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Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.
A method was developed and demonstrated for the direct measurement of aerodynamic forcing and aerodynamic damping of a transonic compressor. The method is based on the inverse solution of the structural dynamic equations of motion of the blade disk system in order to determine the forces acting on the system. The disturbing and damping forces acting on a given blade are determined if the equations of motion are expressed in individual blade coordinates. If the structural dynamic equations are transformed to multiblade coordinates, the damping can be measured for blade disk modes, and related to a reduced frequency and interblade phase angle. In order to measure the aerodynamic damping in this way, the free response to a known excitation is studied.
A method has been developed and demonstrated for the direct measurement of aerodynamic damping in a transonic compressor. The method is based on the inverse solution of the structural dynamic equations of motion of the blade-disk system. The equations are solved inversely to determine the forces acting on the system. If the structural dynamic equations are transformed to multiblade or modal coordinates, the damping can be measured for blade-disk modes, and related to a reduced frequency and interblade phase angle. This method of damping determination was demonstrated using a specially instrumented version of the MIT Transonic Compressor run in the MIT Blowdown Compressor Test Facility. No regions of aeroelastic instability were found. In runs at the operating point, the rotor was aerodynamically excited by a controlled two-per-revolution fixed up-stream disturbance. The disturbance was sharply terminated midway through the test. Analysis of the data in terms of multiblade modes led to a direct measurement of aerodynamic damping for three interblade phase angles.
A new direct matrix abstract program for NASTRAN written to calculate internal stresses and airloads for a flexible wing is described. The difficulties encountered in interfacing the doublet lattice solution to the aerodynamic problem to the finite element solution to the structural problem are discussed. A brief numerical example is included.
This paper looks at the structure of the solution of a matrix Riccati differential equation under a predefined group of transformations. The group of transformations used is an expanded form of the feedback group. It is shown that this group of transformations is a subgroup of the symplectic group. The orbits of the Riccati differential equation under the action of this group are studied and it is seen how these techniques apply to a decentralized optimal control problem.
Design principles suggested here aim toward high conversion efficiency (greater than 15 percent) in polysilicon cells. The principles seek to decrease the liabilities of both intragranular and grain-boundary-surface defects. The advantages of a phosphorus atom concentration gradient in a thin (less than 50 microns) base of a p(+)/n(x)/n(+) drift-field solar cell, which produces favorable gradients in chemical potential, minority-carrier mobility and diffusivity, and recombination lifetime (via phosphorus gettering) are suggested. The degrading effects of grain boundaries are reduced by these three gradients and by substituting atoms (P, H, F or Li) for vacancies on the grain-boundary surface. From recent experiments comes support for the benefits of P diffusion down grain boundaries and, for quasi-grain-boundary-free and related structures. New analytic solutions for the n(x)-base include the effect of a power-law dependence between P concentration and lifetime. These provide an upper-bound estimate on the open circuit voltage. Finite-difference numerical solutions of the six Shockley equations furnish complete information about all solar-cell parameters and add insight concerning design.
An analytical procedure has been used to design an acoustic treatment for cabin noise control of a light aircraft. Using this approach acoustic add-on treatments capable of reducing the average noise levels in the cabin by about 17 dB from the untreated condition are developed. The added weight of the noise control package is about 2 percent of the total gross take-off weight of the aircraft. The analytical model uses modal solutions wherein the structural modes of the sidewall and the acoustic modes of the receiving space are accounted for. The additional noise losses due to add-on treatments are calculated by the impedance transfer method. The input noise spectral levels are selected utilizing experimental flight data. The add-on treatments considered for cabin noise control include aluminum honeycomb panels, constrained layer damping tape, porous acoustic materials, noise barriers and limp trim panels. To reduce the noise transmitted through the double wall aircraft windows to acceptable levels, changes in the design of the aircraft window are recommended.
Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.
An approximate solution which includes the effects of chemical and thermal nonequilibrium and nonequilibrium nongray radiative transfer and which is suitable for rapidly obtaining approximate solutions for flowfield structure and estimates of radiative heat transfer is presented. Comparisons are made with Fire 2 data and example applications to a hypothetical Mars return AOTV are presented. Parametric results indicate that further studies of VUV processes and radiation models are needed.
It is argued that parallel propagating Alfven waves steepen to second order in the wave amplitude, rather than first order, as is the case for oblique MHD waves. An analytical solution for the structure of weak switch-on shocks is derived. The Rankine-Hugoniot relations for finite amplitude switch-on shocks are obtained in a compact form. The differential equation for resistive switch-on shocks is solved, and the resistive critical Mach number is obtained. The differential equation for resistive switch-on shocks with finite ion inertia is identical to the one obtained in the pure resistive case. It is argued that efficient electron heat conduction can significantly extend the range of upstream parameters for which switch-on shocks are expected.
A procedure to couple the Navier-Stokes solutions with modal structural equations of motion is presented for computing aeroelastic responses of swept flexible wings. The Navier-Stokes flow equations are solved by a finite-difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear-acceleration method. The configuration-adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. The calculations are compared with the experiment when available. Effects of flexibility, sweep angle, and pitch rate are demonstrated for flows with vortices.
Real-time simulation of flexible and articulating systems is difficult because of the computational burden of the time varying calculations. The mobile servicing system of the NASA Space Station Freedom will handle heavy payloads by local arm manipulations and by translating along the spline of the Station, it is crucial to have real-time simulation available. To enable such a simulation to be of high fidelity and to be able to be hosted on a modest computer, special care must be made in formulating the structural dynamics. Frontal solution algorithms save considerable time in performing these calculations. In addition, it is necessary to take advantage of parallel processing be compatible to take full advantage of both. An approach is offered which will result in high fidelity, real-time simulation for flexible, articulating systems such as the space Station remote servicing system.
A procedure to couple the Navier-Stokes solutions with modal structural equations of motion is presented for computing aeroelastic responses of flexible fighter wings. The Navier-Stokes flow equations are solved by a finite-difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear-acceleration method. The configuration-adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. The coupled calculations are compared with experiments when available. Effects of flexibility and pitch rate are demonstrated for flows with vortices. Turbulent flow computations are also compared with laminar flow computations.
The structure of nontopological solutions of Einstein field equations as proposed by Friedberg, Lee, and Pang (1987) is examined. This analysis incorporates finite temperature effects and pair creation. Quarks are assumed to be the only species that exist in interior of soliton stars. The possibility of primordial creation of soliton stars in the incomplete decay of the degenerate vacuum in early universe is explored. Because of dominance of pair creation inside soliton stars, the luminosity of soliton stars is not determined by its radiative transfer characteristics, and the surface temperature of soliton stars can be the same as its interior temperature. It is possible that soliton stars are intense X-ray radiators at large distances. Soliton stars are nearly 100 percent efficient energy converters, converting the rest energy of baryons entering the interior into radiation. It is possible that a sizable number of baryons may also be trapped inside soliton stars during early epochs of the universe. In addition, if soliton stars exist they could assume the role played by massive black holes in galactic centers.
Numerical solutions of three-dimensional compressible hydrodynamics (including sound waves) in a stratified medium with open boundaries are presented. Convergent/divergent points play a controlling role in the flows, which are dominated by a single frequency related to the mean sound crossing time. Superposed on these rapid compressive flows, slower eddy-like flows eventually create convective transport. The solutions contain small structures stacked on top of larger ones, with vertical scales equal to the local pressure scale heights, H sub p. Although convective transport starts later in the evolution, vertical scales of H sub p are apparently selected at much earlier times by nonlinear compressive effects.
Quasi-geostrophic beta-plane motion of a homogeneous liquid over topography is considered for situations in which there is a time-periodic forcing of a zonal current. Such an oscillatory current generates a topographic Rossby wave response that has a complicated, but periodic, temporal structure. The linear solution grows resonances at all integer values of the beta-parameter. The nonlinear analysis demonstrates that for weak friction and forcing, the resonances are bent and multiple equilibria of the time-dependent Rossby wave states are possible in certain parameter ranges. While the basic forced flow in the absence of topography has no time-mean, the nonlinear amplitude equations show that a mean retrograde (westward) Eulerian zonal flow is generated in the interactions of the forced flow with the topography.
The early space probes provided our first detailed look at the planets, and demonstrated the critical role played by parts technology. The advanced orbital platform under development, the Space Station Freedom (which represents a pivotal step in the space program) contains about 5 million Electrical, Electronic and Electromechanical (EEE) parts. Thus, EEE parts continue to be crucial to mission success. The NASA EEE parts program establishes and directs policy and integration throughout the Agency. The EEE program structure, issues and solutions are described. The challenge presented by advanced electronic devices is discussed.
Burnett solutions for the structure of normal shock waves for Mach numbers ranging from 1.1 to 50 have been obtained by using the time-dependent equation set in conjunction with modern computational fluid dynamic techniques. The current work seeks to provide corrected and improved high-resolution direct simulation Monte Carlo (DSMC) results for hypersonic shocks in monatomic gases. These DSMC results will serve as a reliable test base for assessing the accuracy of various continuum equations more advanced than Navier-Stokes, such as the Burnett equations. The main conclusion of Fisko and Chapman (1988) that the Burnett equations are more accurate than the Navier-Stokes equations for all gases and at all Mach numbers in matching DSMC shock wave results is reassesed by comparing the improved and corrected DSMC results with continuum Burnett results. Various Burnett results for shocks in a diatomic gas, nitrogen, which include improvements to the work of Lumpkin and Chapman (1989) are presented. It is concluded that the Burnett equations represent a significant improvement over Navier-Stokes equations for flows exhibiting translational nonequilibrium.