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A problem-adaptive solution procedure for improving the reliability of finite element solutions to geometrically nonlinear shell-type problem is presented. The strategy incorporates automatic error detection and control and includes an iterative procedure which utilizes the solution at the same load step on a more refined model. Representative nonlinear shell problem are solved.
A mathematical model for sound transmission into a thin cylindrical shell is used to study sound transmission under flight conditions, i.e., under conditions of external air flow past a pressurized cylinder at flight altitude. Numerical results for different incidence angles are presented for a typical narrow-bodied jet in cruising flight at 10,660 m with interior pressure at 2440 m. A comparison is made between no-flow sound transmission at standard conditions on the ground to sound transmission under flight conditions. It is shown that at M = 0, the cylinder transmission loss (TL) has dips at the cylinder ring frequency (fR) and the critical frequency (fc) for a flat panel of same material and thickness as shell. Between fR and fc, cylinder TL follows a mass-law behavior. Flow provides a modest increase in TL in the mass-law region, and strongly interacts with the cylinder resonances below fR.
The development of a 20 kHz, AC power system by NASA for large space projects has spurred a need to develop models for the equipment which will be used on these single phase systems. To date, models for the AC source (i.e., inverters) have been developed. It is the intent of this paper to develop a method to model the single phase voltage controlled rectifiers which will be attached to the AC power grid as an interface for connected loads. A modified version of EPRI's HARMFLO program is used as the shell for these models. The results obtained from the model developed in this paper are quite adequate for the analysis of problems such as voltage resonance. The unique technique presented in this paper uses the Laplace transforms to determine the harmonic content of the load current of the rectifier rather than a curve fitting technique. Laplace transforms yield the coefficient of the differential equations which model the line current to the rectifier directly.
To support airworthiness assessment of the X-57 electric propulsion demonstrator aircraft, the National Aeronautics and Space Administration (NASA) completed classical flutter analysis of the Mod II, Mod III, and Mod IV aircraft configurations. Aeroelastic analysis was primarily performed using the ZAERO analysis code developed by Zona Technology. Supplemental computational fluid dynamics (CFD) flutter analysis for the Mod III and Mod IV configurations was performed using NASA’s FUN3D software to verify the aeroelastic behavior at deployed flaps conditions. The NASTRAN finite element models (FEMs) used for aeroelastic analysis were developed by NASA. The final Mod II FEM utilized shell elements for the wing and fuselage, and beam elements for the tail and wing control surfaces. For Mod III and Mod IV aircraft models, shell element wing FEMs developed throughout the Mod III/IV wing design cycle were utilized. The fuselage and empennage FEM components were shared between the Mod II, III, and IV aircraft models. ZAERO analyses predicted flutter boundaries were >60% beyond the X-57 flight-test envelope never exceed airspeed (V NE ) for all configurations. Aeroelastic Reynolds-averaged Navier–Stokes (RANS) CFD simulations using FUN3D of the Mod III/IV configurations predicted flap mode instability did not occur until at least speeds of 60% higher than the Mod III/IV maximum flap deployment airspeed (V FE ).
We consider a relativistic spherical shell and calculate its spectral flux as received by a distant observer. Using two different methods, we derive a simple analytical expression of the observed spectral flux and show that the well-known relation α-hat =2+ β-hat (between temporal index α-hat and spectral index β-hat ) of the high-latitude emission is naturally achieved in our derivation but holds only when the shell moves with a constant Lorentz factor Γ. Presenting numerical models in which the shell is undergoing acceleration or deceleration, we show that the simple α-hat =2+ β-hat relation does indeed deviate as long as Γ is not constant. For the models under acceleration, we find that the light curves produced purely by the high-latitude emission initially exhibit much steeper decay than in the constant Γ case and gradually resume the α-hat =2+ β-hat relation in about one and a half orders of magnitude in observer time. For the models under deceleration, the trend is opposite. The light curves made purely by the high-latitude emission initially exhibit a shallower decay than in the constant Γ case and gradually resume the relation α-hat =2+ β-hat in a similar order of magnitude in observer time. We also show that how fast the Lorentz factor Γ of the shell increases or decreases is the main ingredient determining the initial steepness or shallowness of the light curves.
High-energy-density (HED) experiments in convergent geometry are able to test physical models at pressures beyond hundreds of millions of atmospheres. The measurements from these experiments are generally highly integrated and require unique analysis techniques to procure quantitative infor mation. This work describes a methodology to constrain the physics in convergent HED experiments by adapting the methods common to many other fields of physics. As an example, a mechanical model of an imploding shell is constrained by data from a thin-shelled direct-drive exploding-pusher experiment on the OMEGA Laser System using Bayesian inference, resulting in the reconstruction of the shell dynamics and energy transfer during the implosion. The model is tested by analyzing synthetic data from a 1-D hydrodynamics code and is sampled using a Markov chain Monte Carlo to generate the posterior distributions of the model parameters. As a result, the goal of this work is to demonstrate a general methodology that can be used to draw conclusions from a wide variety of HED experiments.
High-energy-density (HED) experiments in convergent geometry are able to test physical models at pressures beyond hundreds of millions of atmospheres. The measurements from these experiments are generally highly integrated and require unique analysis techniques to procure quantitative information. This work describes a methodology to constrain the physics in convergent HED experiments by adapting the methods common to many other fields of physics. As an example, a mechanical model of an imploding shell is constrained by data from a thin-shelled direct-drive exploding-pusher experiment on the OMEGA Laser System using Bayesian inference, resulting in the reconstruction of the shell dynamics and energy transfer during the implosion. The model is tested by analyzing synthetic data from a 1-D hydrodynamics code and is sampled using a Markov chain Monte Carlo to generate the posterior distributions of the model parameters. The goal of this work is to demonstrate a general methodology that can be used to draw conclusions from a wide variety of HED experiments.
The burning core of an inertial confinement fusion (ICF) plasma produces bright x-rays at stagnation that can directly diagnose core conditions essential for comparison to simulations and understanding fusion yields. These x-rays also backlight the surrounding shell of warm, dense matter, whose properties are critical to understanding the efficacy of the inertial confinement and global morphology. In this work, we show that the absorption and fluorescence spectra of mid-Z impurities or dopants in the warm dense shell can reveal the optical depth, temperature, and density of the shell and help constrain models of warm, dense matter. This is illustrated by the example of a high-resolution spectrum collected from an ICF plasma with a beryllium shell containing native iron impurities. Lastly, analysis of the iron K-edge provides model-independent diagnostics of the shell density (2.3 × 10 24 e/cm 3 ) and temperature (10 eV), while a 12-eV red shift in Kβ and 5-eV blue shift in the K-edge discriminate among models of warm dense matter: Both shifts are well described by a self-consistent field model based on density functional theory but are not fully consistent with isolated-atom models using ad-hoc density effects.
Mathematical response model for linear symmetrical displacements about axis of cylindrical shell partially filled with liquid
A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.
A model of an all-plasmonic switch based on a graphene waveguide integrated with a stub nanoresonator loaded with a quantum dot is considered. Using the full-wave numerical simulation, it is shown that successive on/off switching of the control surface plasmon – polariton wave at the input of the waveguide leads to a change in the phase of the signal plasmon – polariton wave in the nanoresonator by π. This causes reversible switching of the device operation regime – from almost complete blocking to stable transmission of the signal plasmon – polariton wave through the waveguide. The effect is implemented at rates of ∼0.5 THz for infrared electromagnetic waves localised in a device with a switching region of 40 × 20 nm. (paper)
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Charged particle motion in static magnetic fields without axial symmetry derived, employing Lagrange equation in transformed coordinate system and Alfven motion
Finite element papers published in the open literature on the static bending and free vibration of layered, anisotropic, and composite plates and shells are reviewed. A literature review of large-deflection bending and large-amplitude free oscillations of layered composite plates and shells is also presented. Non-finite element literature is cited for continuity of the discussion.
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In the development of advanced aircraft-engine fan cases and containment systems, composite materials are beginning to be used due to their low weight and high strength. The design of these structures must include the capability of withstanding impact loads from a released fan blade. Relatively complex triaxially braided fiber architectures have been found to yield the best performance for the fan cases. To properly work with and design these structures, robust analytical tools are required that can be used in the design process. A new analytical approach models triaxially braided carbon fiber composite materials within the environment of a transient dynamic finite-element code, specifically the commercially available transient dynamic finite-element code LS-DYNA. The geometry of the braided composites is approximated by a series of parallel laminated composites. The composite is modeled by using shell finite elements. The material property data are computed by examining test data from static tests on braided composites, where optical strain measurement techniques are used to examine the local strain variations within the material. These local strain data from the braided composite tests are used along with a judicious application of composite micromechanics- based methods to compute the stiffness properties of an equivalent unidirectional laminated composite required for the shell elements. The local strain data from the braided composite tests are also applied to back out strength and failure properties of the equivalent unidirectional composite. The properties utilized are geared towards the application of a continuum damage mechanics-based composite constitutive model available within LS-DYNA. The developed model can be applied to conduct impact simulations of structures composed of triaxially braided composites. The advantage of this technology is that it facilitates the analysis of the deformation and damage response of a triaxially braided polymer matrix composite within the environment of a transient dynamic finite-element code such as LS-DYNA in a manner which accounts for the local physical mechanisms but is still computationally efficient. This methodology is tightly coupled to experimental tests on the braided composite, which ensures that the material properties have physical significance. Aerospace or automotive companies interested in using triaxially braided composites in their structures, particularly for impact or crash applications, would find the technology useful. By the development of improved design tools, the amount of very expensive impact testing that will need to be performed can be significantly reduced.
The structural performance of two advanced composite tow-steered shells is assessed using experiments and analyses. The fiber angles vary continuously around the shell circumference, and one shell has all 24 tows applied during fabrication, while the second shell uses the fiber placement systems tow drop/add capability to achieve a uniform wall thickness. The shells are tested in compression, and their axial stiffnesses and buckling loads are estimated using linear finite element analyses. Scaled passenger and cargo door cutouts are machined into one side of each shell. Axial stiffnesses and buckling loads of the shells with cutouts are computed using linear finite element analyses. The retested shells carry over 90 percent of the axial stiffness, and 85 percent of the buckling loads, of the shells without cutouts. These small reductions demonstrate the potential of tow steering to mitigate adverse effects of cutouts on the structural performance. The good correlation between experimental buckling loads and linear buckling analyses noted here may result from their circumferential stiffness variation, reducing geometric imperfection sensitivity. Analysis models of both shells were evaluated without and with measured geometric imperfections superposed in different longitudinal orientations. Small variations in prebuckling stiffness and buckling load of the shells are observed.
Uranyl fluoride (UO 2 F 2 ) is a hygroscopic powder with two main structural phases: an anhydrous crystal and a partially hydrated crystal of the same R¯3m symmetry. The formally closed-shell electron structure of anhydrous UO 2 F 2 is amenable to density functional theory calculations. We use density functional perturbation theory (DFPT) to calculate the vibrational frequencies of the anhydrous crystal structure and employ complementary inelastic neutron scattering and temperature-dependent Raman scattering to validate those frequencies. As a model closed-shell actinide, we investigated the effect of LDA, GGA, and non-local vdW functionals as well as the spherically-averaged Hubbard +U correction on vibrational frequencies, electronic structure, and geometry of anhydrous UO 2 F 2 . A particular choice of U eff = 5.5 eV yields the correct U Oyl bond distance and vibrational frequencies for the characteristic Eg and A1g modes that are within the resolution of experiment. Inelastic neutron scattering and Raman scattering suggest a degree of water coupling to the lattice vibrations in the more experimentally accessible partially hydrated UO 2 F 2 system, with the symmetric O-U-O stretching vibration shifted approximately 47 cm -1 lower in energy compared to the anhydrous structure. Evidence of water interaction with the uranyl ion is present from a two-peak decomposition of the uranyl stretching vibration in the Raman spectra and anion hydrogen stretching vibrations in the inelastic neutron scattering spectra. A first-order dehydration phase transition temperature is definitively identified to be 125 °C using temperature-dependent Raman scattering.