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NASA NTRS1995

Sensitivity analysis of frictional contact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the static frictional contact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of nodal displacements, and Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for the frictional contact of a composite spherical cap pressed against a rigid plate.

Karaoglan, I.↗

NASA NTRS1995

Dynamic sensitivity analysis of frictional contact/impact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic frictional contact/impact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response to variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the nodal displacements, and the Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. Temporal integration is performed by using Newmark method. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented from the frictional contact/impact response of a composite spherical cap impacting on a rigid plate.

Karaoglan, Levent↗

NASA NTRS2017

A Probabilistic Method of Assessing Carbon Accumulation Rate at Imnavait Creek Peatland, Arctic Long Term Ecological Research Station, Alaska

Arctic peatlands are an important part of the global carbon cycle, accumulating atmospheric carbon as organic matter since the Late glacial. Current methods for understanding the changing efficiency of the peatland carbon sink rely on peatlands with an undisturbed stratigraphy. Here we present a method of estimating primary carbon accumulation rate from a site where permafrost processes have either vertically or horizontally translocated nearby carbon-rich sediment out of stratigraphic order. Briefly, our new algorithm estimates the probability of the age of deposition of a random increment of sediment in the core. The method assumes that if sediment age is measured at even depth increments, dates are more likely to occur during intervals of higher accumulation rate and vice versa. Multiplying estimated sedimentation rate by measured carbon density yields carbon accumulation rate. We perform this analysis at the Imnavait Creek Peatland, near the Arctic Long Term Ecological Research network site at Toolik Lake, Alaska. Using classical radiocarbon age modeling, we find unreasonably high rates of carbon accumulation at various Holocene intervals. With our new method, we find accumulation rate changes that are in improved agreement within the context of other sites throughout Alaska and the rest of the Circum-Arctic region.

carbon accumulation;Imnavait;peatlands;permafrost;↗

NASA NTRS2000

Closed-form integrator for the quaternion (euler angle) kinematics equations

The invention is embodied in a method of integrating kinematics equations for updating a set of vehicle attitude angles of a vehicle using 3-dimensional angular velocities of the vehicle, which includes computing an integrating factor matrix from quantities corresponding to the 3-dimensional angular velocities, computing a total integrated angular rate from the quantities corresponding to a 3-dimensional angular velocities, computing a state transition matrix as a sum of (a) a first complementary function of the total integrated angular rate and (b) the integrating factor matrix multiplied by a second complementary function of the total integrated angular rate, and updating the set of vehicle attitude angles using the state transition matrix. Preferably, the method further includes computing a quanternion vector from the quantities corresponding to the 3-dimensional angular velocities, in which case the updating of the set of vehicle attitude angles using the state transition matrix is carried out by (a) updating the quanternion vector by multiplying the quanternion vector by the state transition matrix to produce an updated quanternion vector and (b) computing an updated set of vehicle attitude angles from the updated quanternion vector. The first and second trigonometric functions are complementary, such as a sine and a cosine. The quantities corresponding to the 3-dimensional angular velocities include respective averages of the 3-dimensional angular velocities over plural time frames. The updating of the quanternion vector preserves the norm of the vector, whereby the updated set of vehicle attitude angles are virtually error-free.

Whitmore, Stephen A.↗

NASA NTRS1992

Progress on single barrier varactors for submillimeter wave power generation

Theoretical work on Single Barrier Varactor (SBV) diodes, indicate that the efficiency for a multiplier has a maximum for a considerably smaller capacitance variation than previously thought. The theoretical calculations are performed, both with a simple theoretical model and a complete computer simulation using the method of harmonic balance. Modeling of the SBV is carried out in two steps. First, the semiconductor transport equations are solved simultaneously using a finite difference scheme in one dimension. Secondly, the calculated I-V, and C-V characteristics are input to a multiplier simulator which calculates the optimum impedances, and output powers at the frequencies of interest. Multiple barrier varactors can also be modeled in this way. Several examples on how to design the semiconductor layers to obtain certain characteristics are given. The calculated conversion efficiencies of the modeled structures, in a multiplier circuit, are also presented. Computer simulations for a case study of a 750 GHz multiplier show that InAs diodes perform favorably compared to GaAs diodes. InAs and InGaAs SBV diodes have been fabricated and their current vs. voltage characteristics are presented. In the InAs diode, was the large bandgap semiconductor AlSb used as barrier. The InGaAs diode was grown lattice matched to an InP substrate with InAlAs as a barrier material. The current density is greatly reduced for these two material combinations, compared to that of GaAs/AlGaAs SBV diodes. GaAs based diodes can be biased to higher voltages than InAs diodes.

Nilsen, Svein M.↗

NASA NTRS1967

Program for calculating optimum dimensions of alpha radioisotope capsules exposed to varying stress and temperature

A method and computer program were developed for calculating the creep and optimizing the dimensions of capsules filled with alpha-emitting radioisotopes. The method solves an integral equation that was developed assuming linear accumulation of partial creep lives and relating life to time-dependent stress and temperature using the Larson-Miller parameter. The computer program, CAPSUL, is written in Fortran language for the IBM 360/75 computer. The program makes a least squares fit of the creep life function using conventional constant stress, constant temperature creep data. Dimensions of capsules having maximum thermal power per unit of weight, volume, or area are calculated for a given creep life and pressure-temperature history using a numerical Lagrange Multiplier formulation. The program also calculates the life to a prescribed strain for capsules of given dimensions and pressure-temperature history. The method has been used to analyze creep data for the alloys 304 stainless steel, Hastelloy N, Cb-1% Zr, FS-85, and T-222.

J. P. Nichols↗

NASA NTRS1993

Shape optimization governed by the Euler equations using an adjoint method

A numerical approach for the treatment of optimal shape problems governed by the Euler equations is discussed. Focus is on flows with embedded shocks. A very simple problem is considered: the design of a quasi-one-dimensional Laval nozzle. A cost function and a set of Lagrange multipliers are introduced to achieve the minimum. The nature of the resulting costate equations is discussed. A theoretical difficulty that arises for cases with embedded shocks is pointed out and solved. Finally, some results are given to illustrate the effectiveness of the method.

Iollo, Angelo↗

NASA NTRS1982

An instrument for rapidly measuring plasma distribution functions with high resolution

An instrument which can rapidly measure plasma particle distribution functions has been developed based upon recent innovations in electrostatic analyzer design and position sensitive particle detection. The new analyzer uses a quadrispherical geometry, but has a completely uniform 360 deg fan-shaped field of view. The polar angular distribution of entering particles is spatially imaged onto a position sensitive detector at the annular exit aperture after a deflection through 90 deg. Several methods of position sensitive detection have been successfully used in conjunction with this analyzer. The simplest is individual channel multipliers spaced around the annular exit. Microchannel plate electron multipliers permit greater position resolution to be obtained, and a detector using microchannel plates followed by a resistive anode image converter obtains angular resolution of about one degree, i.e., 360 individual angle pixels. Instruments of this type were flown on a sounding rocket in early 1982 and will be included on the Giotto comet mission and the AMPTE ion release module (IRM).

Carlson, C. W.↗

NASA NTRS1992

NASTRAN internal improvements for 1992 release

The 1992 NASTRAN release incorporates a number of improvements transparent to users. The NASTRAN executable was made smaller by 70 pct. for the RISC base Unix machines by linking NASTRAN into a single program, freeing some 33 megabytes of system disc space that can be used by NASTRAN for solving larger problems. Some basic matrix operations, such as forward-backward substitution (FBS), multiply-add (MPYAD), matrix transpose, and fast eigensolution extraction routine (FEER), have been made more efficient by including new methods, new logic, new I/O techniques, and, in some cases, new subroutines. Some of the improvements provide ground work ready for system vectorization. These are finite element basic operations, and are used repeatedly in a finite element program such as NASTRAN. Any improvements on these basic operations can be translated into substantial cost and cpu time savings. NASTRAN is also discussed in various computer platforms.

Chan, Gordon C.↗

NASA NTRS1980

Solutions of contact problems by the assumed stress hybrid model

A method was developed for contact problems which may be either frictional or frictionless and may involve extensive sliding between deformable bodies. It was based on an assumed stress hybrid approach and on an incremental variational principle for which the Euler's equations of the functional include the equilibrium and compatibility conditions at the contact surface. The tractions at an assumed contact surface were introduced as Lagrangian multipliers in the formulation. It was concluded from the results of several example solutions that the extensive sliding contact between deformable bodies can be solved by the present method.

Kubomura, K.↗

NASA NTRS1981

Estimating ocean-air heat fluxes during cold air outbreaks by satellite

Nomograms of mean column heating due to surface sensible and latent heat fluxes were developed. Mean sensible heating of the cloud free region is related to the cloud free path (CFP, the distance from the shore to the first cloud formation) and the difference between land air and sea surface temperatures, theta sub 1 and theta sub 0, respectively. Mean latent heating is related to the CFP and the difference between land air and sea surface humidities q sub 1 and q sub 0 respectively. Results are also applicable to any path within the cloud free region. Corresponding heat fluxes may be obtained by multiplying the mean heating by the mean wind speed in the boundary layer. The sensible heating estimated by the present method is found to be in good agreement with that computed from the bulk transfer formula. The sensitivity of the solutions to the variations in the initial coastal soundings and large scale subsidence is also investigated. The results are not sensitive to divergence but are affected by the initial lapse rate of potential temperature; the greater the stability, the smaller the heating, other things being equal. Unless one knows the lapse rate at the shore, this requires another independent measurement. For this purpose the downwind slope of the square of the boundary layer height is used, the mean value of which is also directly proportional to the mean sensible heating. The height of the boundary layer should be measurable by future spaceborn lidar systems.

Chou, S. H.↗

NASA NTRS1989

Reflections, diffractions, and surface waves for an interior impedance wedge of arbitrary angle

The asymptotic-impedance wedge solution for plane-wave illumination at normal incidence is examined for interior wedge diffraction. An efficient method for calculating the diffraction coefficient for arbitrary wedge angle is presented. The asymptotic solution isolates the incident, singly reflected, multiply reflected, diffracted, surface-wave, and associated-surface-wave transition fields. Multiply reflected fields (of any order) from the exact solution arise as ratios of auxiliary Maliuzhinets functions; however, by using properties of these functions, the representation can be reduced to products of reflection coefficients, much more efficient for calculation. A surface-wave transition field is added to the surface wave to retain continuity of the total field at the surface wave boundaries. This formulation is equally valid for both exterior and interior wedges with uniform but different impedances on each face, for both soft and hard polarizations.

Griesser, Timothy↗

NASA NTRS2003

Enhancements to an Atmospheric Ascent Guidance Algorithm

Enhancements to an advanced ascent guidance algorithm for rocket-powered launch vehicles are described. A general method has been developed for conveniently and efficiently handling the common case of (asymmetric) launch vehicles with unbalanced thrust and aerodynamic moments. The new part of this development concerns the treatment of endo-atmospheric flight. An alternative method for handing the transversality conditions has been developed that eliminates the need for a priori elimination of the constant multipliers that adjoin the terminal state constraints to the performance index. As a result, new constraints can be formulated and implemented with relative ease. The problem of burn-coast-burn trajectory optimization is treated using a modified multiple shooting technique.

Dukeman, Greg A.↗

NASA NTRS2009

An Argument Against Augmenting the Lagrangean for Nonholonomic Systems

Although it is known that correct dynamical equations of motion for a nonholonomic system cannot be obtained from a Lagrangean that has been augmented with a sum of the nonholonomic constraint equations weighted with multipliers, previous publications suggest otherwise. An example has been proposed in support of augmentation and purportedly demonstrates that an accepted method fails to produce correct equations of motion whereas augmentation leads to correct equations; this paper shows that in fact the opposite is true. The correct equations, previously discounted on the basis of a flawed application of the Newton-Euler method, are verified by using Kane's method and a new approach to determining the directions of constraint forces. A correct application of the Newton-Euler method reproduces valid equations.

Roithmayr, Carlos M.↗

NASA NTRS1974

Second-order small disturbance theory for hypersonic flow over power-law bodies

A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.

Townsend, J. C.↗

NASA NTRS1981

Satellite temperature soundings: Microwave satellite observations

Tiros satellite microwave measurements together with radiosonde data are used to illustrate a method for deriving vertical temperature distributions in the atmosphere on the scale of 100 km. The method employs N equations in N unknowns. The unknowns are the N coefficients which are needed at each pressure level to multiply the measured N radiances in order to retrieve the vertical temperature distributions. As an example, the spatial variation of the tropopause characteristics is derived over a cyclone. Diurnal variations in the radiances and the consistency of radiosondes and satellite radiance data need further investigation.

Fritz, S.↗

NASA NTRS2011

In-Service Monitoring of Steam Pipe Systems at High Temperatures

An effective, in-service health monitoring system is needed to track water condensation in real time through the walls of steam pipes. The system is required to measure the height of the condensed water from outside the pipe, while operating at temperatures that are as high as 250 C. The system needs to account for the effects of water flow and cavitation. In addition, it is desired that the system does not require perforating the pipes and thereby reducing the structural integrity. Generally, steam pipes are used as part of the district heating system carrying steam from central power stations under the streets to heat, cool, or supply power to high-rise buildings and businesses. This system uses ultrasonic waves in pulse-echo and acquires reflected signal data. Via autocorrelation, it determines the water height while eliminating the effect of noise and multiple reflections from the wall of the pipe. The system performs nondestructive monitoring through the walls of steam pipes, and automatically measures the height of condensed water while operating at the high-temperature conditions of 250 C. For this purpose, the ultrasonic pulse-echo method is used where the time-of-flight of the wave reflections inside the water are measured, and it is multiplied by the wave velocity to determine the height. The pulse-echo test consists of emitting ultrasonic wave pulses from a piezoelectric transducer and receiving the reflections from the top and bottom of the condensed water. A single transducer is used as a transmitter as well as the receiver of the ultrasonic waves. To obtain high resolution, a broadband transducer is used and the frequency can be in the range of 2.25 to 10 MHz, providing sharp pulses in the time domain allowing for higher resolution in identifying the individual reflections.

Bar-Cohen, Yoseph↗

NASA NTRS1972

The radiative transfer equation and environmental effects in the upper atmosphere.

A highly effective approach to the solution of the radiative transfer equation, including the effects of emission, absorption, and multiply scattered radiation, is described. The transfer equation is cast in its unsteady hyperbolic form which is amenable to several different numerical methods of solution. Comparisons of solutions with emission, absorption, and scattering of radiation, are presented to demonstrate the validity of the present approach.

Callis, L. B.↗