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At least 145 records · Page 8

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NASA NTRS1990

Elimination of Gibbs' phenomena from error analysis of finite element results

This paper is one of a series on error analysis and correction of finite element solutions for plates and shells. The error analysis in the earlier papers used half-range double Fourier sine series for numerical harmonic analysis. The half-range formulas are simple to apply, but they can be inaccurate near the ends of the ranges of the independent variables. The Gibbs' phenomenon exhibited by half-range sine series in one independent variable has a two-dimensional analog; a classic example is the Navier solution in a double half-range sine series for the simply supported plate under a uniform load. A simple change of variables is introduced in the paper to improve the accuracy of the double Fourier sine series without adding complexity to the numerical analysis. The change of variables is applied to the problem of approximating a transverse load that is tabulated on a rectangular grid. A solution based on the change of variables is compared with results from the Navier solution for the simply supported plate problem and finite element results for the same problem.

Thurston, Gaylen A.↗

NASA NTRS1985

Contributions to the finite element solution of the fan noise radiation problem

The radiation of fan generated noise to the far field from a nacelle of realistic geometry is investigated using the finite element method. Several innovations have been introduced to minimize the computational requirements and create a highly efficient numerical scheme. The innovations include: (1) formulation of the problem in terms of velocity potential and density in such a way that no inlet mean flow velocity derivatives are required in the field equations, (2) the use of 'wave envelope' elements in an outer region permitting a grid much coarser than would be used for conventional finite elements, (3) the use of a mesh which deforms with an increase of forward flight speed so that mesh lines are always lines of constant phase and rays for a point source, permitting the use of wave envelope elements and simple boundary conditions for any case of forward velocity, (4) an efficient scheme for introducing the noise source via modal amplitude coefficients, and (5) the use of a frontal solution technique which for physically realistic problems drastically reduces the active storage requirements. The finite element scheme is outlined, as are the specific details of the innovations. Results are given for cases where comparable experimental data are available.

Eversman, W.↗

NASA NTRS1983

An investigation of the accuracy of finite difference methods in the solution of linear elasticity problems

The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.

Bauld, N. R., Jr.↗

NASA NTRS1993

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

Szabo, Barna A.↗

NASA NTRS1987

Finite element implementation of Robinson's unified viscoplastic model and its application to some uniaxial and multiaxial problems

A description of the finite element implementation of Robinson's unified viscoplastic model into the General Purpose Finite Element Program (MARC) is presented. To demonstrate its application, the implementation is applied to some uniaxial and multiaxial problems. A comparison of the results for the multiaxial problem of a thick internally pressurized cylinder, obtained using the finite element implementation and an analytical solution, is also presented. The excellent agreement obtained confirms the correct finite element implementation of Robinson's model.

Arya, V. K.↗

NASA NTRS1989

Finite element implementation of Robinson's unified viscoplastic model and its application to some uniaxial and multiaxial problems

Arya, V. K.↗

NASA NTRS1978

A split band-Cholesky equation solving strategy for finite element analysis of transient field problems

The paper describes the split-Cholesky strategy for banded matrices arising from the large systems of equations in certain fluid mechanics problems. The basic idea is that for a banded matrix the computation can be carried out in pieces, with only a small portion of the matrix residing in core. Mesh considerations are discussed by demonstrating the manner in which the assembly of finite element equations proceeds for linear trial functions on a triangular mesh. The FORTRAN code which implements the out-of-core decomposition strategy for banded symmetric positive definite matrices (mass matrices) of a coupled initial value problem is given.

Cooke, C. H.↗

NASA NTRS1980

Application of a Galerkin finite element method to atmospheric transport problems

Numerical simulation of the movement of a contaminant within the atmosphere presents difficulties due to the multidimensionality of the problem and the fact that the horizontal transport is usually convection dominated, that the boundary conditions are mixed, and that both slow and fast atmospheric chemical reactions can be important. In this study, numerical experiments using a Crank-Nicolson Galerkin finite element method to solve the time-dependent partial differential equations demonstrate the applicability and accuracy of this method for the variety of conditions encountered in atmospheric pollutant modeling. The Crank-Nicolson Galerkin method using piecewise linear, piecewise cubic Hermite polynomials, and upwind finite elements is shown to accurately model the pure convection of initial wave forms. Numerical results studying the interactions of convection, diffusion, chemical reaction, pollutant removal, and the effects of contaminant emission source strength, source location and multiple sources are also presented.

Carmichael, G. R.↗

NASA NTRS1986

A finite element surface impedance representation for steady-state problems

A procedure for determining the scattered pressure field resulting from a monochromatic harmonic wave that is incident upon a layer energy absorbing structure is treated. The situation where the structure is modeled with finite elements and the surrounding acoustic medium (water or air) is represented with either acoustic finite elements, or some type of boundary integral formulation, is considered. Finite element modeling problems arise when the construction of the structure, at the fluid structure interface, are nonhomogeneous and in particular, when the inhomogeneities are small relative to the acoustic wave length. An approximate procedure is presented for replacing the detailed microscopic representation of the layered surface configuration with an equivalent simple surface impedance finite element, which is especially designed to work only at limited frequencies. An example problem is presented using NASTRAN. However, the procedure is general enough to adapt to practically any finite element code having a steady state option.

Kalinowski, A. J.↗

NASA NTRS2006

Stochastic Simulation Tool for Aerospace Structural Analysis

Stochastic simulation refers to incorporating the effects of design tolerances and uncertainties into the design analysis model and then determining their influence on the design. A high-level evaluation of one such stochastic simulation tool, the MSC.Robust Design tool by MSC.Software Corporation, has been conducted. This stochastic simulation tool provides structural analysts with a tool to interrogate their structural design based on their mathematical description of the design problem using finite element analysis methods. This tool leverages the analyst's prior investment in finite element model development of a particular design. The original finite element model is treated as the baseline structural analysis model for the stochastic simulations that are to be performed. A Monte Carlo approach is used by MSC.Robust Design to determine the effects of scatter in design input variables on response output parameters. The tool was not designed to provide a probabilistic assessment, but to assist engineers in understanding cause and effect. It is driven by a graphical-user interface and retains the engineer-in-the-loop strategy for design evaluation and improvement. The application problem for the evaluation is chosen to be a two-dimensional shell finite element model of a Space Shuttle wing leading-edge panel under re-entry aerodynamic loading. MSC.Robust Design adds value to the analysis effort by rapidly being able to identify design input variables whose variability causes the most influence in response output parameters.

Knight, Norman F.↗

NASA NTRS2010

Error and Uncertainty Quantification in the Numerical Simulation of Complex Fluid Flows

The failure of numerical simulation to predict physical reality is often a direct consequence of the compounding effects of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from inexact knowledge and/or statistical representation. In this topical lecture, we briefly review systematic theories for quantifying numerical errors and restricted forms of model uncertainty occurring in simulations of fluid flow. A goal of this lecture is to elucidate both positive and negative aspects of applying these theories to practical fluid flow problems. Finite-element and finite-volume calculations of subsonic and hypersonic fluid flow are presented to contrast the differing roles of numerical error and model uncertainty. for these problems.

Barth, Timothy J.↗

NASA NTRS1982

A new capability for elastic aircraft airloads via NASTRAN

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.

Briggs, H. C.↗

NASA NTRS1976

On a 3-D singularity element for computation of combined mode stress intensities

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

Atluri, S. N.↗

NASA NTRS1982

Finite element analysis of aerodynamic heating in three dimensional viscous high speed compressible flow: An assessment

The current capability of the finite element method for solving problems of viscous flow is reviewed. Much work has been directed to the simulation of incompressible flows and the relevant features are described. The methods available for, and the problems associated with, the finite element solution of high speed viscous compressible flows are analyzed. A plan for developing finite element research in this area with experimental support is presented.

Morgan, K.↗

NASA NTRS1987

A microstructural lattice model for strain oriented problems: A combined Monte Carlo finite element technique

A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, was developed which simulates microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. In this approach, the microstructure is discretized onto a fine lattice. Each element in the lattice is labelled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis was validated by comparing this approach with a closed form, analytical method for stress assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analytical for multiparticle problems were also run and in general the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperature.

Gayda, J.↗

NASA NTRS1977

Finite-element analysis of a weld-penetration problem

The stress concentration factor for a weld penetration defect is calculated by the finite-element method. A stress intensity factor is computed by use of the finite-element solution and the J-integral. The results are compared with experimental results.

Rogge, T. R.↗

NASA NTRS2002

Scaling Laws Applied to a Modal Formulation of the Aeroservoelastic Equations

A method of scaling is described that easily converts the aeroelastic equations of motion of a full-sized aircraft into ones of a wind-tunnel model. To implement the method, a set of rules is provided for the conversion process involving matrix operations with scale factors. In addition, a technique for analytically incorporating a spring mounting system into the aeroelastic equations is also presented. As an example problem, a finite element model of a full-sized aircraft is introduced from the High Speed Research (HSR) program to exercise the scaling method. With a set of scale factor values, a brief outline is given of a procedure to generate the first-order aeroservoelastic analytical model representing the wind-tunnel model. To verify the scaling process as applied to the example problem, the root-locus patterns from the full-sized vehicle and the wind-tunnel model are compared to see if the root magnitudes scale with the frequency scale factor value. Selected time-history results are given from a numerical simulation of an active-controlled wind-tunnel model to demonstrate the utility of the scaling process.

Pototzky, Anthony S.↗

NASA NTRS1979

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Periaux, J.↗