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NASA NTRS2004

Parametric Studies of Square Solar Sails Using Finite Element Analysis

Parametric studies are performed on two generic square solar sail designs to identify parameters of interest. The studies are performed on systems-level models of full-scale solar sails, and include geometric nonlinearity and inertia relief, and use a Newton-Raphson scheme to apply sail pre-tensioning and solar pressure. Computational strategies and difficulties encountered during the analyses are also addressed. The purpose of this paper is not to compare the benefits of one sail design over the other. Instead, the results of the parametric studies may be used to identify general response trends, and areas of potential nonlinear structural interactions for future studies. The effects of sail size, sail membrane pre-stress, sail membrane thickness, and boom stiffness on the sail membrane and boom deformations, boom loads, and vibration frequencies are studied. Over the range of parameters studied, the maximum sail deflection and boom deformations are a nonlinear function of the sail properties. In general, the vibration frequencies and modes are closely spaced. For some vibration mode shapes, local deformation patterns that dominate the response are identified. These localized patterns are attributed to the presence of negative stresses in the sail membrane that are artifacts of the assumption of ignoring the effects of wrinkling in the modeling process, and are not believed to be physically meaningful. Over the range of parameters studied, several regions of potential nonlinear modal interaction are identified.

Sleight, David W.↗
NASA NTRS1994

A new look at the simultaneous analysis and design of structures

The minimum weight optimization of structural systems, subject to strength and displacement constraints as well as size side constraints, was investigated by the Simultaneous ANalysis and Design (SAND) approach. As an optimizer, the code NPSOL was used which is based on a sequential quadratic programming (SQP) algorithm. The structures were modeled by the finite element method. The finite element related input to NPSOL was automatically generated from the input decks of such standard FEM/optimization codes as NASTRAN or ASTROS, with the stiffness matrices, at present, extracted from the FEM code ANALYZE. In order to avoid ill-conditioned matrices that can be encountered when the global stiffness equations are used as additional nonlinear equality constraints in the SAND approach (with the displacements as additional variables), the matrix displacement method was applied. In this approach, the element stiffness equations are used as constraints instead of the global stiffness equations, in conjunction with the nodal force equilibrium equations. This approach adds the element forces as variables to the system. Since, for complex structures and the associated large and very sparce matrices, the execution times of the optimization code became excessive due to the large number of required constraint gradient evaluations, the Kreisselmeier-Steinhauser function approach was used to decrease the computational effort by reducing the nonlinear equality constraint system to essentially a single combined constraint equation. As the linear equality and inequality constraints require much less computational effort to evaluate, they were kept in their previous form to limit the complexity of the KS function evaluation. To date, the standard three-bar, ten-bar, and 72-bar trusses have been tested. For the standard SAND approach, correct results were obtained for all three trusses although convergence became slower for the 72-bar truss. When the matrix displacement method was used, correct results were still obtained, but the execution times became excessive due to the large number of constraint gradient evaluations required. Using the KS function, the computational effort dropped, but the optimization seemed to become less robust. The investigation of this phenomenon is continuing. As an alternate approach, the code MINOS for the optimization of sparse matrices can be applied to the problem in lieu of the Kreisselmeier-Steinhauser function. This investigation is underway.

Striz, Alfred G.↗
NASA NTRS1998

Applications of Artificial Neural Networks in Structural Engineering with Emphasis on Continuum Models

The use of continuum models for the analysis of discrete built-up complex aerospace structures is an attractive idea especially at the conceptual and preliminary design stages. But the diversity of available continuum models and hard-to-use qualities of these models have prevented them from finding wide applications. In this regard, Artificial Neural Networks (ANN or NN) may have a great potential as these networks are universal approximators that can realize any continuous mapping, and can provide general mechanisms for building models from data whose input-output relationship can be highly nonlinear. The ultimate aim of the present work is to be able to build high fidelity continuum models for complex aerospace structures using the ANN. As a first step, the concepts and features of ANN are familiarized through the MATLAB NN Toolbox by simulating some representative mapping examples, including some problems in structural engineering. Then some further aspects and lessons learned about the NN training are discussed, including the performances of Feed-Forward and Radial Basis Function NN when dealing with noise-polluted data and the technique of cross-validation. Finally, as an example of using NN in continuum models, a lattice structure with repeating cells is represented by a continuum beam whose properties are provided by neural networks.

Kapania, Rakesh K.↗
NASA NTRS1985

The utilization of satellite data and dynamics in understanding and predicting global weather phenomena

A two layer spectral quasi-geostrophic model is used to simulate the effects of topography on the equilibria, the stability, and the long term evaluation of incipient unstable waves. The flow is forced by latitudinally dependent radiational heating. The nature of the form drag instability of high index equilibria is investigated. The proximity of the equilibrium shear to a resonant value is essential for the instability, provided the equilibrium occurs at a slightly stronger shear than resonance. The properties of the steady Hadley and Rossby required for a thermally forced rotating fluid on a sphere are further explained. An objective parameterization technique is developed for general nonlinear hydrodynamical systems. The typical structure is one in which the rates of change of the dependent variables depend on homogeneous quadratic and linear forms, as well as on inhomogeneous forcing terms. Also documented is a steady, axisymmetric model of the general circulation developed as a basis for climate stability studies. The model includes the effects of heating, rotation, and internal friction, but neglects topography. Included is further research on cloud street phenomena. Orientation angles and horizontal wavelengths of boundary layer rolls and cloud streets are determined from an analysis of a truncated spectral model of three dimensional shallow moist Boussinesq convection in a shearing environment is further explained. Relatively broadly spaced roll clouds have orientations for which the Fourier component of the roll perpendicular shear is nearly zero, but the second corresponds to narrowly spaced rolls having orientations for which the Fourier coefficients of both the perpendicular and the parallel components of the shear are nearly equal.

Shirer, H. N.↗
NASA NTRS2006

Diurnal Variability of Vertical Structure from a TRMM Passive Microwave "Virtual Radar" Retrieval

Robust description of the diurnal cycle from TRMM observations is complicated by the limitations of Low Earth Orbit (LEO) sampling; from a 'climatological' perspective, sufficient sampling must exist to control for both spatial and seasonal variability, before tackling an additional diurnal component (e.g., with 8 additional 3-hourly or 24 1-hourly bins). For documentation of vertical structure, the narrow sample swath of the TRMM Precipitation Radar limits the resolution of any of these components. A neural-network based 'virtual radar" retrieval has been trained and internally validated, using multifrequency / multipolarization passive microwave(TM1) brightness temperatures and textures parameters and lightning (LIS) observations, as inputs, and PR volumetric reflectivity as targets (outputs). By training the algorithms (essentially highly multivariate, nonlinear regressions) on a very large sample of high-quality co-located data from the center of the TRMM swath, 3D radar reflectivity and derived parameters (VIL, IWC, Echo Tops, etc.) can be retrieved across the entire TMI swath, good to 8-9% over the dynamic range of parameters. As a step in the retrieval (and as an output of the process), each TMI multifrequency pixel (at 85 GHz resolution) is classified into one of the 25 archetypal radar profile vertical structure "types", previously identified using cluster analysis. The dynamic range of retrieved vertical structure appears to have higher fidelity than the current (Version 6) experimental GPROF hydrometeor vertical structure retrievals. This is attributable to correct representation of the prior probabilities of vertical structure variability in the neural network training data, unlike the GPROF cloud-resolving model training dataset used in the V6 algorithms. The LIS lightning inputs are supplementary inputs, and a separate offline neural network has been trained to impute (predict) LIS lightning from passive-microwave-only data. The virtual radar retrieval is thus, in principle, extensible to Aqua/AMSR-E and NPOESS/CMIS passive microwave instruments. The virtual radar approach yields a threefold increase in effective sampling from the mission, albeit of lower-quality "retrieved" data, reducing the variance of local estimates by one third (or the standard deviation by-0.57). In this talk, the variance reduction is leveraged to more finely resolve global diurnal variability in both space and time (local hour).

Boccippio, Dennis J.↗
NASA NTRS2015

Variable-Domain Displacement Transfer Functions for Converting Surface Strains into Deflections for Structural Deformed Shape Predictions

Variable-Domain Displacement Transfer Functions were formulated for shape predictions of complex wing structures, for which surface strain-sensing stations must be properly distributed to avoid jointed junctures, and must be increased in the high strain gradient region. Each embedded beam (depth-wise cross section of structure along a surface strain-sensing line) was discretized into small variable domains. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. Through discretization, the embedded beam curvature equation can be piece-wisely integrated to obtain the Variable-Domain Displacement Transfer Functions (for each embedded beam), which are expressed in terms of geometrical parameters of the embedded beam and the surface strains along the strain-sensing line. By inputting the surface strain data into the Displacement Transfer Functions, slopes and deflections along each embedded beam can be calculated for mapping out overall structural deformed shapes. A long tapered cantilever tubular beam was chosen for shape prediction analysis. The input surface strains were analytically generated from finite-element analysis. The shape prediction accuracies of the Variable- Domain Displacement Transfer Functions were then determined in light of the finite-element generated slopes and deflections, and were fofound to be comparable to the accuracies of the constant-domain Displacement Transfer Functions

displacement transfer functions↗
NASA NTRS2015

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential elastic supports were neglected, but resulted in more complex behavior when the supports were included. The nominal flutter dynamic pressure of the 3.7-meter configuration was significantly lower than that of the 3-meter, and it was found that two sets of natural modes coalesce to flutter modes near the same dynamic pressure. This resulted in a significant drop in the limit cycle frequencies at higher dynamic pressures, where the flutter mode with the lower frequency becomes more critical. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with Piston Theory alone. The maximum dynamic pressure predicted by aerodynamic simulations of a proposed 3.7-meter HIAD vehicle was still lower than any of the calculated flutter dynamic pressures, suggesting that aeroelastic effects for this vehicle are of little concern.

Goldman, Benjamin D.↗
NASA NTRS1990

Flexibility effects on the control system performance of large scale robotic manipulators

Structural flexibility of robotic manipulators becomes significant and limits the performance of a control system when manipulators are large structures, manipulating on large payloads, and/or operating at high speeds. The question of when a manipulator can be considered rigid or must be considered flexible is studied as a function of manipulator dynamics and task characteristics. Results are interpreted in simple quantitative forms which can be used as design and analysis tools to decide whether or not the manipulator flexibility will be a significant factor for a given task condition. The limitations imposed by the manipulator flexibility on the joint variable feedback control system performance is determined using linear and nonlinear methods. The closed loop eigenstructure behavior of finite dimensional models under joint variable feedback is studied and results are compared with the previously reported results.

Cetinkunt, Sabri↗
NASA NTRS1989

Space Shuttle Main Engine structural analysis and data reduction/evaluation. Volume 2: High pressure oxidizer turbo-pump turbine end bearing analysis

The high-pressure oxidizer turbopump (HPOTP) consists of two centrifugal pumps, on a common shaft, that are directly driven by a hot-gas turbine. Pump shaft axial thrust is balanced in that the double-entry main inducer/impeller is inherently balanced and the thrusts of the preburner pump and turbine are nearly equal but opposite. Residual shaft thrust is controlled by a self-compensating, non-rubbing, balance piston. Shaft hang-up must be avoided if the balance piston is to perform properly. One potential cause of shaft hang-up is contact between the Phase 2 bearing support and axial spring cartridge of the HPOTP main pump housing. The status of the bearing support/axial spring cartridge interface is investigated under current loading conditions. An ANSYS version 4.3, three-dimensional, finite element model was generated on Lockheed's VAX 11/785 computer. A nonlinear thermal analysis was then executed on the Marshall Space Flight Center Engineering Analysis Data System (EADS). These thermal results were then applied along with the interference fit and bolt preloads to the model as load conditions for a static analysis to determine the gap status of the bearing support/axial spring cartridge interface. For possible further analysis of the local regions of HPOTP main pump housing assembly, detailed ANSYS submodels were generated using I-DEAS Geomod and Supertab (Appendix A).

Sisk, Gregory A.↗
NASA NTRS1993

Nonlinear aerodynamics and the design of wing tips

This contract began in April 1990 with studies on the effect of wingtip shape on induced drag. That work considered problems of determining induced drag from computational aerodynamic methods and examined effects of wake roll up on the induced drag of elliptical and crescent wings. The research contract was continued in April 1991 and again in April 1992 with scope augmented to include considerations other than induced drag. The idea was to develop methods for comparing wing tip shapes on the basis of their effects on total drag, structural weight, and high lift performance. To accomplish this, work was done to improve methods for multidisciplinary analysis and optimization of wings. This report describes results of research conducted from April 1992 through March 1993. The general objective was to improve an existing wing optimization method and apply the method to specific problems of interest. The method, while a valuable tool for wing tip design studies, can be applied to more general problems, and has been applied to some of these other problems during its development. Specific goals that were accomplished are listed below and are explained in more detail in attached reports: analysis methods were improved in the area of structural modeling; small improvements to the high lift model were made, and ideas were collected on how clean wing c(sub l(sub max)) should vary with sweep - these ideas should provide a guide for future examination of high lift with experiment or CFD; and a calculation for drag due to the loss of leading edge suction was added to the wing analysis.

Kroo, Ilan↗
NASA NTRS1985

A design technique for determining actuator gains in spacecraft vibration control

A design procedure is described which determines the gains of a diagonal damping matrix to control the vibrations of a flexible structure with application to orbiting spacecraft. The procedure is based on minimizing the energy dissipated by control actuators using nonlinear mathematical programming. Each damping gain is assumed to be an active viscous damper and the design process is formulated so that the force or torque output of the actuator does not exceed a specified value. The response of the structure at some specified time after the termination of the disturbance is constrained to be less than some prescribed value based upon spacecraft mission performance requirements. A grillage example is used to demonstrate the design process for determining gains for two representative cases. Resulting designs are verified by a finite element analysis of the structure augmented by the control actuators.

Horner, G. C.↗
NASA NTRS1988

MHOST: An efficient finite element program for inelastic analysis of solids and structures

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Nakazawa, S.↗
NASA NTRS1985

Large eddy interactions in a turbulent channel flow

The dynamic processes of large eddies in a turbulent channel flow have been examined by utilizing an orthogonal expansion of the velocity fluctuation, known in the literature as the Proper Orthogonal Decomposition Theorem. The mathematical form of these functions is unknown in contrast to the Fourier analysis. Attention is focused on the nonlinear, turbulence-turbulence interaction process in the dynamical equation for large eddies (the first term in the expansion). The nonlinear interactions of the components of the first mode are treated exactly, but influences of higher modes are modeled. This requires adjustment of both the skewness and the effective Reynolds number so that the energy equilibrium of the large eddies is ensured when the mean velocity distribution is assumed known for experiments. Computational results show that the first mode contributes significantly to turbulent intensities and possesses a structural and statistical character similar to that of the entire flow.

Hong, S. K.↗
NASA NTRS1994

User's guide for ENSAERO: A multidisciplinary program for fluid/structural/control interaction studies of aircraft (release 1)

Strong interactions can occur between the flow about an aerospace vehicle and its structural components resulting in several important aeroelastic phenomena. These aeroelastic phenomena can significantly influence the performance of the vehicle. At present, closed-form solutions are available for aeroelastic computations when flows are in either the linear subsonic or supersonic range. However, for aeroelasticity involving complex nonlinear flows with shock waves, vortices, flow separations, and aerodynamic heating, computational methods are still under development. These complex aeroelastic interactions can be dangerous and limit the performance of aircraft. Examples of these detrimental effects are aircraft with highly swept wings experiencing vortex-induced aeroelastic oscillations, transonic regime at which the flutter speed is low, aerothermoelastic loads that play a critical role in the design of high-speed vehicles, and flow separations that often lead to buffeting with undesirable structural oscillations. The simulation of these complex aeroelastic phenomena requires an integrated analysis of fluids and structures. This report presents a summary of the development, applications, and procedures to use the multidisciplinary computer code ENSAERO. This code is based on the Euler/Navier-Stokes flow equations and modal/finite-element structural equations.

Guruswamy, Guru P.↗
NASA NTRS2001

Dynamic Finite Element Predictions for Mars Sample Return Cellular Impact Test #4

The nonlinear finite element program MSC.Dytran was used to predict the impact pulse for (he drop test of an energy absorbing cellular structure. This pre-test simulation was performed to aid in the design of an energy absorbing concept for a highly reliable passive Earth Entry Vehicle (EEV) that will directly impact the Earth without a parachute. In addition, a goal of the simulation was to bound the acceleration pulse produced and delivered to the simulated space cargo container. EEV's are designed to return materials from asteroids, comets, or planets for laboratory analysis on Earth. The EEV concept uses an energy absorbing cellular structure designed to contain and limit the acceleration of space exploration samples during Earth impact. The spherical shaped cellular structure is composed of solid hexagonal and pentagonal foam-filled cells with hybrid graphite-epoxy/Kevlar cell walls. Space samples fit inside a smaller sphere at the enter of the EEV's cellular structure. The material models and failure criteria were varied to determine their effect on the resulting acceleration pulse. Pre-test analytical predictions using MSC.Dytran were compared with the test results obtained from impact test #4 using bungee accelerator located at the NASA Langley Research Center Impact Dynamics Research Facility. The material model used to represent the foam and the proper failure criteria for the cell walls were critical in predicting the impact loads of the cellular structure. It was determined that a FOAMI model for the foam and a 20% failure strain criteria for the cell walls gave an accurate prediction of the acceleration pulse for drop test #4.

Fasanella, Edwin L.↗
NASA NTRS2001

Temperature Effects in Varactors and Multipliers

Varactor diode multipliers are a critical part of many THz measurement systems. The power and efficiencies of these devices limit the available power for THz sources. Varactor operation is determined by the physics of the varactor device and a careful doping profile design is needed to optimize the performance. Higher doped devices are limited by junction breakdown and lower doped structures are limited by current saturation. Higher doped structures typically have higher efficiencies and lower doped structures typically have higher powers at the same operating frequency and impedance level. However, the device material properties are also a function of the operating temperature. Recent experimental evidence has shown that the power output of a multiplier can be improved by cooling the device. We have used a particle Monte Carlo simulation to investigate the temperature dependent velocity vs. electric field in GaAs. This information was then included in a nonlinear device circuit simulator to predict multiplier performance for various temperatures and device designs. This paper will describe the results of this analysis of temperature dependent multiplier operation.

East, J.↗
NASA NTRS2003

Application of Probability Methods to Assess Crash Modeling Uncertainty

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stress-strain behaviors, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the effects of finite element modeling assumptions on the predicted responses. The vertical drop test of a Fokker F28 fuselage section will be the focus of this paper. The results of a probabilistic analysis using finite element simulations will be compared with experimental data.

Lyle, Karen H.↗
NASA NTRS2004

Dynamics of Earth orbiting formations

In this paper the equations of motion of a formation consisting of n spacecraft in Earth orbit are derived via Lagrange's equations. The equations of motion of the formation are developed with respect to both (1) a bound Keplerian reference orbit, and (2) a specific spacecraft in the formation. The major orbital perturbations acting on a formation in low Earth orbit are also included in the analysis. In contrast to the traditional approach based on the balance of linear momentum, the use of Lagrange's equations leads to a high-level matrix derivation of the formation equations of motion. The matrix form of the nonlinear motion equations is then linearized about a bound Keplerian reference orbit. Next, it is demonstrated that under the assumption of a circular reference orbit, the linearized equations of motion reduce to the well-known Hill-Clohessy-Wiltshire equations. The resulting linear and nonlinear dynamic equations lead to maximal physical insight into the structure of formation dynamics, and are ideally suited for use in the design and validation of formation guidance and control laws.

formation flying↗