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NASA NTRS2001

Free Vibration of Uncertain Unsymmetrically Laminated Beams

Monte Carlo Simulation and Stochastic FEA are used to predict randomness in the free vibration response of thin unsymmetrically laminated beams. For the present study, it is assumed that randomness in the response is only caused by uncertainties in the ply orientations. The ply orientations may become random or uncertain during the manufacturing process. A new 16-dof beam element, based on the first-order shear deformation beam theory, is used to study the stochastic nature of the natural frequencies. Using variational principles, the element stiffness matrix and mass matrix are obtained through analytical integration. Using a random sequence a large data set is generated, containing possible random ply-orientations. This data is assumed to be symmetric. The stochastic-based finite element model for free vibrations predicts the relation between the randomness in fundamental natural frequencies and the randomness in ply-orientation. The sensitivity derivatives are calculated numerically through an exact formulation. The squared fundamental natural frequencies are expressed in terms of deterministic and probabilistic quantities, allowing to determine how sensitive they are to variations in ply angles. The predicted mean-valued fundamental natural frequency squared and the variance of the present model are in good agreement with Monte Carlo Simulation. Results, also, show that variations between plus or minus 5 degrees in ply-angles can affect free vibration response of unsymmetrically and symmetrically laminated beams.

Kapania, Rakesh K.↗

NASA NTRS1971

Phenol Analysis -- Some Analytical Considerations

Contamination of potable water supplies with halogenated phenols in concentrations of 2-10 parts per billion (ppb) produces objectionable tastes and odors capable of influencing consumer acceptability. Routine analysis by the distillation/ 4-aminoantipyrine method is limited by lack of sensitivity and subject to interference by aryl amines. This has been overcome by developing a continuous liquid-liquid extraction system to selectively isolate phenols and eliminate major interfering substances. Stable reagents have been formulated to reduce blank color and extend sensitivity. Equipment suitable for analysis of phenols at the 1 ppb level or less in 20 minutes is described.

Starkey, R. J., Jr.↗

NASA NTRS1992

Multidisciplinary analysis and sensitivity derivatives for isolated helicopter rotors in hover

A new method is presented for using Navier-Stokes results in the system analysis and sensitivity derivative computations for a helicopter rotor in hover. The system coupling includes the interactions between rotor performance, rotor structural properties and aerodynamics (i.e., airfoil shape). Emphasis is placed on the use of high fidelity Navier-Stokes algorithms for the aerodynamic problem. The present formulation is chosen to reduce the number of sensitivity derivative equations and their dimensions as much as possible. In addition, an alternative adjoint formulation is presented which dramatically reduces the computational requirement for disciplines in which there may be a large number of design variables (e.g., aerodynamics). The theoretical method makes use of a combination of derivatives from each discipline; the computation of these derivatives has already been shown to be feasible. Sample computations for the aerodynamic-rotor model coupling and an associated sensitivity derivative are also presented.

Jones, Henry E.↗

NASA NTRS1984

A Study of the Relation Between Crop Growth and Spectra Reflectance Parameters

A differential equation describing the temporal behavior of greenness, G(t), with time was developed. The basic equation, dG(t)/dt=k(t)(1-G/G sub m) where G sub m is the saturation value of greenness at time, t sub p. It demonstrated that k(t) is linearly proportional to the rate of change of leaf area index. It was also demonstrated that G sub m, t sub p and profile width, are the key to vegetation identification and that the inflection points of the profile are related to the ontogenic state of the plant. These profile features were shown to hold not only throughout the United States corn/soybean growing area, but for the first time in Argentina. A mathematical technique that maximizes the sensitivity of spectral transformation to Leaf Area Index and simultaneously minimizes the sensitivity to all other variables was formulated. Initial results on corn and wheat were obtained.

Badhwar, G.↗

NASA NTRS1984

Imaging system design for improved information capacity

Shannon's theory of information for communication channels is used to assess the performance of line-scan and sensor-array imaging systems and to optimize the design trade-offs involving sensitivity, spatial response, and sampling intervals. Formulations and computational evaluations account for spatial responses typical of line-scan and sensor-array mechanisms, lens diffraction and transmittance shading, defocus blur, and square and hexagonal sampling lattices.

Fales, C. L.↗

NASA NTRS1985

Finite elements based on consistently assumed stresses and displacements

Finite element stiffness matrices are derived using an extended Hellinger-Reissner principle in which internal displacements are added to serve as Lagrange multipliers to introduce the equilibrium constraint in each element. In a consistent formulation the assumed stresses are initially unconstrained and complete polynomials and the total displacements are also complete such that the corresponding strains are complete in the same order as the stresses. Several examples indicate that resulting properties for elements constructed by this consistent formulation are ideal and are less sensitive to distortions of element geometries. The method has been used to find the optimal stress terms for plane elements, 3-D solids, axisymmetric solids, and plate bending elements.

Pian, T. H. H.↗

NASA NTRS1991

Application of a monotonic upstream-biased transport scheme to three-dimensional constituent transport calculations

The application of van Leer's scheme, a monotonic, upstream-biased differencing scheme, to three-dimensional constituent transport calculations is shown. The major disadvantage of the scheme is shown to be a self-limiting diffusion. A major advantage of the scheme is shown to be its ability to maintain constituent correlations. The scheme is adapted for a spherical coordinate system with a hybrid sigma-pressure coordinate in the vertical. Special consideration is given to cross-polar flow. The vertical wind calculation is shown to be extremely sensitive to the method of calculating the divergence. This sensitivity implies that a vertical wind formulation consistent with the transport scheme is essential for accurate transport calculations. The computational savings of the time-splitting method used to solve this equation are shown. Finally, the capabilities of this scheme are illustrated by an ozone transport and chemistry model simulation.

Allen, Dale J.↗

NASA NTRS1993

Finite state aeroelastic model for use in rotor design optimization

In this article, a rotor aeroelastic model based on a newly developed finite state dynamic wake, coupled with blade finite element analysis, is described. The analysis is intended for application in rotor blade design optimization. A coupled simultaneous system of differential equations combining blade structural dynamics and aerodynamics is established in a formulation well-suited for design sensitivity computation. Each blade is assumed to be an elastic beam undergoing flap bending, lead-lag bending, elastic twist, and axial deflections. Aerodynamic loads are computed from unsteady blade element theory where the rotor three-dimensional unsteady wake is described by a generalized dynamic wake model. Correlation of results obtained from the analysis with flight test data is provided to assess model accuracy.

He, Chengjian↗

NASA NTRS2009

Overview of Proposal on High Resolution Climate Model Simulations of Recent Hurricane and Typhoon Activity: The Impact of SSTs and the Madden Julian Oscillation

This talk gives an update on the progress and further plans for a coordinated project to carry out and analyze high-resolution simulations of tropical storm activity with a number of state-of-the-art global climate models. Issues addressed include, the mechanisms by which SSTs control tropical storm. activity on inter-annual and longer time scales, the modulation of that activity by the Madden Julian Oscillation on sub-seasonal time scales, as well as the sensitivity of the results to model formulation. The project also encourages companion coarser resolution runs to help assess resolution dependence, and. the ability of the models to capture the large-scale and long-terra changes in the parameters important for hurricane development. Addressing the above science questions is critical to understanding the nature of the variability of the Asian-Australian monsoon and its regional impacts, and thus CLIVAR RAMP fully endorses the proposed tropical storm simulation activity. The project is open to all interested organizations and investigators, and the results from the runs will be shared among the participants, as well as made available to the broader scientific community for analysis.

Schubert, Siegfried↗

NASA NTRS1999

Viscoplastic Constitutive Theory Demonstrated for Monolithic Ceramic Materials

Development of accurate three-dimensional (multiaxial) inelastic stress-strain models is critical in utilizing advanced ceramics for challenging 21st century high-temperature structural applications. The current state of the art uses elastic stress fields as a basis for both subcritical crack growth and creep life prediction efforts aimed at predicting the time dependent reliability response of ceramic components subjected to elevated service temperatures. However, to successfully design components that will meet tomorrow's challenging requirements, design engineers must recognize that elastic predictions are inaccurate for these materials when subjected to high-temperature service conditions such as those encountered in advanced heat engine components. Analytical life prediction methodologies developed for advanced ceramics and other brittle materials must employ accurate constitutive models that capture the inelastic response exhibited by these materials at elevated service temperatures. A constitutive model recently developed at the NASA Lewis Research Center helps address this issue by accounting for the time-dependent (inelastic) material deformation phenomena (e.g., creep, rate sensitivity, and stress relaxation) exhibited by monolithic ceramics exposed to high-temperature service conditions. In addition, the proposed formulation is based on a threshold function that is sensitive to hydrostatic stress and allows different behavior in tension and compression, reflecting experimental observations obtained for these material systems.

Janosik, Lesley A.↗

NASA NTRS2012

Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology

This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.

Rallabhandi, Siriam K.↗

NASA NTRS1979

Effects of secondary yield parameter variation on predicted equilibrium potential of an object in a charging environment

The sensitivity of predicted equilibrium potential to changes in secondary electron yield parameters was investigated using MATCHG, a simple charging code which incorporates the NASCAP material property formulations. The equilibrium potential was found to be a sensitive function of one of the two parameters specifying secondary electron yield due to proton impact and of essentially all the parameters specifying yield due to electron impact. The information on the electron generated secondary yield parameters was discovered to be obtainable from monoenergetic beam charging data if charging rates as well as equilibrium potentials are accurately recorded.

Purvis, C. K.↗

NASA NTRS1979

Effects of secondary yield parameter variation on predicted equilibrium potential of an object in a charging environment

A study is presented in which the sensitivity of predicted equilibrium potential to changes in secondary electron yield parameters is investigated using MATCHG, a simple charging code which incorporates the NASCAP material property formulations. It is found that equilibrium potential is a sensitive function of one of the two parameters specifying secondary electron yield due to proton impact and of essentially all the parameters specifying yield due to electron impact. In addition, it is found that information on the electron generated secondary yield parameters can be obtained from monoenergetic beam charging data if charging rates as well as equilibrium potentials are accurately recorded.

Purvis, C. K.↗

NASA NTRS1988

An investigation of new methods for estimating parameter sensitivities

Parameter sensitivity is defined as the estimation of changes in the modeling functions and the design variables due to small changes in the fixed parameters of the formulation. There are currently several methods for estimating parameter sensitivities requiring either difficult to obtain second order information, or do not return reliable estimates for the derivatives. Additionally, all the methods assume that the set of active constraints does not change in a neighborhood of the estimation point. If the active set does in fact change, than any extrapolations based on these derivatives may be in error. The objective here is to investigate more efficient new methods for estimating parameter sensitivities when the active set changes. The new method is based on the recursive quadratic programming (RQP) method and in conjunction a differencing formula to produce estimates of the sensitivities. This is compared to existing methods and is shown to be very competitive in terms of the number of function evaluations required. In terms of accuracy, the method is shown to be equivalent to a modified version of the Kuhn-Tucker method, where the Hessian of the Lagrangian is estimated using the BFS method employed by the RPQ algorithm. Inital testing on a test set with known sensitivities demonstrates that the method can accurately calculate the parameter sensitivity. To handle changes in the active set, a deflection algorithm is proposed for those cases where the new set of active constraints remains linearly independent. For those cases where dependencies occur, a directional derivative is proposed. A few simple examples are included for the algorithm, but extensive testing has not yet been performed.

Beltracchi, Todd J.↗

NASA NTRS1992

Three-dimensional boundary element thermal shape sensitivity analysis

A computationally efficient and accurate shape design sensitivity analysis approach for the thermal response of 3D solid objects is presented which utilizes a direct, singular, boundary element analysis formulation. The theoretical formulation for the primary response (the surface temperature and normal heat flux) sensitivities and the secondary response (tangential components of the heat flux, vector, interior point temperature and heat flux vector components) sensitivities are presented. A number of computational issues related to the overall efficiency of implementation of these formulations are discussed. Numerical results are presented to demonstrate the accuracy and efficiency of this approach.

Prasad, K. G.↗

NASA NTRS2019

A New Recycling Method to Generate Turbulent Inflow Profiles

The accuracy of the scale-resolving simulations for practical geometries strongly depends on the inflow boundary conditions. Imposing experimentally observed turbulent inflow profiles for the numerical simulations is a major challenge. Existing methods available in the literature assume self-similar behavior, which is not true for most of the experiments. In the present work, we formulate the turbulent inflow profile generation technique as an optimization problem. An adjoint technique is exploited to evaluate the sensitivities of multiple input parameters for the present problem. The present formulation is then tested to generate a laminar boundary layer profile, turbulent boundary layer profile, and turbulent jet profile.

Garai, Anirban↗

NASA NTRS1976

Heat transfer evaluation in a plasma core reactor

Numerical evaluations of heat transfer in a fissioning uranium plasma core reactor cavity, operating with seeded hydrogen propellant, was performed. A two-dimensional analysis is based on an assumed flow pattern and cavity wall heat exchange rate. Various iterative schemes were required by the nature of the radiative field and by the solid seed vaporization. Approximate formulations of the radiative heat flux are generally used, due to the complexity of the solution of a rigorously formulated problem. The present work analyzes the sensitivity of the results with respect to approximations of the radiative field, geometry, seed vaporization coefficients and flow pattern. The results present temperature, heat flux, density and optical depth distributions in the reactor cavity, acceptable simplifying assumptions, and iterative schemes. The present calculations, performed in cartesian and spherical coordinates, are applicable to any most general heat transfer problem.

Smith, D. E.↗

NASA NTRS1993

Semi-analytical static nonlinear structural sensitivity analysis

The paper discusses two uses of the semianalytical methods for nonlinear sensitivity analysis. First, the application to noncritical response is analyzed. It is shown that the semianalytical method is equivalent to a particular form of the overall finite difference approach. It is concluded that the difference between overall finite differences and the semianalytical approach is blurred for the case of nonlinear static response. Next, the application of the semianalytical method to calculating sensitivities of limit loads is discussed. A formulation that is easy to implement in general purpose finite element programs is derived. Three examples are used to demonstrate the application of the formulation and to explore its accuracy.

Haftka, Raphael T.↗