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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Use of global functions for improvement in efficiency of nonlinear analysis

A method for improving the efficiency of nonlinear structural analysis by the use of global displacement functions is presented. The computer programs include options to define the global functions as input or let the program automatically select and update these functions. The program was applied to a number of structures: (1) 'pear-shaped cylinder' in compression, (2) bending of a long cylinder, (3) spherical shell subjected to point force, (4) panel with initial imperfections, (5) cylinder with cutouts. The sample cases indicate the usefulness of the procedure in the solution of nonlinear structural shell problems by the finite element method. It is concluded that the use of global functions for extrapolation will lead to savings in computer time.

Almroth, B. O.↗
NASA NTRS1988

Estimation of time- and state-dependent delays and other parameters in functional differential equations

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Murphy, K. A.↗
NASA NTRS1990

Estimation of time- and state-dependent delays and other parameters in functional differential equations

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Murphy, K. A.↗
NASA NTRS1987

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Tiffany, Sherwood H.↗
NASA NTRS1990

Linear and non-linear dynamic models of a geared rotor-bearing system

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Kahraman, Ahmet↗
NASA NTRS1988

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

Tiffany, Sherwood H.↗
NASA NTRS2001

Aeroelastic Modeling and Behavior of Lifting Surfaces Incorporating Aerodynamic and Structural Nonlinearities: Volterra Series and Indicial Function Approach

Within this NASA Grant, the following points should be emphasized: 1) All the objectives stated in the proposal of the grant have been accomplished. Moreover, the activity within the project has addressed additional issues, of the linear and nonlinear aeroelasticity, not included in the objectives of the grant. 2) During the activities within the grant, we have been in a permanent contact with Dr. Walter A. Silva, the monitor of the NASA Project, to whom we have reported continuously our achievements. 3) As a result of the activities within the grant a number of papers: a. have been submitted for publication to the AIAA Journals, namely the AIAA Journal and the Journal of Guidance, Control, and Dynamics, b. have been presented at the specialized National Conferences and an International Congress, and have appeared in the proceedings of these Conferences, 4) A list of papers submitted for publication and presented at Conferences is appended herewith. 5) In all these papers, an acknowledgment to NASA Langley Research Center was included.

Librescu, Liviu↗
NASA NTRS2001

Aeroelastic Modeling and Behavior of Lifting Surfaces Incorporating Aerodynamic and Structural Nonlinearities: Volterra Series and Indicial Function Approach

Within this NASA Grant, the following points should be emphasized: 1) All the objectives stated in the proposal of the grant have been accomplished. Moreover. the activity within the project has addressed additional issues, of the linear and nonlinear aeroelasticity, not included in the objectives of the grant. 2) During the activities within the grant, we have been in a permanent contact with Dr. Walter A. Silva, the monitor of the NASA Project, to whom we have reported continuously our achievements. 3) As a result of the activities within the grant a number of papers: a. have been submitted for publication to the AIAA Journals, namely the AIAA Journal and the Journal of Guidance, Control, and Dynamics, and b. have been presented at the specialized National Conferences and an International Congress, and have appeared in the proceedings of these Conferences. 4) A list of papers submitted for publication and presented at Conferences is appended herewith. 5) In all these papers, an acknowledgment to NASA Langley Research Center was included.

Librescu, Liviu↗
NASA NTRS1993

Design of fuzzy system by NNs and realization of adaptability

The issue of designing and tuning fuzzy membership functions by neural networks (NN's) was started by NN-driven Fuzzy Reasoning in 1988. NN-driven fuzzy reasoning involves a NN embedded in the fuzzy system which generates membership values. In conventional fuzzy system design, the membership functions are hand-crafted by trial and error for each input variable. In contrast, NN-driven fuzzy reasoning considers several variables simultaneously and can design a multidimensional, nonlinear membership function for the entire subspace.

Takagi, Hideyuki↗
NASA NTRS1989

Parallel processors and nonlinear structural dynamics algorithms and software

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Belytschko, Ted↗
NASA NTRS1983

Programming the gradient projection algorithm

The gradient projection method of numerical optimization which is applied to problems having linear constraints but nonlinear objective functions is described and analyzed. The algorithm is found to be efficient and thorough for small systems, but requires the addition of auxiliary methods and programming for large scale systems with severe nonlinearities. In order to verify the theoretical results a digital computer is used to simulate the algorithm.

Hargrove, A.↗
NASA NTRS1996

Vibration Control in Turbomachinery Using Active Magnetic Journal Bearings

The effective use of active magnetic bearings for vibration control in turbomachinery depends on an understanding of the forces available from a magnetic bearing actuator. The purpose of this project was to characterize the forces as functions shaft position. Both numerical and experimental studies were done to determine the characteristics of the forces exerted on a stationary shaft by a magnetic bearing actuator. The numerical studies were based on finite element computations and included both linear and nonlinear magnetization functions. Measurements of the force versus position of a nonrotating shaft were made using two separate measurement rigs, one based on strain gage measurement of forces, the other based on deflections of a calibrated beam. The general trends of the measured principal forces agree with the predictions of the theory while the magnitudes of forces are somewhat smaller than those predicted. Other aspects of theory are not confirmed by the measurements. The measured forces in the normal direction are larger than those predicted by theory when the rotor has a normal eccentricity. Over the ranges of position examined, the data indicate an approximately linear relationship between the normal eccentricity of the shaft and the ratio of normal to principal force. The constant of proportionality seems to be larger at lower currents, but for all cases examined its value is between 0.14 and 0.17. The nonlinear theory predicts the existence of normal forces, but has not predicted such a large constant of proportionality for the ratio. The type of coupling illustrated by these measurements would not tend to cause whirl, because the coupling coefficients have the same sign, unlike the case of a fluid film bearing, where the normal stiffness coefficients often have opposite signs. They might, however, tend to cause other self-excited behavior. This possibility must be considered when designing magnetic bearings for flexible rotor applications, such as gas turbines and other turbomachinery.

Knight, Josiah D.↗