CIRCAL - On-line circuit design.
On-line nonlinear circuit design, discussing computer program for evaluating performance resulting from modifications
COMPUTER METHOD↗
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Results for “nonlinear analysis”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Some new rearrangement inequalities having application in stability analysis.
Rearrangement inequalities in stability analysis applied to difference equations governing nonlinear feedback loop
Brockett, R. W.↗
The prediction of nonlinear longitudinal combustion instability in liquid propellant rockets
An analytical technique was developed to solve nonlinear longitudinal combustion instability problems. The analysis yields the transient and limit cycle behavior of unstable motors and the threshold amplitude required to trigger a linearly stable motor into unstable operation. The limit cycle waveforms were found to exhibit shock wave characteristics for most unstable engine operating conditions. A method of correlating the analytical solutions with experimental data was developed. Calculated results indicate that a second-order solution adequately describes the behavior of combustion instability oscillations over a broad range of engine operating conditions, but that higher order effects must be accounted for in order to investigate engine triggering.
Lores, M. E.↗
A variable step incremental procedure
Description of a variable step incremental procedure for the solution of nonlinear equations in finite element structural analysis. The proposed procedure is effective in improving the accuracy of the basic incremental technique and in providing, in addition, an accurate estimate of the discretization error. The proposed approach is highly appropriate for solving problems for which the user has no a priori estimate of the step size to use.
Thomas, G. R.↗
Indirect synthesis of multi-degree of freedom transient systems
An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.
Pilkey, W. D.↗
Inelastic micromechanics of curing stresses in composites
The combined finite element/laminate analysis method is used to study the thermal curing stresses in composite materials with a nonlinearly elastic matrix subject to creep. The application of this analysis to boron/epoxy composites shows that curing stress levels in the laminate are of sufficient magnitude to cause widespread yielding in the matrix. The stress levels, based on the creep analysis of a typical laminate cure cycle, indicate that the residual stresses can vary from 80 to 100% of the residual stress estimates based on linear thermoelastic analysis. It is shown that there is virtually no change in the static longitudinal or shear response of unidirectional and cross-ply boron/epoxy laminates as a result of curing stresses. Results of a series of constant-stress, high temperature creep tests are presented.
Foye, R. L.↗
Buckling behavior and structural efficiency of open-section stiffened composite compression panels
Several experiments with J- and blade-stiffened graphite/epoxy panels were conducted to obtain insight into how well experimental data could be correlated with analysis for the buckling behavior of open-section stiffened composite compression panels. Although some nonlinear behavior was observed during the experiments, adequate correlation with analysis was obtained to justify the use of linear, thin-plate buckling analysis in a minimum-weight design synthesis program for J- and blade-configurations. Results from two design studies using this program are presented. In the first study the minimum weights of Jand blade-configurations for two different material systems (graphite/epoxy and aluminum) are determined subject to buckling and strength constraints for a wide range of the compressive load index. In the second study the minimum weights required for graphite/epoxy blade-stiffened panels to satisfy additional stiffness constraints typical of medium-size commercial aircraft wing structures are determined. Both minimum-weight studies indicate that graphite/epoxy open-section stiffened panels can be designed so that weight savings of 30 to 50% are possible compared with the most efficient aluminum designs.
Williams, J. G.↗
Progressive failure of structures
A procedure is presented for determining the nonlinear behavior of structures subjected to extreme loading and the possibility of development of potential for progressive failure. The methodology takes into account the effect of both material and geometric nonlinearities. At a given stage of analysis, the individual components of the structure are checked against predetermined failure criteria. Subsequently, the failing components are removed and the modified structure is analyzed for overall failure. Examples, obtained from a computer program based on the proposed procedure, showing the applicability of the method are presented.
Khozeimeh, K.↗
Analytical study of STOL Aircraft in ground effect. Part 1: Nonplanar, nonlinear wing/jet lifting surface method
A nonlinear, nonplanar three dimensional jet flap analysis, applicable to the ground effect problem, is presented. Lifting surface methodology is developed for a wing with arbitrary planform operating in an inviscid and incompressible fluid. The classical, infintely thin jet flap model is employed to simulate power induced effects. An iterative solution procedure is applied within the analysis to successively approximate the jet shape until a converged solution is obtained which closely satisfies jet and wing boundary conditions. Solution characteristics of the method are discussed and example results are presented for unpowered, basic powered and complex powered configurations. Comparisons between predictions of the present method and experimental measurements indicate that the improvement of the jet with the ground plane is important in the analyses of powered lift systems operating in ground proximity. Further development of the method is suggested in the areas of improved solution convergence, more realistic modeling of jet impingement and calculation efficiency enhancements.
Shollenberger, C. A.↗
Analysis and simulation of a magnetic bearing suspension system for a laboratory model annular momentum control device
A linear analysis and the results of a nonlinear simulation of a magnetic bearing suspension system which uses permanent magnet flux biasing are presented. The magnetic bearing suspension is part of a 4068 N-m-s (3000 lb-ft-sec) laboratory model annular momentum control device (AMCD). The simulation includes rigid body rim dynamics, linear and nonlinear axial actuators, linear radial actuators, axial and radial rim warp, and power supply and power driver current limits.
Groom, N. J.↗
Focusing of waves in turbulent inhomogeneous media
A stochastic method using geometrical acoustics is employed to investigate the growth of a large fluctuation in the amplitude of high-frequency waves or shocks propagating through turbulent, inhomogeneous media. Nonlinear terms are retained in the analysis to correctly model focusing and growth of singular fluctuations in the amplitude. A two-dimensional analysis reveals that fluctuations in the ray-tube area grow exponentially and every ray displays caustics. Probability densities for the appearance of caustics are provided, and moments of the ray-tube area distribution and amplitude-related statistics are formulated for distances far into the region of caustic formation. Finally, a relationship is defined between theoretical predictions and measurements on an image plane.
Kulkarny, V. A.↗
Ponderomotive force in a warm two-fluid plasma
A general expression for the ponderomotive force of electromagnetic field with slowly varying amplitude in a warm plasma is obtained in the collisionless two-fluid model. Compared to the existing expression obtained for a cold and stationary plasma, this result contains two additional terms for the general case. One of them is involved with the density gradient and the wavenumber derivative of the dielectric tensor of a plasma. Thus, for an inhomogeneous plasma, it accounts for the effects of spatial dispersion, hence of finite temperature of the plasma. The other term is proportional to the time derivative of the density and the frequency derivative of the dielectric tensor, and is nonzero unless the plasma is stationary or nondispersive. Inclusion of these new terms in the ponderomotive force will enable self-consistent analysis of the general behavior of nonlinear waves with finite wavelengths in a warm plasma.
Lee, N. C.↗
Mathematical modeling of the aerodynamic characteristics in flight dynamics
Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.
Tobak, M.↗
Analysis of a transport fuselage section drop test
Transport fuselage section drop tests provided useful information about the crash behavior of metal aircraft in preparation for a full-scale Boeing 720 controlled impact demonstration (CID). The fuselage sections have also provided an operational test environment for the data acquisition system designed for the CID test, and data for analysis and correlation with the DYCAST nonlinear finite-element program. The correlation of the DYCAST section model predictions was quite good for the total fuselage crushing deflection (22 to 24 inches predicted versus 24 to 26 inches measured), floor deformation, and accelerations for the floor and fuselage. The DYCAST seat and occupant model was adequate to approximate dynamic loading to the floor, but a more sophisticated model would be required for good correlation with dummy accelerations. Although a full-section model using only finite elements for the subfloor was desirable, constraints of time and computer resources limited the finite-element subfloor model to a two-frame model. Results from the two-frame model indicate that DYCAST can provide excellent correlation with experimental crash behavior of fuselage structure with a minimum of empirical force-deflection data representing structure in the analytical model.
E. L. Fasanella↗
Large eddy interactions in a turbulent channel flow
The dynamic processes of large eddies in a turbulent channel flow have been examined by utilizing an orthogonal expansion of the velocity fluctuation, known in the literature as the Proper Orthogonal Decomposition Theorem. The mathematical form of these functions is unknown in contrast to the Fourier analysis. Attention is focused on the nonlinear, turbulence-turbulence interaction process in the dynamical equation for large eddies (the first term in the expansion). The nonlinear interactions of the components of the first mode are treated exactly, but influences of higher modes are modeled. This requires adjustment of both the skewness and the effective Reynolds number so that the energy equilibrium of the large eddies is ensured when the mean velocity distribution is assumed known for experiments. Computational results show that the first mode contributes significantly to turbulent intensities and possesses a structural and statistical character similar to that of the entire flow.
Hong, S. K.↗
PIAS: A program for an iterative aeroelastic solution
A Program for an Iterative Aeroelastic Solution (PIAS) is discussed. This will be a modular computer program that combines the use of a finite-element structural analysis code with any linear or nonlinear aerodynamic code. At this point in time, PIAS has been designed but the software has not been written. The idea for this development originated with P. J. (Bud) Bobbitt of the NASA Langley Research Center. There was initial interest in an aeroelastic solution for a separation-induced leading-edge vortex. Some examples of the flow patterns for a low aspect ratio wing are shown. The Leading-Edge Vortex Program, which calculates pressure distributions including the effects of a separation-induced leading-edge vortex, uses an iterative solution method. This led to the concept of an iteration cycle on configuration shape external to the aerodynamic code.
Manro, M. E.↗
Winglets on low aspect ratio wings
The drag reduction potentially available from the use of winglets at the tips of low aspect ratio (1.75-2.67) wings with pronounced (45-60 deg) leading edge sweep is assessed numerically for the case of a cruise design point at Mach of 0.8 and a lift coefficient of 0.3. Both wing-winglet and wing-alone design geometries are derived from a linear-theory, minimum induced drag design methodology. Relative performance is evaluated with a nonlinear extended small disturbance potential flow analysis code. Predicted lift coefficient/pressure drag coefficient increases at equal lift for the wing-winglet configurations over the wing-alone planform are of the order of 14.6-15.8, when boundary layer interaction is included.
Kuhlman, John M.↗
Extrapolation methods for vector sequences
This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.
Smith, David A.↗