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At least 235 records · Page 13

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NASA NTRS1979

Finite-element numerical modeling of atmospheric turbulent boundary layer

A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.

Lee, H. N.↗

NASA NTRS1982

Investigation of rotational transonic flows through ducts using a finite element scheme

An application of the finite element method is presented in order to study the flow through a two-dimensional channel including the choked and nearly-choked flow conditions. The mathematical procedure provides a combined treatment of potential and Euler equations, where the steady Euler equations are solved through the integration of a pseudo-time system which is equivalent to a relaxation scheme; the isentropic, potential flow equations are embedded in this formulation. To analyze the transonic flow through a channel with near-choked flow conditions, the flow through a parallel channel with a 10 percent circular arc bump is calculated as a sample problem.

Akay, H. U.↗

NASA NTRS1993

On the use of the consistent mass matrix in flexible multibody systems

Two different methods are used in finite element structural analysis to define element mass distribution: consistent and lumped mass approximations. The lumped mass method is currently favored in multibody dynamics software packages because of its computational efficiency. This paper, however, presents a multibody dynamics formulation based on the consistent mass approach which should prove to be as computationally efficient as the lumped mass approach. It is shown that when component flexibility is modelled using modal coordinates, the equations of motion, as formulated by these two methods, are very similar in appearance, thereby facilitating their comparison. It is also shown, through simulation of a simple multibody system, that a system formulated with the lumped mass approximation will often require more finite elements and smaller integration step sizes than the corresponding consistent mass system.

Anthony, Tobin C.↗

NASA NTRS1990

Trees, bialgebras and intrinsic numerical algorithms

Preliminary work about intrinsic numerical integrators evolving on groups is described. Fix a finite dimensional Lie group G; let g denote its Lie algebra, and let Y(sub 1),...,Y(sub N) denote a basis of g. A class of numerical algorithms is presented that approximate solutions to differential equations evolving on G of the form: dot-x(t) = F(x(t)), x(0) = p is an element of G. The algorithms depend upon constants c(sub i) and c(sub ij), for i = 1,...,k and j is less than i. The algorithms have the property that if the algorithm starts on the group, then it remains on the group. In addition, they also have the property that if G is the abelian group R(N), then the algorithm becomes the classical Runge-Kutta algorithm. The Cayley algebra generated by labeled, ordered trees is used to generate the equations that the coefficients c(sub i) and c(sub ij) must satisfy in order for the algorithm to yield an rth order numerical integrator and to analyze the resulting algorithms.

Crouch, Peter↗

NASA NTRS1988

Finite element discrete ordinates method for radiative transfer in non-rotationally invariant scattering media - Application to the leaf canopy problem

A finite element discrete ordinates method for solving the radiative transfer equation in nonrotationally invariant scattering media has been applied to the lead-canopy problem, and results are presented on the cross sections and the reflection functions. The method is based on a unique implementation of the Galerkin integral law formulation of the transport equation. For both near-normal and grazing incidences, the transfer functions of leaf canopies are found to be strongly anisotropic, with relatively more scattered flux in the vertical directions. It is suggested that the assumption of isotropic scattering in leaf canopies is not valid.

Myneni, Ranga B.↗

NASA NTRS1993

Contact-impact analysis of deployable space systems

This paper presents simulation results of a flexible, deployable space system with multiple contact-impact events, using three different modeling approaches. In the first two approaches, the equations of motion of the system are written in terms of generalized coordinates of each component, with modal coordinates used to account for flexibility in the components. Two different methods are used to model contact-impact events in the systems. In the momentum balance method, as contact-impact occurs, momentum equations of the systems are solved for the jump discontinuity in velocity of generalized coordinates. Integration of the system is restarted with the new initial conditions from solutions of momentum equations. In the logical function method, a virtual spring connecting the two contact points is assumed. The virtual spring is active only when impact occurs. No special treatment is needed in the integration algorithm using this method. In the third approach, instead of using modal coordinates, a finite element based formulation for the transient dynamics of mechanical system is used to model flexibility of the components. The logical function method is used to model contact-impact in the third approach.

Wu, Shih-Chin↗

NASA NTRS1992

A finite element: Boundary integral method for electromagnetic scattering

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.

Collins, J. D.↗

NASA NTRS1972

Assessment of advances in structural analysis for space shuttle

The latest technology for structural analysis in relation to the design tasks that lie ahead for the space shuttle is reviewed. For shell-of-revolution structures, the analysis can be formulated as a one-dimensional problem which is readily solved by using finite-difference or numerical-integration techniques. For more general asymmetric shells, a two-dimensional formulation is required. However, the governing equations are readily formulated and are amenable to solution by finite-difference techniques. For a completely general structural arrangement, such as structural frameworks, recourse is usually made to discretized formulations using finite elements. Of course, the finite-element programs could be used for shell structures, but at a loss in accuracy and increase in computer time compared with the special purpose programs.

Dixon, S. C.↗

NASA NTRS1988

MHOST: An efficient finite element program for inelastic analysis of solids and structures

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Nakazawa, S.↗

NASA NTRS1989

Analysis of finite phased arrays of circular microstrip patches

A method is presented for analyzing a finite planar array of circular microstrip patches fed by coaxial probes. The self- and mutual impedances between array elements are calculated using the method of moments with the dyadic Green's function for a dielectric layer on a ground plane. The patch circuits are determined by using the reaction integral equation. The active input impedance as well as the active element pattern of the array are computed from a knowledge of the resultant patch currents. The calculated results for two-element and eight-element linear arrays are in good agreement with experimental data. The active reflection coefficient and element pattern for the center and edge elements of a two-dimensional array as a function of scan angle are also presented.

Deshpande, Manohar D.↗

NASA NTRS1999

Development of Analysis Methods for Designing with Composites

The project involved the development of new analysis methods to achieve efficient design of composite structures. We developed a complex variational formulation to analyze the in-plane and bending coupling response of an unsymmetrically laminated plate with an elliptical cutout subjected to arbitrary edge loading as shown in Figure 1. This formulation utilizes four independent complex potentials that satisfy the coupled in-plane and bending equilibrium equations, thus eliminating the area integrals from the strain energy expression. The solution to a finite geometry laminate under arbitrary loading is obtained by minimizing the total potential energy function and solving for the unknown coefficients of the complex potentials. The validity of this approach is demonstrated by comparison with finite element analysis predictions for a laminate with an inclined elliptical cutout under bi-axial loading.The geometry and loading of this laminate with a lay-up of [-45/45] are shown in Figure 2. The deformed configuration shown in Figure 3 reflects the presence of bending-stretching coupling. The validity of the present method is established by comparing the out-of-plane deflections along the boundary of the elliptical cutout from the present approach with those of the finite element method. The comparison shown in Figure 4 indicates remarkable agreement. The details of this method are described in a manuscript by Madenci et al. (1998).

Madenci, E.↗

NASA NTRS2001

Computational Aeroacoustics by the Space-time CE/SE Method

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Loh, Ching Y.↗

NASA NTRS1996

Simulation of Spiral Slot Antennas on Composite Platforms

The project goals, plan and accomplishments up to this point are summarized in the viewgraphs. Among the various accomplishments, the most important have been: the development of the prismatic finite element code for doubly curved platforms and its validation with many different antenna configurations; the design and fabrication of a new slot spiral antennas suitable for automobile cellular, GPS and PCs communications; the investigation and development of various mesh truncation schemes, including the perfectly matched absorber and various fast integral equation methods; and the introduction of a frequency domain extrapolation technique (AWE) for predicting broadband responses using only a few samples of the response. This report contains several individual reports most of which have been submitted for publication to referred journals. For a report on the frequency extrapolation technique, the reader is referred to the UM Radiation Laboratory report A total of 14 papers have been published or accepted for publication with the full or partial support of this grant. Several more papers are in preparation.

Volakis, John L.↗

NASA NTRS1998

Closed Form Equations for the Preliminary Design of a Heat-Pipe-Cooled Leading Edge

A set of closed form equations for the preliminary evaluation and design of a heat-pipe-cooled leading edge is presented. The set of equations can provide a leading-edge designer with a quick evaluation of the feasibility of using heat-pipe cooling. The heat pipes can be embedded in a metallic or composite structure. The maximum heat flux, total integrated heat load, and thermal properties of the structure and heat-pipe container are required input. The heat-pipe operating temperature, maximum surface temperature, heat-pipe length, and heat pipe-spacing can be estimated. Results using the design equations compared well with those from a 3-D finite element analysis for both a large and small radius leading edge.

Glass, David E.↗

NASA NTRS1982

On the dynamic collapse of a column impacting a rigid surface

Results are presented of an analytical investigation on the dynamic collapse of an elastic periodically supported column. The column has an attached mass at one end and impacts a rigid surface with prescribed velocity and angle of incidence at the other end. A first-order approximate nonlinear analysis is developed in which it is assumed that only first-order nonlinear terms need be retained. Differential equations are derived and solved numerically by explicit time integration in order to determine specific ranges of the basic nondimensional parameters for which the response characteristics are markedly different. To assess modeling sophistication relative to prediction accuracy, a comparison is made of the results from this approximate analysis with those of a finite element computer code based on a convected coordinate formulation.

Housner, J. M.↗

NASA NTRS1982

Subsonic aerodynamic and flutter characteristics of several wings calculated by the SOUSSA P1.1 panel method

Several applications of the steady, oscillatory, and unsteady subsonic and supersonic aerodynamics (SOUSSA) computer program to wings with steady and oscillatory motion, including flutter, are discussed. The program employs a generalized Green's function to the full, time-dependent potential-flow equation to obtain an integral equation for the velocity potential at any point in a flow, even points on a body or whole bodies in a flow. Aerodynamic calculations are provided for two rectangular wings, a clipped-tip delta wing, and two swept wings with and without a fuselage. The number and distribution of the finite element panels are varied in order to demonstrate the convergence of the results. The results are shown to be close to those of lifting-surface theory, and further applications with bodies having deformities, arbitrary shapes, motions, and deformations are indicated.

Yates, E. C., Jr.↗

NASA NTRS1989

A new uniformly valid asymptotic integration algorithm for elasto-plastic-creep and unified viscoplastic theories including continuum damage

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

Chulya, A.↗

NASA NTRS1991

A new uniformly valid asymptotic integration algorithm for elasto-plastic creep and unified viscoplastic theories including continuum damage

Chulya, Abhisak↗