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All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

Chang, S. C.↗
NASA NTRS1986

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

Chang, S. C.↗
NASA NTRS1986

Solution of elliptic PDEs by fast Poisson solvers using a local relaxation factor

A large class of two- and three-dimensional, nonseparable elliptic partial differential equations (PDEs) is presently solved by means of novel one-step (D'Yakanov-Gunn) and two-step (accelerated one-step) iterative procedures, using a local, discrete Fourier analysis. In addition to being easily implemented and applicable to a variety of boundary conditions, these procedures are found to be computationally efficient on the basis of the results of numerical comparison with other established methods, which lack the present one's: (1) insensitivity to grid cell size and aspect ratio, and (2) ease of convergence rate estimation by means of the coefficient of the PDE being solved. The two-step procedure is numerically demonstrated to outperform the one-step procedure in the case of PDEs with variable coefficients.

Chang, Sin-Chung↗
NASA NTRS1971

Sonic boom in turbulence

Poisson density functions and factor analysis of shock wave propagation and sonic boom spectra in turbulent flow

Horning, W. A.↗
NASA NTRS1974

Shear-stress intensity factors for elastic sheets with cover plates

Shear stress intensity factors are calculated for three problems concerning inextensible cover plates either bonded to or embedded in an elastic sheet which is under uniaxial tension. The stress intensity factors are small when the ratio of sheet thickness to cover plate length is small and, as the ratio increase, rapidly approach their asymptotic values for infinite sheet thickness. In the problem of the embedded cover plate, the stress intensity factor also depends on the Poisson's ratio of the sheet material. The dependence on Poisson's ratio, however, is significant only when the ratio of sheet thickness to cover plate length is small. Some possible implications of the present results for debonding of reinforced sheets under cyclic loading are briefly discussed.

Fichter, W. B.↗
NASA NTRS2013

Development of Polyimide Foam for Aircraft Sidewall Applications

In this paper, the use of polyimide foam as a lining in double panel applications is considered. It is being investigated here as a replacement for aircraft grade glass fiber and has a number of attractive functional attributes, not the least of which is its high fire resistance. The test configuration studied here consisted of two 1mm (0.04 in.) thick, flat aluminum panels separated by 12.7 cm (5.0 in.) with a 7.6 cm (3.0 in.) thick layer of foam centered in that space. Random incidence transmission loss measurements were conducted on this buildup, and conventional poro-elastic models were used to predict the performance of the lining material. Results from two densities of foam are considered. The Biot parameters of the foam were determined by a combination of direct measurement (for density, flow resistivity and Young s modulus) and inverse characterization procedures (for porosity, tortuosity, viscous and thermal characteristic length, Poisson s ratio and loss factor). The inverse characterization procedure involved matching normal incidence standing wave tube measurements of absorption coefficient and transmission loss of the isolated foam with finite element predictions. When the foam parameters determined in this way were used to predict the performance of the complete double panel system, reasonable agreement was obtained between the measured transmission loss and predictions made using a commercial statistical energy analysis code.

Silcox, Richard↗
NASA NTRS1983

Internal and edge cracks in a plate of finite width under bending

Internal and edge cracks were studied by using Reissner's transverse shear theory. The effect of stress-free boundaries on the stress intensity factors in plates under bending were investigated. Among the results found, particularly interesting are those relating to the limiting cases of the crack geometries. The numerical results are given for a single internal crack, two collinear cracks, and two edge cracks. The effect of Poisson's ratio on the stress intensity factors was studied.

Boduroglu, H.↗
NASA NTRS1983

Internal and edge cracks in a plate of finite width under bending

In this paper the title problem is studied by using Reissner's transverse shear theory. The main purpose of the paper is to investigate the effect of stress-free boundaries on the stress intensity factors in plates under bending. Among the results found particularly interesting are those relating to the limiting cases of the crack geometries. The numerical results are given for a single internal crack, two collinear cracks, and two edge cracks. Also studied is the effect of Poisson's ratio on the stress intensity factors.

Boduroglu, H.↗
NASA NTRS1979

Transverse shear effect in a circumferentially cracked cylindrical shell

The objectives of the paper are to solve the problem of a circumferentially-cracked cylindrical shell by taking into account the effect of transverse shear, and to obtain the stress intensity factors for the bending moment as well as the membrane force as the external load. The formulation of the problem is given for a specially orthotropic material within the framework of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions as to moment and stress resultants on the crack surface. The effect of Poisson's ratio on the stress intensity factors and the nature of the out-of-plane displacement along the edges of the crack, i.e., bulging, are also studied.

Delale, F.↗
NASA NTRS1979

The effect of transverse shear in a cracked plate under skew-symmetric loading

The problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered. By using a bending theory which allows the satisfaction of the boundary conditions on the crack surface regarding the normal and the twisting moments and the transverse shear load separately, it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems. The problem is solved for uniformly distributed or concentrated twisting moment or transverse shear load and the normalized Mode II and Mode III stress-intensity factors are tabulated. The results also include the effect of the Poisson's ratio and material orthotropy for specially orthotropic materials on the stress-intensity factors.

Delale, F.↗
NASA NTRS1992

Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Rosenfeld, Moshe↗
NASA NTRS1992

Elevated temperature axial and torsional fatigue behavior of Haynes 188

The results of high-temperature axial and torsional low-cycle fatigue experiments performed on Haynes 188, a wrought cobalt-base superalloy, are reported. Fatigue tests were performed at 760 C in air on thin-walled tubular specimens at various ranges under strain control. Data are also presented for coefficient of thermal expansion, elastic modulus, and shear modulus at various temperatures from room to 1000 C, and monotonic and cyclic stress-strain curves in tension and in shear at 760 C. The data set is used to evaluate several multiaxial fatigue life models (most were originally developed for room temperature multiaxial life prediction) including von Mises equivalent strain range (ASME boiler and pressure vessel code), Manson-Halford, Modified Multiaxiality Factor (proposed here), Modified Smith-Watson-Topper, and Fatemi-Socie-Kurath. At von Mises equivalent strain ranges (the torsional strain range divided by the square root of 3, taking the Poisson's ratio to be 0.5), torsionally strained specimens lasted, on average, factors of 2 to 3 times longer than axially strained specimens. The Modified Multiaxiality Factor approach shows promise as a useful method of estimating torsional fatigue life from axial fatigue data at high temperatures. Several difficulties arose with the specimen geometry and extensometry used in these experiments. Cracking at extensometer probe indentations was a problem at smaller strain ranges. Also, as the largest axial and torsional strain range fatigue tests neared completion, a small amount of specimen buckling was observed.

Bonacuse, Peter J.↗
NASA NTRS1995

Elevated temperature axial and torsional fatigue behavior of Haynes 188

The results are reported for high-temperature axial and torsional low-cycle fatigue experiments performed at 760 C in air on thin-walled tubular specimens of Haynes 188, a wrought cobalt-based superalloy. Data are also presented for mean coefficient of thermal expansion, elastic modulus, and shear modulus at various temperatures from room to 1000 C, and monotonic and cyclic stress-strain curves in tension and in shear at 760 C. This data set is used to evaluate several multiaxial fatigue life models (most were originally developed for room temperature multiaxial life prediction) including von Mises equivalent strain range (ASME Boiler and Pressure Code), Manson-Halford, modified multiaxiality factor (proposed in this paper), modified Smith-Watson-Topper, and Fatemi-Socie-Kurath. At von Mises equivalent strain ranges (the torsional strain range divided by the square root of 3, taking the Poisson's ratio to be 0.5), torsionally strained specimens lasted, on average, factors of 2 to 3 times longer than axially strained specimens. The modified multiaxiality factor approach shows promise as a useful method of estimating torsional fatigue life from axial fatigue data at high temperatures. Several difficulties arose with the specimen geometry and extensometry used in these experiments. Cracking at extensometer probe indentations was a problem at smaller strain ranges. Also, as the largest axial and torsional strain range fatigue tests neared completion, a small amount of specimen buckling was observed.

Bonacuse, Peter J.↗
NASA NTRS1987

Finite-element analysis of corner cracks in rectangular bars

Stress intensity factors for a wide range of quarter-elliptical corner cracks in rectangular bars are presented. Cracked configurations were subjected to remote tension, in-plane bending, or out-of-plane bending. Results were compared with other numerical results for a quarter-circular corner crack configuration. The present results along the interior of the crack generally agreed within 3 percent with those from the literature. Some larger differences (3 to 13 percent) were observed near the intersection of the crack front and the free surfaces in the boundary layer region. Analyses were performed to study the effect of mesh refinement in the boundary layer region and the influence of Poisson's ratio on the distribution of stress-intensity factors.

Raju, L. S.↗
NASA NTRS1992

Algorithm Calculates Cumulative Poisson Distribution

Algorithm calculates accurate values of cumulative Poisson distribution under conditions where other algorithms fail because numbers are so small (underflow) or so large (overflow) that computer cannot process them. Factors inserted temporarily to prevent underflow and overflow. Implemented in CUMPOIS computer program described in "Cumulative Poisson Distribution Program" (NPO-17714).

Bowerman, Paul N.↗
NASA NTRS1999

Direct Detection Doppler Lidar for Spaceborne Wind Measurement

Aerosol and molecular based versions of the double-edge technique can be used for direct detection Doppler lidar spaceborne wind measurement. The edge technique utilizes the edge of a high spectral resolution filter for high accuracy wind measurement using direct detection lidar. The signal is split between an edge filter channel and a broadband energy monitor channel. The energy monitor channel is used for signal normalization. The edge measurement is made as a differential frequency measurement between the outgoing laser signal and the atmospheric backscattered return for each pulse. As a result the measurement is insensitive to laser and edge filter frequency jitter and drift at a level less than a few parts in 10(exp 10). We have developed double edge versions of the edge technique for aerosol and molecular-based lidar measurement of the wind. Aerosol-based wind measurements have been made at Goddard Space Flight Center and molecular-based wind measurements at the University of Geneva. We have demonstrated atmospheric measurements using these techniques for altitudes from 1 to more than 10 km. Measurement accuracies of better than 1.25 m/s have been obtained with integration times from 5 to 30 seconds. The measurements can be scaled to space and agree, within a factor of two, with satellite-based simulations of performance based on Poisson statistics. The theory of the double edge aerosol technique is described by a generalized formulation which substantially extends the capabilities of the edge technique. It uses two edges with opposite slopes located about the laser frequency at approximately the half-width of each edge filter. This doubles the signal change for a given Doppler shift and yields a factor of 1.6 improvement in the measurement accuracy compared to the single edge technique. The use of two high resolution edge filters substantially reduces the effects of Rayleigh scattering on the measurement, as much as order of magnitude, and allows the signal to noise ratio to be substantially improved in areas of low aerosol backscatter. We describe a method that allows the Rayleigh and aerosol components of the signal to be independently determined using the two edge channels and an energy monitor channel. The effects of Rayleigh scattering may then subtracted from the measurement and we show that the correction process does not significantly increase the measurement noise for Rayleigh to aerosol ratios up to 10. We show that for small Doppler shifts a measurement accuracy of 0.4 m/s can be obtained for 5000 detected photon, 1.2 m/s for 1000 detected photons, and 3.7 m/s for 50 detected photons for a Rayleigh to aerosol ratio of 5. Methods for increasing the dynamic range of the aerosol-based system to more than +/- 100 m/s are given.

Korb, C. Laurence↗
NASA NTRS2012

Role of Temperature, Humidity and Rainfall on Influenza Transmission in Guatemala, El Salvador and Panama

Worldwide, seasonal influenza causes about 500,000 deaths and 5 million severe illnesses per year. The environmental drivers of influenza transmission are poorly understood especially in the tropics. We aimed to identify meteorological factors for influenza transmission in tropical Central America. We gathered laboratory-confirmed influenza case-counts by week from Guatemala City, San Salvador Department (El Salvador) and Panama Province from 2006 to 2010. The average total cases per year were: 390 (Guatemala), 99 (San Salvador) and 129 (Panama). Meteorological factors including daily air temperature, rainfall, relative and absolute humidity (RH, AH) were obtained from ground stations, NASA satellites and land models. For these factors, we computed weekly averages and their deviation from the 5-yr means. We assessed the relationship between the number of influenza case-counts and the meteorological factors, including effects lagged by 1 to 4 weeks, using Poisson regression for each site. Our results showed influenza in San Salvador would increase by 1 case within a week of every 1 day with RH>75% (Relative Risk (RR)= 1.32, p=.001) and every 1C increase in minimum temperature (RR=1.29, p=.007) but it would decrease by 1 case for every 1mm-above mean weekly rainfall (RR=0.93,p<.001) (model pseudo-R2=0.55). Within 2 weeks, influenza in Panama was increased by 1 case for every 1% increase in RH (RR=1.04, p=.003), and it was increased by 2 cases for every 1C increase of minimum temperature (RR=2.01, p<.001) (model pseudo-R2=0.4). Influenza counts in Guatemala had 1 case increase for every 1C increase in minimum temperature in the previous week (RR=1.21, p<.001), and for every 1mm/day-above normal increase of rainfall rate (RR=1.03, p=.03) (model pseudo-R2=0.54). Our findings that cases increase with temperature and humidity differ from some temperate-zone studies. But they indicate that climate parameters such as humidity and temperature could be predictive of influenza activity and should be incorporated into country-specific influenza transmission models

Soebiyanto, Radina P.↗
NASA NTRS1989

Fast, adaptive summation of point forces in the two-dimensional Poisson equation

A comparatively simple procedure is presented for the direct summation of the velocity field introduced by point vortices which significantly reduces the required number of operations by replacing selected partial sums by asymptotic series. Tables are presented which demonstrate the speed of this algorithm in terms of the mere doubling of computational time in dealing with a doubling of the number of vortices; current methods involve a computational time extension by a factor of 4. This procedure need not be restricted to the solution of the Poisson equation, and may be applied to other problems involving groups of points in which the interaction between elements of different groups can be simplified when the distance between groups is sufficiently great.

Van Dommelen, Leon↗