impact that joints have on the overall response of structures will be evaluated.

Crawley, Edward F.↗

NASA NTRS1989

Effects of nonlinear aerodynamics and static aeroelasticity on mission performance calculations for a fighter aircraft

During conceptual design studies of advanced aircraft, the usual practice is to use linear theory to calculate the aerodynamic characteristics of candidate rigid (nonflexible) geometric external shapes. Recent developments and improvements in computational methods, especially computational fluid dynamics (CFD), provide significantly improved capability to generate detailed analysis data for the use of all disciplines involved in the evaluation of a proposed aircraft design. A multidisciplinary application of such analysis methods to calculate the effects of nonlinear aerodynamics and static aeroelasticity on the mission performance of a fighter aircraft concept is described. The aircraft configuration selected for study was defined in a previous study using linear aerodynamics and rigid geometry. The results from the previous study are used as a basis of comparison for the data generated herein. Aerodynamic characteristics are calculated using two different nonlinear theories, potential flow and rotational (Euler) flow. The aerodynamic calculations are performed in an iterative procedure with an equivalent plate structural analysis method to obtain lift and drag data for a flexible (nonrigid) aircraft. These static aeroelastic data are then used in calculating the combat and mission performance characteristics of the aircraft.

Giles, Gary L.↗

NASA NTRS1987

Nonlinear feedback control of multiple robot arms

Multiple coordinated robot arms are modeled by considering the arms: (1) as closed kinematic chains, and (2) as a force constrained mechanical system working on the same object simultaneously. In both formulations a new dynamic control method is discussed. It is based on a feedback linearization and simultaneous output decoupling technique. Applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, by choosing a general output equation, researchers can superimpose the position and velocity error feedback with the force-torque error feedback in the task space simultaneously.

Tarn, T. J.↗

NASA NTRS1989

Algorithms and software for nonlinear structural dynamics

The objective of this research is to develop efficient methods for explicit time integration in nonlinear structural dynamics for computers which utilize both concurrency and vectorization. As a framework for these studies, the program WHAMS, which is described in Explicit Algorithms for the Nonlinear Dynamics of Shells (T. Belytschko, J. I. Lin, and C.-S. Tsay, Computer Methods in Applied Mechanics and Engineering, Vol. 42, 1984, pp 225 to 251), is used. There are two factors which make the development of efficient concurrent explicit time integration programs a challenge in a structural dynamics program: (1) the need for a variety of element types, which complicates the scheduling-allocation problem; and (2) the need for different time steps in different parts of the mesh, which is here called mixed delta t integration, so that a few stiff elements do not reduce the time steps throughout the mesh.

Belytschko, Ted↗

NASA NTRS1988

Numerical solution of turbulent flow past a backward facing step using a nonlinear K-epsilon model

The problem of turbulent flow past a backward facing step is important in many technological applications and has been used as a standard test case to evaluate the performance of turbulence models in the prediction of separated flows. It is well known that the commonly used kappa-epsilon (and K-l) models of turbulence yield inaccurate predictions for the reattachment points in this problem. By an analysis of the mean vorticity transport equation, it will be argued that the intrinsically inaccurate prediction of normal Reynolds stress differences by the kappa-epsilon and K-l models is a major contributor to this problem. Computations using a new nonlinear Kappa-epsilon model (which alleviates this deficiency) are made with the TEACH program. Comparisons are made between the improved results predicted by this nonlinear kappa-epsilon model and those obtained from the linear kappa-epsilon model as well as from second-order closure models.

Speziale, C. G.↗