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All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

The use of parabolic variations and the direct determination of stress intensity factors using the BIE method

Two advances in the numerical techniques of utilizing the BIE method are presented. The boundary unknowns are represented by parabolas over each interval which are integrated in closed form. These integrals are listed for easy use. For problems involving crack tip singularities, these singularities are included in the boundary integrals so that the stress intensity factor becomes just one more unknown in the set of boundary unknowns thus avoiding the uncertainties of plotting and extrapolating techniques. The method is applied to the problems of a notched beam in tension and bending, with excellent results.

Mendelson, A.↗
NASA NTRS1977

The use of parabolic variations and the direct determination of stress intensity factors using the BIE method

Two advances in the numerical techniques of utilizing the BIE method are presented. The boundary unknowns are represented by parabolas over each interval which are integrated in closed form. These integrals are listed for easy use. For problems involving crack tip singularities, these singularities are included in the boundary integrals so that the stress intensity factor becomes just one more unknown in the set of boundary unknowns thus avoiding the uncertainties of plotting and extrapolating techniques. The method is applied to the problems of a notched beam in tension and bending, with excellent results.

Mendelson, A.↗
NASA NTRS1975

Application of boundary integral equations to elastoplastic problems

The application of the boundary integral equation method (BIE) to the elastoplastic torsion problem is considered. It is found that the BIE is very suitable for the elastoplastic analysis of the torsion of prismatic bars. A comparison of the BIE with the finite difference method shows savings for the BIE concerning the number of unknowns which have to be determined and also a much faster convergence rate. Attention is given to the problem of an edge-notched beam in pure bending, taking into account a biharmonic formulation and a displacement formulation.

Mendelson, A.↗
NASA NTRS1982

Boundary integral equation method calculations of surface regression effects in flame spreading

A solid-phase conduction problem that is a modified version of one that has been treated previously in the literature and is applicable to flame spreading over a pyrolyzing fuel is solved using a boundary integral equation (BIE) method. Results are compared to surface temperature measurements that can be found in the literature. In addition, the heat conducted through the solid forward of the flame, the heat transfer responsible for sustaining the flame, is also computed in terms of the Peclet number based on a heated layer depth using the BIE method and approximate methods based on asymptotic expansions. Agreement between computed and experimental results is quite good as is agreement between the BIE and the approximate results.

Altenkirch, R. A.↗
NASA NTRS1993

Symmetric Galerkin boundary formulations employing curved elements

Accounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e., double) integration strategy that is competitive with its counterpart (i.e., singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C 1 continuity, a fact that allows the employment of the popular continuous element technology. The behavior of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation-based BEA, for large-scale problems.

Kane, J. H.↗
NASA NTRS1984

Methods for analysis of cracks in three-dimensional solids

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Raju, I. S.↗
NASA NTRS2002

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

Atluri, Satya N.↗
NASA NTRS1982

Experimental boundary integral equation applications in speckle interferometry

A complete data analysis system utilizing laser speckle interferometry and Experimental Integral Equation Method (EBIE) is described. A host computer provides the optical data analysis and serves as an input device to a PDP11/VAX computer for numerical analysis. The basic theory of pointwise filtering and digital correlation is described as experimental data input to the BIE method.

Fraley, J. E.↗
NASA NTRS1985

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

Homicz, G. F.↗
NASA NTRS1992

Prediction of two-dimensional sound propagation over an arbitrarily-shaped barrier using the boundary element method

2D sound propagation over an arbitrarily-shaped barrier situated on a locally reacting infinite plane in a homogeneous medium is treated utilizing the BEM. The BIE is formulated so that the integral along an infinite homogeneous plane disappears if the half space Green's function is selected to satisfy the boundary condition of this plane. Comparison of the BEM results with test results by Habault and by Kearns shows good agreement of the sound field utilizing the BEM.

Park, Jong M.↗
NASA NTRS2002

Data from TRMM Field Experiments at the Goddard Earth Sciences (GES) DISC DAAC Tropical Rainfall Measuring Mission Field Experiments (TRMM FEs)

The basic objectives of TRMM Field Experiments (FEs) are to evaluate the physical assumptions made by TRMM. rainfall algorithms, initialize and validate the cloud resolving models, test latent heating retrievals from TRMM mea- surements, and evaluate methods to estimate rainfall and latent heating from ground-based radars. The field experiments were designed as a group, so that specific measure ments could be compared between experiments in order to gain insight into the regional dependence of any findings. The TExas FLorida UNderflight Experiments (TEFLUN) were designed to provide validation measurements for TRMM and for the enhancement of TRMM precipitation algorithms. TEFLUN-A focused on east Texas. TEFLUN-B was conducted in close coordination with the Third Convection And Moisture Experiment (CAMEX-3) in Florida. The TRMM-LBA was conducted in coordination with the Large Scale Biosphere-Atmosphere Experiment in Amazonia (LBA). The LBA objectives are to further our understanding of the climatological, ecological, bie geochemical, and hydrological processes in Amazonia and the impact of land use/land change on these processes. Specifically, TRMM-LBA addressed issues related to land precipitation algorithms. The Kwa jalein Experiment (KWAJEX), conducted on the Kwajalein Island in the Republic of Marshall Islands (RMI), was designed to address issues of TRMM products over the ocean. The purpose of the South China Sea Monsoon Experiment (SCSMEX) was to study the water and energy cycle of the Asian monsoon in order to provide better understanding and improve prediction. and instruments of the TRMM FEs. The platforms and instruments of the TRMM FEs are given.

Source record↗
NASA NTRS1974

Relation between near field and far field acoustic measurements

Several approaches to the problem of determining the far field directivity of an acoustic source located in a reverberant environment, such as a wind tunnel, are investigated analytically and experimentally. The decrease of sound pressure level with distance is illustrated; and the spatial extent of the hydrodynamic and geometric near fields, the far field, and the reverberant field are described. A previously-prosposed analytical technique for predicting the far field directivity of the acoustic source on the basis of near field data is investigated. Experiments are conducted with small acoustic sources and an analysis is performed to determine the variation with distance from the source of the directionality of the sound field. A novel experiment is conducted in which the sound pressure measured at various distances from an acoustic driver located in the NASA Ames 40 x 80 ft wind tunnel is crosscorrelated with the driver excitation voltage.

Bies, D. A.↗
NASA NTRS1979

Pilot interministerial operation for remote sensing

Advantages and disadvantages of traditional methods of obtaining required information for land and resources management and the possibilities of remote sensing are discussed. The services available, organization and objectives of the pilot operation are presented. Emphasis is placed on multidisciplinary dialog among designers, builders, operators, interpreters and users in all phases. The principles, operation and practical applications of remote sensing systems and processing systems under the pilot operation are presented.

Delamare, J. M.↗