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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables

Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.

Fenyes, Peter A.↗
NASA NTRS1990

Free vibrations of thin-walled semicircular graphite-epoxy composite frames

A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modelled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frames. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a 1-D thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.

Noor, Ahmed K.↗
NASA NTRS1992

Underlying modal data issues for detecting damage in truss structures

The modal strain energy distribution and frequency and mode shape sensitivities to structural stiffness changes are studied in order to overcome the current limits of modal data limit measurements in damage location. It is established that damage detection is feasible for members significantly contributing to the strain energy of the measured modes; the modes that are most effective in detecting the damage of critical members are identifiable, and a relationship is formulated between the accuracy of the measured modes and frequencies and the probability of damage detection.

Kashangaki, Thomas A.-L.↗
NASA NTRS1990

Free vibrations of thin-walled semicircular graphite-epoxy composite frames

A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modeled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a non-dimensional thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.

Carden, Huey D.↗
NASA NTRS1990

Free vibrations of thin-walled semicircular graphite-epoxy composite frames

A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modeled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a non-dimensional thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.

Carden, Huey D.↗
NASA NTRS1993

The evolution equation for the flame surface density in turbulent premixed combustion

The mean reaction rate in flamelet models for turbulent premixed combustion depends on two basic quantities: a mean chemical rate, called the flamelet speed, and the flame surface density. Our previous work had been primarily focused on the problem of the structure and topology of turbulent premixed flames, and it was then determined that the flamelet speed, when space-averaged, is only weakly sensitive to the turbulent flow field. Consequently, the flame surface density is the key quantity that conveys most of the effects of the turbulence on the rate of energy release. In flamelet models, this quantity is obtained via a modeled transport equation called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact but unclosed formulation for the turbulent Sigma-equation. In the exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the turbulent flame stretch as well as the flame surface density is not available from experiments, and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the alternative approach to get basic information on these fundamental quantities. In the present work, three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, our objective is to extract the turbulent flame stretch from the DNS data base and then perform extensive comparisons with flamelet models. Thanks to the detailed information produced by the DNS-based analysis, it is expected that this type of comparison will not only underscore the shortcomings of current models, but also suggest ways to improve them.

Trouve, Arnaud↗
NASA NTRS1995

An a priori model for the reduction of nutation observations: KSV(1994.3) nutation series

We discuss the formulation of a new nutation series to be used in the reduction of modern space geodetic data. The motivation for developing such a series is to develop a nutation series that has smaller short period errors than the IAU 1980 nutation series and to provide a series that can be used with techniques such as the Global Positioning System (GPS) that have sensitivity to nutations but can directly separate the effects of nutations from errors in the dynamical force models that effect the satellite orbits. A modern nutation series should allow the errors in the force models for GPS to be better understood. The series is constructed by convolving the Kinoshita and Souchay rigid Earth nutation series with an Earth response function whose parameters are partly based on geophysical models of the Earth and partly estimated from a long series (1979-1993) of very long baseline interferometry (VLBI) estimates of nutation angles. Secular rates of change of the nutation angles to represent corrections to the precession constant and a secular change of the obliquity of the ecliptic are included in the theory. Time dependent amplitudes of the Free Core Nutation (FCN) that is most likely excited by variations in atmospheric pressure are included when the geophysical parameters are estimated. The complex components of the prograde annual nutation are estimated simultaneously with the geophysical parameters because of the large contribution to the nutation from the S(sub 1) atmospheric tide. The weighted root mean square (WRMS) scatter of the nutation angle estimates about this new model are 0.32 mas and the largest correction to the series when the amplitudes of the ten largest nutations are estimated is 0.18 +/- 0.03 mas for the in phase component of the prograde 18. 6 year nutation.

Herring, T. A.↗
NASA NTRS1985

Seasonal simulations of the planetary boundary layer and boundary-layer stratocumulus clouds with a general circulation model

The formulation of the planetary boundary layer (PBL) and stratocumulus parametrizations in the UCLA general circulation model (GCM) are briefly summarized, and extensive new results are presented illustrating some aspects of the simulated seasonal changes of the global distributions of PBL depth, stratocumulus cloudiness, cloud-top entrainment instability, the cumulus mass flux, and related fields. Results from three experiments designed to reveal the sensitivity of the GCM results to aspects of the PBL and stratocumulus parametrizations are presented. The GCM results show that the layer cloud instability appears to limit the extent of the marine subtropical stratocumulus regimes, and that instability frequently occurs in association with cumulus convection over land. Cumulus convection acts as a very significant sink of PBL mass throughout the tropics and over the midlatitude continents in winter.

Randall, D. A.↗
NASA NTRS2006

Gain-Scheduled Fault Tolerance Control Under False Identification

An active fault tolerant control (FTC) law is generally sensitive to false identification since the control gain is reconfigured for fault occurrence. In the conventional FTC law design procedure, dynamic variations due to false identification are not considered. In this paper, an FTC synthesis method is developed in order to consider possible variations of closed-loop dynamics under false identification into the control design procedure. An active FTC synthesis problem is formulated into an LMI optimization problem to minimize the upper bound of the induced-L2 norm which can represent the worst-case performance degradation due to false identification. The developed synthesis method is applied for control of the longitudinal motions of FASER (Free-flying Airplane for Subscale Experimental Research). The designed FTC law of the airplane is simulated for pitch angle command tracking under a false identification case.

Shin, Jong-Yeob↗
NASA NTRS2006

Development of a Test Facility for Air Revitalization Technology Evaluation

An active fault tolerant control (FTC) law is generally sensitive to false identification since the control gain is reconfigured for fault occurrence. In the conventional FTC law design procedure, dynamic variations due to false identification are not considered. In this paper, an FTC synthesis method is developed in order to consider possible variations of closed-loop dynamics under false identification into the control design procedure. An active FTC synthesis problem is formulated into an LMI optimization problem to minimize the upper bound of the induced-L2 norm which can represent the worst-case performance degradation due to false identification. The developed synthesis method is applied for control of the longitudinal motions of FASER (Free-flying Airplane for Subscale Experimental Research). The designed FTC law of the airplane is simulated for pitch angle command tracking under a false identification case.

Lu, Sao-Dung↗
NASA NTRS1980

Illustration of airfoil shape effect on forward-swept wing divergence

A static aeroelastic analysis is presented of the divergence of untapered wings with conventional and supercritical airfoil sections at sweep angles of zero and -15 deg. One bending and one torsion mode were employed for a uniform rectangular cantilevered beam with the elastic axis at midchord, and calculations were based on a two-dimensional differential equations formulation in the structural coordinate system and in simple strip theory. A minimum divergence speed in the transonic range is obtained which is associated with the rearward shift of the aerodynamic center, and a 17% difference in minimum divergence dynamic pressure is found between a supercritical and a conventional wing. It is noted that although the strip method employed allows the assessment of the sensitivity of airfoil shapes to divergence, three-dimensional transonic aerodynamic methods should be used to predict wing divergence characteristics.

Bland, S. R.↗
NASA NTRS1987

On computing eigensolution sensitivity data using free vibration solutions

A simplified method of computing eigensolution sensitivity derivatives in structural dynamics is developed. It is shown that if the elements of stiffness and mass matrices associated with a design variable are homogeneous functions of that design variable, then eigenvalue derivatives can be computed from element strain and kinetic energies. Furthermore, if cross-mode energies are known, eigensolution derivatives of modified systems can be computed approximately using assume mode reanalysis formulation. A ten bar truss example is used to illustrate the present formulations.

Wang, B. P.↗
NASA NTRS1990

An interactive chemical dynamical radiative two-dimensional model of the middle atmosphere

A new two-dimensional model of the stratosphere and the mesosphere was formulated in transformed Eulerian coordinates, in which dynamics, radiation, and chemistry are treated interactively. The model includes a detailed radiative scheme which derives the diabatic heating rates consistently with calculated distributions of temperature and trace species densities. Results are presented on the present-day and perturbed atmosphere, showing that the calculated distributions of source gases, such as nitrous oxide and methane, are very sensitive to the calculated (and parameterized) dynamical quantities, and that species produced in the atmosphere, like carbon monoxide and odd nitrogen, can provide valuable information on the role of atmospheric transport.

Brasseur, G.↗
NASA NTRS1996

Nonlinear Analysis and Modeling of Tires

The objective of the study was to develop efficient modeling techniques and computational strategies for: (1) predicting the nonlinear response of tires subjected to inflation pressure, mechanical and thermal loads; (2) determining the footprint region, and analyzing the tire pavement contact problem, including the effect of friction; and (3) determining the sensitivity of the tire response (displacements, stresses, strain energy, contact pressures and contact area) to variations in the different material and geometric parameters. Two computational strategies were developed. In the first strategy the tire was modeled by using either a two-dimensional shear flexible mixed shell finite elements or a quasi-three-dimensional solid model. The contact conditions were incorporated into the formulation by using a perturbed Lagrangian approach. A number of model reduction techniques were applied to substantially reduce the number of degrees of freedom used in describing the response outside the contact region. The second strategy exploited the axial symmetry of the undeformed tire, and uses cylindrical coordinates in the development of three-dimensional elements for modeling each of the different parts of the tire cross section. Model reduction techniques are also used with this strategy.

Noor, Ahmed K.↗
NASA NTRS2006

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Helenbrook, B. T.↗
NASA NTRSDate not supplied

Development of Laser Powder Bed Fusion NASA HR-2 for Hydrogen Sensitive Liquid Rocket Engine Applications

The National Aeronautics and Space Administration (NASA) has been involved in the development and maturation of metal additive manufacturing (AM) for space applications since the late 2000’s. AM has provided new design and manufacturing opportunities to reduce cost and schedule, consolidate parts, and optimize performance. Laser Powder Bed Fusion (L-PBF) is one of the most commonly used AM processes to fabricate components that have complex shape and need fine feature resolution. Due to exposure to high pressure gaseous hydrogen, mechanical property degradation caused by hydrogen environment embrittlement (HEE) is a critical concern for many materials in liquid hydrogen propulsion systems. NASA has identified the need to develop and advance new materials in unique engine applications using liquid hydrogen as a propellant. One such material being developed at NASA Marshall Space Flight Center is L-PBF NASA HR-2 (Hydrogen Resistant-2), a high-strength Fe-Ni-based superalloy resistant to HEE. The chemistry of NASA HR-2 was formulated to meet requirements for key liquid rocket engine (LRE) components that operate in high-pressure hydrogen environments. Initial development and material characterization found NASA HR-2 has excellent L-PBF printability and its microstructure evolves well after heat treatment. This new alloy has undergone fundamental metallurgical evaluations, heat treatment studies, detailed microstructure characterization, and mechanical testing across a range of temperatures. Tensile testing was performed in pressurized gaseous hydrogen (GH2) environment to assess its resistance to HEE. L-PBF NASA HR-2 has an average yield stress of 95 ksi, ultimate tensile stress of 165 ksi, and very high fracture elongation at 34 - 36% when tested in a 5 ksi high pressure hydrogen environment. The tensile property data confirms hydrogen has little influence on its ductility, strength, and fracture behavior. L-PBF NASA HR-2 is a promising option for many hydrogen sensitive LRE components that require exceptional resistance to HEE. The development of L-PBF NASA HR-2 is funded under the grants provided by Jacobs TIPI program and the Liquid Engine Office at NASA Marshall Space Flight Center. This paper will provide an overview of the L-PBF process development, material characterization, mechanical and thermophysical properties, and LRE hardware development for NASA HR-2.

NASA HR-2↗
NASA NTRSDate not supplied

Development of Laser Powder Bed Fusion NASA HR-2 for Hydrogen Sensitive Liquid Rocket Engine Applications

The National Aeronautics and Space Administration (NASA) has been involved in the development and maturation of metal additive manufacturing (AM) for space applications since the late 2000’s. AM has provided new design and manufacturing opportunities to reduce cost and schedule, consolidate parts, and optimize performance. Laser Powder Bed Fusion (L-PBF) is one of the most commonly used AM processes to fabricate components that have complex shape and need fine feature resolution. Due to exposure to high pressure gaseous hydrogen, mechanical property degradation caused by hydrogen environment embrittlement (HEE) is a critical concern for many materials in liquid hydrogen propulsion systems. NASA has identified the need to develop and advance new materials in unique engine applications using liquid hydrogen as a propellant. One such material being developed at NASA Marshall Space Flight Center is L-PBF NASA HR-2 (Hydrogen Resistant-2), a high-strength Fe-Ni-based superalloy resistant to HEE. The chemistry of NASA HR-2 was formulated to meet requirements for key liquid rocket engine (LRE) components that operate in high-pressure hydrogen environments. Initial development and material characterization found NASA HR-2 has excellent L-PBF printability and its microstructure evolves well after heat treatment. This new alloy has undergone fundamental metallurgical evaluations, heat treatment studies, detailed microstructure characterization, and mechanical testing across a range of temperatures. Tensile testing was performed in pressurized gaseous hydrogen (GH2) environment to assess its resistance to HEE. L-PBF NASA HR-2 has an average yield stress of 95 ksi, ultimate tensile stress of 165 ksi, and very high fracture elongation at 34 - 36% when tested in a 5 ksi high pressure hydrogen environment. The tensile property data confirms hydrogen has little influence on its ductility, strength, and fracture behavior. L-PBF NASA HR-2 is a promising option for many hydrogen sensitive LRE components that require exceptional resistance to HEE. The development of L-PBF NASA HR-2 is funded under the grants provided by Jacobs TIPI program and the Liquid Engine Office at NASA Marshall Space Flight Center. This paper will provide an overview of the L-PBF process development, material characterization, mechanical and thermophysical properties, and LRE hardware development for NASA HR-2.

NASA HR-2↗
NASA NTRS1987

Optimal cure cycle design of a resin-fiber composite laminate

A unified computed aided design method was studied for the cure cycle design that incorporates an optimal design technique with the analytical model of a composite cure process. The preliminary results of using this proposed method for optimal cure cycle design are reported and discussed. The cure process of interest is the compression molding of a polyester which is described by a diffusion reaction system. The finite element method is employed to convert the initial boundary value problem into a set of first order differential equations which are solved simultaneously by the DE program. The equations for thermal design sensitivities are derived by using the direct differentiation method and are solved by the DE program. A recursive quadratic programming algorithm with an active set strategy called a linearization method is used to optimally design the cure cycle, subjected to the given design performance requirements. The difficulty of casting the cure cycle design process into a proper mathematical form is recognized. Various optimal design problems are formulated to address theses aspects. The optimal solutions of these formulations are compared and discussed.

Hou, Jean W.↗