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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Postbuckling analysis using a general purpose code

A new capability for solving postbuckling problems in shell structures is described. The matrix theory to adapt Newton's method to nonlinear finite element shell analysis is outlined first. The matrix theory is directed at writing consistent linear algebratic equations for problems where the tangent stiffness matrix is singular or nearly singular. The matrix theory suggests a change of variables as part of the usual iterative procedure in Newton's method. The change of variables is shown to be feasible for introduction into the algorithm programmed in general purpose codes for finite element analysis of structures. Numerical results from a new option that has been programmed in an existing general purpose code are presented. The analysis of shell structures for collapse and for branching at bifurcation loads is illustrated by the numerical examples.

Thurston, G. A.↗
NASA NTRS1989

Globally convergent techniques in nonlinear Newton-Krylov

Some convergence theory is presented for nonlinear Krylov subspace methods. The basic idea of these methods is to use variants of Newton's iteration in conjunction with a Krylov subspace method for solving the Jacobian linear systems. These methods are variants of inexact Newton methods where the approximate Newton direction is taken from a subspace of small dimensions. The main focus is to analyze these methods when they are combined with global strategies such as linesearch techniques and model trust region algorithms. Most of the convergence results are formulated for projection onto general subspaces rather than just Krylov subspaces.

Brown, Peter N.↗
NASA NTRS1995

Structural Optimization Using the Newton Modified Barrier Method

The Newton Modified Barrier Method (NMBM) is applied to structural optimization problems with large a number of design variables and constraints. This nonlinear mathematical programming algorithm was based on the Modified Barrier Function (MBF) theory and the Newton method for unconstrained optimization. The distinctive feature of the NMBM method is the rate of convergence that is due to the fact that the design remains in the Newton area after each Lagrange multiplier update. This convergence characteristic is illustrated by application to structural problems with a varying number of design variables and constraints. The results are compared with those obtained by optimality criteria (OC) methods and by the ASTROS program.

Khot, N. S.↗
NASA NTRS1976

A quasi-Newton approach to optimization problems with probability density constraints

A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

Tapia, R. A.↗
NASA NTRS1960

A Self-Adaptive Missile Guidance System for Statistical Inputs

A method of designing a self-adaptive missile guidance system is presented. The system inputs are assumed to be known in a statistical sense only. Newton's modified Wiener theory is utilized in the design of the system and to establish the performance criterion. The missile is assumed to be a beam rider, to have a g limiter, and to operate over a flight envelope where the open-loop gain varies by a factor of 20. It is shown that the percent of time that missile acceleration limiting occurs can be used effectively to adjust the coefficients of the Wiener filter. The result is a guidance system which adapts itself to a changing environment and gives essentially optimum filtering and minimum miss distance.

Peery, H. Rodney↗
NASA NTRS1977

Optimal solar sail planetocentric trajectories

The analysis of solar sail planetocentric optimal trajectory problem is described. A computer program was produced to calculate optimal trajectories for a limited performance analysis. A square sail model is included and some consideration is given to a heliogyro sail model. Orbit to a subescape point and orbit to orbit transfer are considered. Trajectories about the four inner planets can be calculated and shadowing, oblateness, and solar motion may be included. Equinoctial orbital elements are used to avoid the classical singularities, and the method of averaging is applied to increase computational speed. Solution of the two-point boundary value problem which arises from the application of optimization theory is accomplished with a Newton procedure. Time optimal trajectories are emphasized, but a penalty function has been considered to prevent trajectories which intersect a planet's surface.

Sackett, L. L.↗
NASA NTRSDate not supplied

Mechanics of Structure Genome-Based Nonlinear Shell Analysis

In this paper, a mechanics of structure genome (MSG)-based nonlinear shell theory is introduced. The theory uses an implicit algorithm combining the Euler’s and Newton’s method that can be applied for shell modeling as well as 3D homogenization. This theory has been implemented into the general-purpose constitutive modeling code SwiftComp, which was originally developed for linear analyses. For the convenience of implementing different nonlinear material models, the SwiftComp user material (SCUMAT), which has a similar interface to the Abaqus user subroutine UMAT, is developed. The capability of the MSG-based nonlinear shell is validated with numerical examples with different material models. A 2-step nonlinear homogenization, with a micromechanics step and a shell analysis step, is demonstrated.

Yufei Long↗
NASA NTRS1980

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗
NASA NTRS1988

Quasi-Newton methods for parameter estimation in functional differential equations

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Brewer, Dennis W.↗
NASA NTRS1990

Newton modified barrier method in constrained optimization

In this paper, we develop and investigate the Newton method for solving constrained (non-smooth) optimization problems. This approach is based on the modified barrier functions (MBF) theory and on the global converging step-size version of the Newton method for smooth unconstrained optimization. Due to the excellent properties of the MBF near primal-dual solution, the Newton modified barrier method (NMBM) has a better rate of convergence, better complexity bound, and is much more stable in the final stage of the computational process than the methods which are based on the classical barrier functions (CBF).

Polyak, R.↗
NASA NTRS1984

Flow properties of concentrated suspensions

The viscosity and flow behavior of a concentrated suspension, with special emphasis on fresh concrete containing a superplasticizer, is analyzed according to Newton's law of viscosity. The authors interpreted Newton's law in a new way, and explain non-Newton flow from Newton's law. The outline of this new theory is given. Viscosity of suspensions, and the effect of dispersants are analyzed.

Hattori, K.↗
NASA NTRS2004

What Information Theory Says About Best Response and About Binding Contracts

Product Distribution (PD) theory is the information-theoretic extension of conventional full- rationality game theory to bounded rational games. Here PD theory is used to investigate games in which the players use bounded rational best-response strategies. This investigation illuminates how to determine the optimal organization chart for a corporation, or more generally how to order the sequence of moves of the players / employees so as to optimize an overall objective function. It is then shown that in the continuum-time limit, bounded rational best response games result in a variant of the replicator dynamics of evolutionary game theory. This variant is then investigated for team games, in which the players share the same utility function, by showing that such continuum- limit bounded rational best response is identical to Newton-Raphson iterative optimization of the shared utility function. Next PD theory is used to investigate changing the coordinate system of the game, i.e., changing the mapping from the joint move of the players to the arguments in the utility functions. Such a change couples those arguments, essentially by making each players move be an offered binding contract.

Wolpert, David H.↗
NASA NTRS1981

Recent developments in quasi-Newton methods for structural analysis and synthesis

Unlike the Newton-Raphson method, quasi-Newton methods by virture of the updates and step length control procedures are globally convergent and hence better suited for the solution of nonlinear problems of structural analysis and synthesis. Extension of quasi-Newton algorithms to large scale problems has led to the development of sparse update algorithms and to economical strategies for evaluating sparse Hessians. Ill-conditioning problems have led to the development of self-scaled variable metric and conjugate gradient algorithms, as well as the use of the singular perturbation theory. This paper emphasizes the effectiveness of such quasi-Newton algorithms for nonlinear structural analysis and synthesis.

Kamat, M. P.↗
DOE OSTI2026

The Physics Imposed on a Streaming Operator by Spherical Transport Problems

The streaming operator, which generates a displacement of a particle on a straight line at a constant speed in transport theory, is derived algebraically from a spherical coordinate formulation of Newton’s second law. This derivation leads to an operator that has more partial derivatives than a Cartesian coordinate formulation of the operator. The additional partial derivatives, which are with respect to the normalized velocity variables of a particle, take into account the intrinsic curvature of a ball. Moreover, these partial derivatives mitigate ray effects, which arise when a finite number of normalized velocities (also called directions or discrete ordinates) are used to simulate a continuous S 2 sphere of directions, by rotating the polar axis of the S 2 sphere into the radial direction of the coordinate system. As a consequence of this rotation, the number of actual discrete ordinates is greatly amplified to an enormous number of effective discrete ordinates by a multiplier that is equal to the number of patches that partitions a spherical surface. In addition to the derivation of the streaming operator, we provide in closed form a solution to the system of characteristic equations that is equivalent to the streaming operator. Furthermore, the solution to the system of characteristic equations enables the construction of an integral operator that is the inverse to the streaming operator. Examples in which ray effects are immensely mitigated by spherical coordinates are presented.

integral operator↗
NASA NTRS1985

Structural parameter identification of distributed systems using finite element approximation

A system identification technique is developed for classes of distributed systems using finite element approximations. Vibrating systems represented by partial differential equations have physical parameters associated with mass, stiffness, and damping distributions which need to be known in order to properly control and design mathematical models of the system. In order to identify these parameters a weighted least-squares algorithm and modified Newton-Raphson method is used for the identification process. The theory and technique is demonstrated by estimating the system parameters of a vibrating cantilever beam made up of several different structural properties.

Lee, K. Y.↗