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At least 91 records · Page 5

State space approach to mixed boundary value problems.

A state-space procedure for the formulation and solution of mixed boundary value problems is established. This procedure is a natural extension of the method used in initial value problems; however, certain special theorems and rules must be developed. The scope of the applications of the approach includes beam, arch, and axisymmetric shell problems in structural analysis, boundary layer problems in fluid mechanics, and eigenvalue problems for deformable bodies. Many classical methods in these fields developed by Holzer, Prohl, Myklestad, Thomson, Love-Meissner, and others can be either simplified or unified under new light shed by the state-variable approach. A beam problem is included as an illustration.

Chen, C. F.↗

Sensitivity analysis for the dynamic response of viscoplastic shells of revolution

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric response of viscoplastic shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be isothermal viscoplasticity, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. Spatial discretization is performed using finite elements, with discontinuous stress resultants across element interfaces. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) with an implicit constitutive update. The sensitivity coefficients are evaluated using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading, and a circular plate subjected to impulsive loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to thickness, mass density, Young's modulus, and two of the material parameters characterizing the viscoplastic response. Time histories of the response and sensitivity coefficients are presented, along with spatial distributions of these quantities at selected times.

Kulkarni, Makarand↗

Stability and instability of thermocapillary convection in models of the float-zone crystal-growth process

This project was concerned with the determination of conditions of guaranteed stability and instability for thermocapillary convection in a model of the float-zone crystal-growth process. This model, referred to as the half-zone, was studied extensively, both experimentally and theoretically. Our own earlier research determined, using energy-stability theory, sufficient conditions for stability to axisymmetric disturbances. Nearly all results computed were for the case of a liquid with Prandtl Number Pr = 1. Attempts to compute cases for higher Prandtl numbers to allow comparison with the experimental results of other researchers were unsuccessful, but indicated that the condition guaranteeing stability against axisymmetric disturbances would be a value of the Marangoni number (Ma), significantly higher than that at which oscillatory convection was observed experimentally. Thus, additional results were needed to round out the stability picture for this model problem. The research performed under this grant consisted of the following: (1) computation of energy-stability limits for non-axisymmetric disturbances; (2) computation of linear-stability limits for axisymmetric and non-axisymmetric disturbances; (3) numerical simulation of the basic state for half- and full-zones with a deformable free surface; and (4) incorporation of radiation heat transfer into a model energy-stability problem. Each of these is summarized briefly below.

Neitzel, G. P.↗

Toric offset three-reflector antenna for the advanced microwave limb sounder

An advanced Microwave Limb Sounder (MLS), now in concept development for a potential future mission, is a space-borne heterodyne instrument to measure pressure, temperature, and atmospheric constituents from thermal emission between 120 and 2400 GHz. Previous MLS instruments used pencil-beam antennas sized to resolve N 1 vertical scale height. Current atmospheric models need better horizontal resolution than orbit spacing provides. To meet these needs, a new antenna concept combines the wide scan range of the parabolic torus with unblocked offset Cassegrain optics. The resulting system is diffraction-limited in the vertical plane but extremely astigmatic, with beamwidths 0.13~2.5. Nadir axis symmetry ensures that this Beam AspectRatio (BAR) is invariant over f33' of azimuth. The antenna can feed either an array of receivers or multiplexed low-noise receivers whose FOVs are swept by a small scanning mirror. We describe 3 stages of antenna design: First, using a paraxial-optics method, we choose conic profiles given vertical resolution orbit geometry, then develop the surfaces by nadir axis rotation, matching axisymmetric feeds to the BAR. A ray-trace program validates the design and generates alignment and deformation tolerances. Finally, a physical optics analysis verifies reflector surface currents and radiation patterns.

microwave↗

Axisymmetric shell analysis of the Space Shuttle solid rocket booster field joint

The Space Shuttle Challenger (STS 51-L) accident led to an intense investigation of the structural behavior of the solid rocket booster (SRB) tang and clevis field joints. The presence of structural deformations between the clevis inner leg and the tang, substantial enough to prevent the O-ring seals from eliminating hot gas flow through the joints, has emerged as a likely cause of the vehicle failure. This paper presents results of axisymmetric shell analyses that parametrically assess the structural behavior of SRB field joints subjected to quasi-steady-state internal pressure loading for both the original joint flown on mission STS 51-L and the redesigned joint recently flown on the Space Shuttle Discovery. Discussion of axisymmetric shell modeling issues and details is presented and a generic method for simulating contact between adjacent shells of revolution is described. Results are presented that identify the performance trends of the joints for a wide range of joint parameters.

Nemeth, Michael P.↗

Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas

We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The equilibrium system comprises a Grad–Shafranov partial differential equation and an integral equation. These equations can be utilized to calculate the equilibrium magnetic field and ion distribution function, respectively, for given particle density or given ion and electron toroidal current density profiles. The resulting solutions describe states characterized by toroidal plasma rotation and toroidal electric current density. Additionally, due to the presence of fluid electrons, these equilibria also exhibit a poloidal current density component. This is in contrast to the fully kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate toroidal currents and flows, given the absence of a third integral of the microscopic motion.

Physics↗

Shear stabilization of the capillary breakup of a cylindrical interface

A cylindrical interface containing a viscous liquid set into axial motion is subject to a capillary and to a surface-wave instability. Clues from previous studies suggest that, even though both mechanisms separately are destabilizing, under certain circumstances their mutual interaction can lead to a stable interface; shear can stabilize capillary breakup. Here, an axial flow through an annular cross section bounded on the inside by a rigid rod and on the outside by a deformable interface is considered. The competition between the two mechanisms is studied through the temporal growth of infinitesimal axisymmetric and nonaxisymmetric disturbances. This examination of temporal stability shows that, indeed, for geometries corresponding to thin annular layers both instabilities can be completely suppressed (disturbances of all wavelengths decay).

Russo, Mathew J.↗

Response of moderately thick laminated cross-ply composite shells subjected to random excitation

This study deals with the dynamic response of transverse shear deformable laminated shells subjected to random excitation. The analysis encompasses the following problems: (1) the dynamic response of circular cylindrical shells of finite length excited by an axisymmetric uniform ring loading, stationary in time, and (2) the response of spherical and cylindrical panels subjected to stationary random loadings with uniform spatial distribution. The associated equations governing the structural theory of shells are derived upon discarding the classical Love-Kirchhoff (L-K) assumptions. In this sense, the theory is formulated in the framework of the first-order transverse shear deformation theory (FSDT).

Elishakoff, Isaak↗

Estimates of elastic plate thicknesses beneath large volcanos on Venus

Megellan radar imaging and topography data are now available for a number of volcanos on Venus greater than 100 km in radius. These data can be examined to reveal evidence of the flexural response of the lithosphere to the volcanic load. On Earth, flexure beneath large hotspot volcanos results in an annual topographic moat that is partially to completely filled in by sedimentation and mass wasting from the volcano's flanks. On Venus, erosion and sediment deposition are considered to be negligible at the resolution of Magellan images. Thus, it may be possible to observe evidence of flexure by the ponding of recent volcanic flows in the moat. We also might expect to find topographic signals from unfilled moats surrounding large volcanos on Venus, although these signals may be partially obscured by regional topography. Also, in the absence of sedimentation, tectonic evidence of deformation around large volcanos should be evident except where buried by very young flows. We use analytic solutions in axisymmetric geometry for deflections and stresses resulting from loading of a plate overlying an inviscid fluid. Solutions for a set of disk loads are superimposed to obtain a solution for a conical volcano. The deflection of the lithosphere produces an annular depression or moat, the extent of which can be estimated by measuring the distance from the volcano's edge to the first zero crossing or to the peak of the flexural arch. Magellan altimetry data records (ARCDRs) from data cycle 1 are processed using the GMT mapping and graphics software to produce topographic contour maps of the volcanos. We then take topographic profiles that cut across the annular and ponded flows seen on the radar images. By comparing the locations of these flows to the predicted moat locations from a range of models, we estimate the elastic plate thickness that best fits the observations, together with the uncertainty in that estimate.

Mcgovern, Patrick J.↗

Sensitivity analysis for the dynamic response of thermoviscoplastic shells of revolution

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric, fully-coupled, thermoviscoplastic response of shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of large-strain, transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be viscoplasticity with strain hardening and thermal hardening, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used for the shell equations with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. The energy-balance equation is solved using a Galerkin procedure, with the temperature as the fundamental unknown. Spatial discretization is performed in one dimension (meridional direction) for the momentum and constitutive equations of the shell, and in two dimensions (meridional and thickness directions) for the energy-balance equation. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) for the momentum equation; a predictor-corrector version of the trapezoidal rule is used for the energy-balance equation; and an explicit scheme consistent with the central difference method is used to integrate the constitutive equations. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading.

Kulkarni, Makarand↗

Experiments on the stability of a liquid bridge in an axial electric field

The behavior of a neutrally buoyant liquid bridge was studied in the presence of axial electric fields. Silicone oil and a castor-oil-eugenol mixture were used to form cylinders with slenderness ratios larger than pi with strong, axial, dc electric fields. Below a certain field strength, a smooth transition to an axisymmetric, vaselike shape occurred. Circulation patterns were observed in these bridges. At lower field strengths, the bridge shape was more deformed and, at a well-defined field, pinch-off occurred. With ac fields, the field strength required to stabilize the bridge was higher and the collapse of the cylinder was much sharper. Upon interchanging the fluids, a steady axial field was found to destabilize cylinders with slenderness ratios less than 3. This behavior is consistent with that anticipated if the fluids behave as leaky dielectrics but not if they act as perfect dielectrics.

Sankaran, Subramanian↗

Nonaxisymmetric Shapes of Biological Membranes from Locally Induced Curvature

In various biological processes such as endocytosis and caveolae formation, the cell membrane is locally deformed into curved morphologies. Previous models to study membrane morphologies resulting from locally induced curvature often only consider the possibility of axisymmetric shapes-an indeed unphysical constraint. Past studies predict that the cell membrane buds at low resting tensions and stalls at a flat pit at high resting tensions. In this work, we lift the restriction to axisymmetry to study all possible membrane morphologies. Only if the resting tension of the membrane is low, we reproduce axisymmetric membrane morphologies. When the resting tension is moderate to high, we show that 1) axisymmetric membrane pits are unstable and 2) nonaxisymmetric ridge-shaped structures are energetically favorable. Furthermore, we find the interplay between intramembrane viscous flow and the rate of induced curvature affects the membrane's ability to transition into nonaxisymmetric ridges and axisymmetric buds. In particular, we show that axisymmetric buds are favored when the induced curvature is rapidly increased, whereas nonaxisymmetric ridges are favored when the curvature is slowly increased. Overall, our results hold relevant implications for biological processes such as endocytosis and physical phenomena like phase separation in lipid bilayers.

59 BASIC BIOLOGICAL SCIENCES↗

Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact

A geometrically nonlinear finite-element analysis was developed to calculate the strain energy released by delamination plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, G sub I, and shear sliding, G sub II, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding (G sub II) was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, G sub I, for a near-surface delamination can be as high as 0.5G sub II and can contribute significantly to the delamination growth.

Shivakumar, K. N.↗

Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact

A geometrically nonlinear finite-element analysis has been developed to calculate the strain energy released by delaminating plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, GI, and shear sliding, GII, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow first before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, GI, for a near-surface delamination can be as high as 0.5GII, and can contribute significantly to the delamination growth.

Shivakumar, K. N.↗

Dynamic centering of liquid shells

The moderate-amplitude axisymmetric oscillations of an inviscid liquid shell surrounding an incompressible gas bubble are calculated by a multiple-time-scale expansion for initial deformations composed of two-lobed perturbations of the shell and a displacement of the bubble from the center of mass of the liquid. Two types of small-amplitude motion are identified and lead to very different nonlinear dynamic interactions, as described by the results valid up to second order in the amplitude of the initial deformation. In the 'bubble mode', the oscillations of the captive bubble and the liquid shell are exactly in phase and the bubble vibrates about its initial eccentric location. The bubble moves toward the center of the drop when the shell is perturbed into a 'sloshing mode' of oscillation where both interfaces move out of phase. These results explain the centering of liquid shells observed in several experiments.

Tsamopoulos, John A.↗

Restraint of Liquid Jets by Surface Tension in Microgravity Modeled

Tension in Microgravity Modeled Microgravity poses many challenges to the designer of spacecraft tanks. Chief among these are the lack of phase separation and the need to supply vapor-free liquid or liquidfree vapor to the spacecraft processes that require fluid. One of the principal problems of phase separation is the creation of liquid jets. A jet can be created by liquid filling, settling of the fluid to one end of the tank, or even closing a valve to stop the liquid flow. Anyone who has seen a fountain knows that jets occur in normal gravity also. However, in normal gravity, the gravity controls and restricts the jet flow. In microgravity, with gravity largely absent, jets must be contained by surface tension forces. Recent NASA experiments in microgravity (Tank Pressure Control Experiment, TPCE, and Vented Tank Pressure Experiment, VTRE) resulted in a wealth of data about jet behavior in microgravity. VTRE was surprising in that, although it contained a complex geometry of baffles and vanes, the limit on liquid inflow was the emergence of a liquid jet from the top of the vane structure. Clearly understanding the restraint of liquid jets by surface tension is key to managing fluids in low gravity. To model this phenomenon, we need a numerical method that can track the fluid motion and the surface tension forces. The fluid motion is modeled with the Navier-Stokes equation formulated for low-speed incompressible flows. The quantities of velocity and pressure are placed on a staggered grid, with velocity being tracked at cell faces and pressure at cell centers. The free surface is tracked via the introduction of a color function that tracks liquid as 1/2 and gas as -1/2. A phase model developed by Jacqmin is used. This model converts the discrete surface tension force into a barrier function that peaks at the free surface and decays rapidly. Previous attempts at this formulation have been criticized for smearing the interface. However, by sharpening the phase function, double gridding the fluid function, and using a higher order solution for the fluid function, interface smearing is avoided. These equations can be rewritten as two coupled Poisson equations that also include the velocity. The method of solution is as follows: first, the phase equations are solved from this solution, a velocity field is generated, then a successive overrelaxation scheme is used to solve for a pressure field consistent with the velocity solution. After the code was implemented in axisymmetric form and verified by several test cases, the drop tower runs of Aydelott were modeled. The model handed the free-surface deformation quite nicely, even to the point of modeling geyser growth in the regime where the free surface was no longer restrained. A representative run is shown.

Chato, David J.↗

Writhed Analytical Magnetic Flux Rope Model

Observations of magnetic clouds, within interplanetary coronal mass ejections (ICMEs), are often well described by flux rope models. Most of these assume either a cylindrical or toroidal geometry. In some cases, these models are also capable of accounting for non-axisymmetric cross-sections but they generally all assume axial invariance. It can be expected that any ICME, and its flux rope, will be deformed along its axis due to influences such as the solar wind. In this work, we aim to develop a writhed analytical magnetic flux rope model which would allow us to analytically describe a flux rope structure with varying curvature and torsion so that we are no longer constrained to a cylindrical or toroidal geometry. In this first iteration of our model we will solely focus on a circular cross-section of constant size. We describe our flux rope geometry in terms of a parametrized flux rope axis and a parallel transport frame. We derive expressions for the axial and poloidal magnetic field components under the assumption that the total axial magnetic flux is conserved. We find an entire class of possible solutions, which differ by the choice of integration constants, and present the results for a specific example. In general, we find that the twist of the magnetic field locally changes when the geometry deviates from a cylinder or torus. This new approach also allows us to generate completely new types of in situ magnetic field profiles which strongly deviate from those generated by cylindrical or toroidal models.

A. J. Weiss↗

Shock effects from a large impact on the moon

The paper calculates the shock and shear deformation-induced internal energy distribution associated with a major basin-forming hypervelocity meteorite impact on the moon. The Hageman and Walsh formulation of the axisymmetric two-dimensional conservation equations in finite difference form is used, and the flow field induced upon impact of an iron meteorite traveling at 15 km/sec with a gabbroic anorthosite lunar crust is calculated for sequential time steps over a grid of hoop-shaped zones fixed in space. If an energy of 5 times 10 to the 32nd power ergs for the projectile energy is required to excavate a basin of Imbrium size, than a flow field of approximately 210 km in radius approximately 19 seconds after impact is indicated. The meteorite residue, the melt, and the ejecta are discussed, and the results are compared with the Gault and Heitowit (1963) formulation.

Okeefe, J. D.↗