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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Numerical analysis of stiffened shear webs in the postbuckling range

The postbuckling behavior of shear webs divided into rectangular panels by stiffeners (uprights) was studied numerically, using the STAGS program in which two-dimensional finite differences are used to solve buckling and nonlinear problems. Universal nondimensional parameters, suggested by linear buckling data, are found to hold for the postbuckling range. Results indicate that the postbuckling stiffness of shear webs with isotropic panels is roughly two thirds of the prebuckling stiffness. The postbuckling behavior of shear webs with isotropic and orthotropic material properties is compared. Some practical aspects of solving nonlinear problems of this type by the numerical method employed are examined.

Stein, M.↗
NASA NTRS2002

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Yan, Jue↗
NASA NTRS1992

Boundary formulations for shape sensitivity of temperature dependent conductivity problems

Used in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a nonlinear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems is presented that have closed form solutions. Exact analytical expressions for the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.

Kane, James H.↗
NASA NTRS1979

Some Problems of Nonlinear Waves in Solid Propellant Rocket Motors

This paper is concerned with analyses of nonlinear waves in solid propellant rockets. Most attention is given to an approximate technique which inexpensively provides results which appear to be quite accurate at least up to amplitudes of ten percent. The connection with linear stability analysis is shown. Primarily to study nonlinear stability, or triggering, the method is extended to third order in the amplitude of wave motion; no explicit results have been obtained. Application of the approximate method to the behavior of pulses is described.

F E C Culick↗
NASA NTRS1986

An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable

The present adaptive FEM technique for convection-dominated problems is based on a Petrov-Galerkin scheme for spatial approximation, whose typical time-step employs test functions chosen to yield an approximate solution coinciding with the exact solutions at the finite element grid nodes. The derivation of truly local a posteriori error estimates is made possible by this procedure, which is also shown to be a very effective solver by the numerical examples presented.

Demkowicz, L.↗
NASA NTRS1991

Solution of geometrically nonlinear statics problems by the p-version of the finite element method

This project is concerned with the possibility of using computers for the simulation of structural systems with the same degree of reliability as full scale physical experiments. Reliable numerical simulation will make it possible to reduce the costs of engineering and improve the quality of engineering decisions based on computed information. An error of idealization is an error between the actual physical quantities on which engineering decisions are based (e.g., maximum principal stress, first natural frequency, etc.) and the same data corresponding to the exact solution of the mathematical model. An error of discretization is an error between the quantities of interest corresponding to the exact and approximate solutions of a mathematical model. A high degree of reliability can be achieved in numerical simulation only if both the errors of idealization and errors of discretization can be shown to be small.

Szabo, Barna A.↗
NASA NTRS2005

New Algorithms for Estimating Spacecraft Position Using Scanning Techniques for Deep Space Network Antennas

As more and more nonlinear estimation techniques become available, our interest is in finding out what performance improvement, if any, they can provide for practical nonlinear problems that have been traditionally solved using linear methods. In this paper we examine the problem of estimating spacecraft position using conical scan (conscan) for NASA's Deep Space Network antennas. We show that for additive disturbances on antenna power measurement, the problem can be transformed into a linear one, and we present a general solution to this problem, with the least square solution reported in literature as a special case. We also show that for additive disturbances on antenna position, the problem is a truly nonlinear one, and we present two approximate solutions based on linearization and Unscented Transformation respectively, and one 'exact' solution based on Markov Chain Monte Carlo (MCMC) method. Simulations show that, with the amount of data collected in practice, linear methods perform almost the same as MCMC methods. It is only when we artificially reduce the amount of collected data and increase the level of noise that nonlinear methods show significantly better accuracy than that achieved by linear methods, at the expense of more computation.

Metropolis-Hastings (MH)↗
NASA NTRS2001

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗