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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Distributed system modeling of a large space antenna

A general approach for distributed parameter modeling of complex dynamical systems is described. The method consists of dividing the system in parts which can be modeled by simple partial differential equations and coupling the equations thus obtained by applying Hamilton's variational formalism to the entire system. The modeling of a large, offset-fed, wrap-rib antenna is presented to illustrate the approach. Although such models are perhaps not as precise as finite element models, they can be useful for initial physical insight and parametric design.

Hamidi, M.↗
NASA NTRS1990

Optimal controllers for finite wordlength implementation

There exist realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take into account the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the LQG (linear quadratic Gaussian) theory since they reduce to the standard LQG controller when infinite-precision computation is used, but for finite precision the separation principle does not hold.

Liu, K.↗
NASA NTRS1991

Optimal controllers for finite wordlength implementation

When a controller is implemented in a digital computer, with A/D and D/A conversion, the numerical errors of the computation can drastically affect the performance of the control system. There exists realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take account of the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the Linear Quadratic Gaussian (LQG) theory since they reduce to the standard LQG controller when infinite precision computation is used. But for finite precision the separation principle does not hold.

Liu, K.↗
NASA NTRS1991

Boundary implications for frequency response of interval FIR and IIR filters

It is shown that vertex implication results in parameter space apply to interval trigonometric polynomials. Subsequently, it is shown that the frequency responses of both interval FIR and IIR filters are bounded by the frequency responses of certain extreme filters. The results apply directly in the evaluation of properties of designed filters, especially because it is more realistic to bound the filter coefficients from above and below instead of determining those with infinite precision because of finite arithmetic effects. Illustrative examples are provided to show how the extreme filters might be easily derived in any specific interval FIR or IIR filter design problem.

Bose, N. K.↗
NASA NTRS1982

Feedback stabilization and control of linear neutral systems

The first problem treated here is the realization and stabilization of linear neutral systems with discrete delays. It is shown that any autonomous linear neutral system with discrete delays is zero-state equivalent to an abstract linear system over a local ring of operators. Using the abstract model, the basic existence question for neutral realization is then settled. For general infinite dimensional linear systems, there is no precise analog of the finite dimensional state space isomorphism theorem. Because of this, the notion of spectral minimality must be introduced. For the case of single input-single output systems, realizations are obtained that are both minimal and spectrally minimal. Using the Cruz-Hale theory of stable D-operators, conditions are given that ensure that any poles introduced into the realization are strictly contained in the left half plane and indeed are characterized as characteristic values of the D-operator. The problem of the feedback stabilization of neutral systems is then considered using the abstract model. It is shown that, for neutral systems with commensurable delays and a stable D-operator in the sense of Cruz and Hale, Morses theorem (1976) on pole assignment over a PID implies stabilizability in the reachable case.

Tarn, T. J.↗
NASA NTRS1993

Temperature induced distortions in space telescope mirrors

In this paper, it is illustrated how measured instantaneous coefficients of thermal expansion (CTE) can be accurately taken into account when modeling the structural behavior of space based optical systems. In particular, the importance of including CTE spatial variations in the analysis of optical elements is emphasized. A comparison is made between the CTE's of three optical materials commonly used in the construction of space mirrors (ULE, Zerodur, and beryllium). The overall impact that selection of any one of these materials has on thermal distortions is briefly discussed. As an example of how temperature dependent spatial variations in thermal strain can be accurately incorporated in the thermo-structural analysis of a precision optical system, a finite element model is developed, which is used to estimate the thermally induced distortions in the Hubble Space Telescope's (HST) primary mirror. In addition to the structural analysis, the optical aberrations due to thermally induced distortions are also examined. These calculations indicate that thermal distortions in HST's primary mirror contribute mainly to defocus error with a relatively small contribution to spherical aberration.

Nied, H. F.↗
NASA NTRS2011

On Calculation Methods and Results for Straight Cylindrical Roller Bearing Deflection, Stiffness, and Stress

The purpose of this study was to assess some calculation methods for quantifying the relationships of bearing geometry, material properties, load, deflection, stiffness, and stress. The scope of the work was limited to two-dimensional modeling of straight cylindrical roller bearings. Preparations for studies of dynamic response of bearings with damaged surfaces motivated this work. Studies were selected to exercise and build confidence in the numerical tools. Three calculation methods were used in this work. Two of the methods were numerical solutions of the Hertz contact approach. The third method used was a combined finite element surface integral method. Example calculations were done for a single roller loaded between an inner and outer raceway for code verification. Next, a bearing with 13 rollers and all-steel construction was used as an example to do additional code verification, including an assessment of the leading order of accuracy of the finite element and surface integral method. Results from that study show that the method is at least first-order accurate. Those results also show that the contact grid refinement has a more significant influence on precision as compared to the finite element grid refinement. To explore the influence of material properties, the 13-roller bearing was modeled as made from Nitinol 60, a material with very different properties from steel and showing some potential for bearing applications. The codes were exercised to compare contact areas and stress levels for steel and Nitinol 60 bearings operating at equivalent power density. As a step toward modeling the dynamic response of bearings having surface damage, static analyses were completed to simulate a bearing with a spall or similar damage.

Krantz, Timothy L.↗
NASA NTRS2011

High Precision Thermal, Structural and Optical Analysis of an External Occulter Using a Common Model and the General Purpose Multi-Physics Analysis Tool Cielo

The efficient simulation of multidisciplinary thermo-opto-mechanical effects in precision deployable systems has for years been limited by numerical toolsets that do not necessarily share the same finite element basis, level of mesh discretization, data formats, or compute platforms. Cielo, a general purpose integrated modeling tool funded by the Jet Propulsion Laboratory and the Exoplanet Exploration Program, addresses shortcomings in the current state of the art via features that enable the use of a single, common model for thermal, structural and optical aberration analysis, producing results of greater accuracy, without the need for results interpolation or mapping. This paper will highlight some of these advances, and will demonstrate them within the context of detailed external occulter analyses, focusing on in-plane deformations of the petal edges for both steady-state and transient conditions, with subsequent optical performance metrics including intensity distributions at the pupil and image plane.

integrated modeling↗
NASA NTRS2000

Dynamic Response of a Planetary Gear System Using a Finite Element/Contact Mechanics Model

The dynamic response of a helicopter planetary gear system is examined over a wide range of operating speeds and torques. The analysis tool is a unique, semianalytical finite element formulation that admits precise representation of the tooth geometry and contact forces that are crucial in gear dynamics. Importantly, no a priori specification of static transmission error excitation or mesh frequency variation is required; the dynamic contact forces are evaluated internally at each time step. The calculated response shows classical resonances when a harmonic of mesh frequency coincides with a natural frequency. However, peculiar behavior occurs where resonances expected to be excited at a given speed are absent. This absence of particular modes is explained by analytical relationships that depend on the planetary configuration and mesh frequency harmonic. The torque sensitivity of the dynamic response is examined and compared to static analyses. Rotation mode response is shown to be more sensitive to input torque than translational mode response.

Parker, Robert G.↗
NASA NTRS1983

On the off-axis tension test for unidirectional composites

The off axis tensile test was examined experimentally to obtain actual displacement fields over the surface of graphite polyimide coupon specimens. The experimental results were compared with approximate analytical solutions and generated finite element results. An optical method of high sensitivity moireinterferometry was used to determine the actual displacements to high precision. The approximate analytical solution and the finite element results compare very favorably with the measured centerline displacements in the test section, and the finite element displacement fields provide excellent agreement with the moiredisplacements throughout the specimen. A 15 degree fiber orientation and coupon aspect ratios of 5 and 15 are presented. Previously announced in STAR as N82-23553

Herakovich, C. T.↗
NASA NTRS1982

On the off-axis tensile test for unidirectional composites

The off axis tensile test was examined experimentally to obtain actual displacement fields over the surface of graphite polyimide coupon specimens. The experimental results were compared with approximate analytical solutions and generated finite element results. An optical method of high sensitivity moire interferometry was used to determine the actual displacements to high precision. The approximate analytical solution and the finite element results compare very favorably with the measured centerline displacements in the test section, and the finite element displacement fields provide excellent agreement with the moire displacements throughout the specimen. A 15 degree fiber orientation and coupon aspect ratios of 5 and 15 are presented.

Nemeth, M. P.↗
NASA NTRS1987

Application of optimization techniques to spacecaft fuel usage minimization in deep space navigation

Mathematical analysis of the minimization of spacecraft fuel usage for both impulsive and finite motor burns is presented. A high precision integrated trajectory search program (SEPV) and several optimization software libraries are used to solve minimum fuel usage problems. The SEPV program has the capacity to vary either the initial spacecraft state or the finite burn parameters to acquire a specified set of target values. Several test examples for the Voyager 2 Uranus Encounter and the Galileo Jupiter Orbiter are presented to show that spacecraft fuel consumption can be minimized in targeting maneuver strategies. The fuel savings achieved by the optimum solution can be significant.

Wang, Tseng-Chan↗
NASA NTRS1990

Nonlinear viscoelastic response of highly filled elastomers under multiaxial finite deformation

A biaxial tester was used to obtain precise biaxial stress responses of highly filled, high strain capability elastomers. Stress-relaxation experiments show that the time-dependent part of the relaxation response can be reasonably approximated by a function which is strain and biaxiality independent. Thus, isochronal data from the stress-relaxation curves can be used to determine the stored energy density function. The complex behavior of the elastomers under biaxial deformation may be caused by dewetting.

Peng, Steven T. J.↗
NASA NTRS1979

Recent finite element studies in plasticity and fracture mechanics

The paper reviews recent work on fundamentals of elastic-plastic finite-element analysis and its applications to the mechanics of crack opening and growth in ductile solids. The presentation begins with a precise formulation of incremental equilibrium equations and their finite-element forms in a manner valid for deformations of arbitrary magnitude. Special features of computational procedures are outlined for accuracy in view of the near-incompressibility of elastic-plastic response. Applications to crack mechanics include the analysis of large plastic deformations at a progressively opening crack tip, the determination of J integral values and of limitations to J characterizations of the intensity of the crack tip field, and the determination of crack tip fields in stable crack growth.

Rice, J. R.↗
NASA NTRS1993

A comparison of viscoelastic damping models

Modern finite element methods (FEM's) enable the precise modeling of mass and stiffness properties in what were in the past overwhelmingly large and complex structures. These models allow the accurate determination of natural frequencies and mode shapes. However, adequate methods for modeling highly damped and high frequency dependent structures did not exist until recently. The most commonly used method, Modal Strain Energy, does not correctly predict complex mode shapes since it is based on the assumption that the mode shapes of a structure are real. Recently, many techniques have been developed which allow the modeling of frequency dependent damping properties of materials in a finite element compatible form. Two of these methods, the Golla-Hughes-McTavish method and the Lesieutre-Mingori method, model the frequency dependent effects by adding coordinates to the existing system thus maintaining the linearity of the model. The third model, proposed by Bagley and Torvik, is based on the Fractional Calculus method and requires fewer empirical parameters to model the frequency dependence at the expense of linearity of the governing equations. This work examines the Modal Strain Energy, Golla-Hughes-McTavish and Bagley and Torvik models and compares them to determine the plausibility of using them for modeling viscoelastic damping in large structures.

Slater, Joseph C.↗
NASA NTRS1979

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.

Rodal, J. J. A.↗