Showing papers on "Shell (structure) published in 1996"

Liquid dispensing apparatus and methods

Abstract: The invention provides methods and apparatus for nebulizing liquids. In one exemplary embodiment, an apparatus is provided which comprises a thin shell member having a front surface, a rear surface, and a plurality of apertures extending therebetween. The apertures are tapered to narrow from the rear surface to the front surface. A liquid supplier is further provided which delivers a predetermined unit volume of liquid to the rear surface. A vibrator vibrates the thin shell member to eject liquid droplets from the front surface of the thin shell member.

Atomic shell structure and electron numbers

Abstract: rn The electron localization function (ELF) was calculated for the atoms Li to Sr The ELF maxima reveal the atomic shell structure for all these atoms The shells are separated from each other by ELF minima The integration of the electron density in a shell gives electron numbers For the valence shell those are in good agreement with the ones expected from the Periodic Table of Elements 0 1996 John Wiley & Sons, Inc

Small and large deformation of thick and thin-film multi-layers: Effects of layer geometry, plasticity and compositional gradients

Abstract: The thermomechanical response of multi-layered materials subjected to small and large deformation during temperature excursions is examined in this paper. General bilayer and trilayer plates with comparable layer thicknesses, as well as the limiting cases of thin films on thicker substrates with and without compositionally graded interfaces are examined, all within the context of the classical Kirchoff theory for thin plates. Closed-form analytical formulations for small elastic deformation are presented whereby explicit expressions for stress/curvature relations are obtained for any general bilayer or graded trilayer with isotropic elastic properties, but anisotropic strains. The effects of the variation of Poisson ratio through the thickness of layered and compositionally graded materials on the evolution of multiple curvatures are analyzed. New theoretical results are presented on the effects of layer geometry, plastic flow and compositional gradation on large deformation (small strains and small rotations) in bilayer and trilayer systems comprising thick or thin-film layers. It is shown that the small deformation theory predictions for the generalized plane strain state provide an upper bound for curvature evolution among all the cases considered. By recourse to analytical methods and three-dimensional finite element modeling involving shell elements, particular attention is devoted to the occurrence of bifurcation in the solution for curvature evolution and the associated geometry changes in the thermoelastoplastic response of layered materials during thermal excursions. The model systems chosen for analyses include NiAl2O3 layers with a sharp or compositionally graded interfaces, AlSi thin-film bilayers and a compositionally graded interlayer sandwiched between layers in In0.12Ga0.88As and GaAs for applications in microelectronics and optoelectronics, and a carbon/ epoxy laminated composite.

Expanding Relativistic Shells and Gamma-Ray Burst Temporal Structure

Abstract: Many models of gamma-ray bursts (GRBs) involve a shell expanding at extreme relativistic speeds. The shell of material expands in a photon-quiet phase for a period t0 and then becomes gamma-ray active, perhaps due to inhomogeneities in the interstellar medium or the generation of shocks. Based on kinematics, we relate the envelope of the emission of the event to the characteristics of the photon-quiet and photon-active phases. We initially assume local spherical symmetry wherein, on average, the same conditions prevail over the shell's surface within angles the order of Γ–1, where Γ is the Lorentz factor for the bulk motion. The contribution of the curvature to the temporal structure is comparable to the contribution from the overall expansion. As a result, GRB time histories from a shell should have an envelope similar to "FRED" (fast rise, exponential decay) events in which the rise time is related to the duration of the photon-active phase and the fall time is related to the duration of the photon-quiet phase. This result depends only on local spherical symmetry and, since most GRBs do not have such envelopes, we introduce the "shell symmetry" problem: the observed time history envelopes of most GRBs do not agree with that expected for a relativistic expanding shell.Although FREDs have the signature of a relativistic shell, they may not be due to a single shell, as required by some cosmological models. Some FREDs have precursors in which the peaks are separated by more than the expansion time required to explain FRED shape. Such a burst is most likely explained by a central engine; that is, the separation of the multiple peaks occurs because the central site produced multiple releases of energy on timescales comparable to the duration of the event. Alternatively, there still could be local spherical symmetry of the bulk material, but with a low "filling factor"; that is, only a few percent of the viewable surface (which is already very small, 4πΓ–2) ever becomes gamma-ray active.Long complex bursts present a myriad of problems for the models. The duration of the event at the detector is ~t0/(2Γ2). The long duration cannot be due to large t0, since it requires too much energy to sweep up the interstellar medium. Nor can it be due to small Σ if the time variation is due to ambient objects, since the density of such objects is unreasonable (~1018Γ–4 pc–3 for typical parameters). Long events must explain why they almost always violate local spherical symmetry or why they have low filling factors.Both precursor and long complex events are likely to be "central engines" that produce multiple releases of energy over ~100 s. One promising alternative scenario is one in which the shell becomes thicker than the radius of the curvature within Γ–1. Then it acts as a parallel slab, eliminating the problems associated with local spherical symmetry.

Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements

Abstract: In the recent development of active structural systems and microelectromechanical systems, piezoelectrics are widely used as sensors and actuators. Because of the limitations of theoretical and experimental models in design applications, finite element development and analysis are proposed and presented in this paper. A new laminated quadratic C° piezoelastic triangular shell finite element is developed using the layerwise constant shear angle theory. Element and system equations are also derived. The developed piezoelastic triangular shell element is used to model 1) a piezoelectric bimorph pointer and 2) a semicircular ring shell. Finite element (triangular shell finite element) solutions are compared closely with the theoretical, experimental, and finite element (thin solid finite element) results in the bimorph pointer case. Natural frequencies and distributed control effects of the ring shell with piezoelectric actuators of various length are also studied. Finite element analyses suggested that the inherent piezoelectric effect has little effect on natural frequencies of the ring shell. Vibration control effect increases as the actuator length increases, and it starts leveling off at the seven-patch (70%) actuator. Coupling and control spillover of lower natural modes are also observed.

The membrane shell model in nonlinear elasticity: A variational asymptotic derivation

Abstract: We consider a shell-like three-dimensional nonlinearly hyperelastic body and we let its thickness go to zero We show, under appropriate hypotheses on the applied loads, that the deformations that minimize the total energy weakly converge in a Sobolev space toward deformations that minimize a nonlinear shell membrane energy The nonlinear shell membrane energy is obtained by computing the Γ-limit of the sequence of three-dimensional energies

Expanding relativistic shells and gamma-ray burst temporal structure

Abstract: Many models of gamma-ray bursts (GRBs) involve a shell expanding at extreme relativistic speeds The shell of material expands in a photon-quiet phase for a period t0 and then becomes gamma-ray active, perhaps due to inhomogeneities in the interstellar medium or the generation of shocks Based on kinematics, we relate the envelope of the emission of the event to the characteristics of the photon-quiet and photon-active phases We initially assume local spherical symmetry wherein, on average, the same conditions prevail over the shell's surface within angles the order of Γ–1, where Γ is the Lorentz factor for the bulk motion The contribution of the curvature to the temporal structure is comparable to the contribution from the overall expansion As a result, GRB time histories from a shell should have an envelope similar to "FRED" (fast rise, exponential decay) events in which the rise time is related to the duration of the photon-active phase and the fall time is related to the duration of the photon-quiet phase This result depends only on local spherical symmetry and, since most GRBs do not have such envelopes, we introduce the "shell symmetry" problem: the observed time history envelopes of most GRBs do not agree with that expected for a relativistic expanding shellAlthough FREDs have the signature of a relativistic shell, they may not be due to a single shell, as required by some cosmological models Some FREDs have precursors in which the peaks are separated by more than the expansion time required to explain FRED shape Such a burst is most likely explained by a central engine; that is, the separation of the multiple peaks occurs because the central site produced multiple releases of energy on timescales comparable to the duration of the event Alternatively, there still could be local spherical symmetry of the bulk material, but with a low "filling factor"; that is, only a few percent of the viewable surface (which is already very small, 4πΓ–2) ever becomes gamma-ray activeLong complex bursts present a myriad of problems for the models The duration of the event at the detector is ~t0/(2Γ2) The long duration cannot be due to large t0, since it requires too much energy to sweep up the interstellar medium Nor can it be due to small Σ if the time variation is due to ambient objects, since the density of such objects is unreasonable (~1018Γ–4 pc–3 for typical parameters) Long events must explain why they almost always violate local spherical symmetry or why they have low filling factorsBoth precursor and long complex events are likely to be "central engines" that produce multiple releases of energy over ~100 s One promising alternative scenario is one in which the shell becomes thicker than the radius of the curvature within Γ–1 Then it acts as a parallel slab, eliminating the problems associated with local spherical symmetry

The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation

Abstract: A model problem in the scattering of a time-harmonic wave by an obstacle coated with a thin penetrable shell is examined. In previous studies, the contrast coefficients of the thin shell are assumed to tend to infinity in order to compensate for the thickness considered. In this paper, these coefficients are assumed to remain finite. Such a treatment leads to a singular perturbation term that creates a typical difficulty for the asymptotic analysis of the problem with respect to the thickness of the coating. As a result, the asymptotic analysis is essentially based on a suitable handling of the stability of the solution relative to the thickness. As a consequence, it is shown how effective boundary conditions which can be substituted to the thin shell can then be obtained and analyzed in a simple way.

Reinforced door beam

Abstract: A reinforced door beam has a hollow shell with an internal localized reinforcement. The localized internal reinforcement is positioned at the midspan of the shell and has a length of less than about one-third of the door beam shell. The localized internal reinforcement includes an inner shell which is spaced apart from the door beam shell by a layer of thermally expanded resin.

Stabilization of the resistive shell mode in tokamaks

Abstract: The stability of current-driven external-kink modes is investigated in a tokamak plasma surrounded by an external shell of finite electrical conductivity. According to conventional theory, the ideal mode can be stabilized by placing the shell sufficiently close to the plasma, but the non-rotating `resistive shell mode`, which grows as the characteristic L/R time of the shell, always persists. It is demonstrated, using both analytic and numerical techniques, that a combination of strong edge plasma rotation and dissipation somewhere inside the plasma is capable of stabilizing the resistive shell mode. This stabilization mechanism is similar to that found recently by Bondeson and Ward (1994), except that it does not necessarily depend on toroidicity, plasma compressibility or the presence of resonant surfaces inside the plasma. The general requirements for the stabilization of the resistive shell mode are elucidated

Finite-element modeling of a smart cantilever plate and comparison with experiments

Abstract: The behavior of a cantilever plate instrumented with a piezoelectric sensor and actuator is described using finite-element modeling. To demonstrate the accuracy of the numerical model, a parallel experimental study was carried out in the laboratory for the same geometric dimensions. The two results are compared and show excellent agreement, demonstrating that finite-element modeling is a good approach for optimized smart structure design. A three-dimensional finite-element formulation is employed in the piezoelectric material region and a small neighboring region of the plate structure on which it is mounted. Shell elements, approximated by many flat-shell elements, are used in modeling the remaining part of the plate structure. Transition elements that connect the three-dimensional solid elements to the flat-shell element are used. For the cantilever plate example, the electrical input admittance as well as the sensor response are found from the finite-element analysis and they are compared with experimental measurements. From this, the accuracy and efficiency of this approach is demonstrated. In contrast to many other modeling techniques used for smart structures which are approximate and hence limited, the finite-element model is applicable to complicated geometries.

The influence of a protein on water dynamics in its vicinity investigated by molecular dynamics simulation

Abstract: A system containing the globular protein ubiquitin and 4,197 water molecules has been used for the analysis of the influence exerted by a protein on solvent dynamics in its vicinity. Using Voronoi polyhedra, the solvent has been divided into three subsets, i.e., the first and second hydration shell, and the remaining bulk, which is hardly affected by the protein. Translational motion in the first shell is retarded by a factor of 3 in comparison to bulk. Several molecules in the first shell do not reach the diffusive regime within 100 ps. Shell-averaged orientational autocorrelation functions, which are also subject to a retardation effect, cannot be modeled by a single exponential time law, but are instead well-described by a Kohlrausch-Williams-Watts (KWW) function. The underlying distribution of single-molecule rotational correlation times is both obtained directly from the simulation and derived theoretically. The temperature dependence of reorientation is characterized by a strongly varying correlation time, but a virtually temperature-independent KWW exponent. Thus, the coupling of water structure relaxation with the respective environment, which is characteristic of each solvation shell, is hardly affected by temperature. In other words, the functional form of the distributions of single-molecule rotational correlation times is not subject to a temperature effect. On average, a correlation between reorientation and lifetimes of neighborhood relations is observed. © 1996 Wiley-Liss, Inc.

Layerwise mechanics and finite element model for laminated piezoelectric shells

Abstract: A discrete-layer shell theory and associated finite element model is constructed for general laminated piezoelectric composite shells The discrete-layer shell theory is based on linear piezoelectricity and accounts for general through-thickness variations of displacement and electrostatic potential by implementing one-dimensional piece-wise continuous Lagrange interpolation approximations over a specified number of sublayers The formulation applies to shells of general shape and lamination Initially, the static and dynamic behavior of a simply supported flat plate is studied to compare with available exact solutions, with excellent agreement being obtained Static loading and free vibration of a cylindrical ring are then considered to evaluate the element and to study the fundamental behavior of active/sensory piezoelectric shells

Finite Element Methods for Thin Shell Problems

Abstract: Partial table of contents: GENERAL PRESENTATION OF THIN SHELL EQUATIONS EXISTENCE AND UNIQUENESS RESULTS Description of the Geometry of a Thin Shell The Linear Model of Koiter APPROXIMATIONS OF KOITER'S MODEL BY VARIOUS FINITE ELEMENT METHODS Mixed Finite Element Methods JOINT APPROXIMATION OF THE GEOMETRY AND OF THE DISPLACEMENT OF THE SHELL Approximation by Flat Facets Junctions Between Thin Shells LINEAR BUCKLING OF A GENERAL THIN SHELL Increase in Total Potential Energy of a Thin Elastic Shell Numerical Results SHAPE OPTIMIZATION OF THIN ELASTIC SHELLS UNDER VARIOUS CRITERIA Derivative of a Functional with Respect to the Shell Geometry From Equations to Program References Index of Quoted Authors Glossary of Symbols Subject Index.

Finite element implementation

Abstract: Preface FACILE Program Disks Notation Part I 1 Introduction 2 Two-Dimensional and Axisymmetric Problems 3 Three-Dimensional Problems 4 Plate and Shell Elements Part II 5 Substructure, Symmetry and Periodicity 6 The Two Level Finite Element Method 7 Finite Elements Mesh Generation Part III 8 Implementation Index

Artificial cotyloid cavity

Abstract: The artificial cotyloid cavity has a concave outer shell (1) and a concave inner shell (2) forming a hollow space (3) between them, where the outer and inner shells (1, 2) are permanently bonded together at their edges (5, 6) and the outer shell (1) merges beneath the transition curve (7) into a reinforced edge (5). From the centre (4), the wall thickness of the outer shell (1) increases substantially continuously to the transition curve (7). This simple and economical design ensures that the cotyloid cavity is as elastic as possible.

Insulated drinking cup

Abstract: A disposable insulated drinking cup includes an inner liner, an outer annular shell, and an air-filled spacer between the liner and shell. The spacer includes a corrugated wall adhered to a backing sheet. Both the corrugated wall and backing sheet are of thin-wall construction to maximize the air volume and insulation properties of the spacer.

Sound Transmission through a Cylindrical Sandwich Shell with Honeycomb Core

Abstract: Sound transmission through an infinite cylindrical sandwich shell is studied in the context of the transmission of airborne sound into aircraft interiors. The cylindrical shell is immersed in fluid media and excited by an oblique incident plane sound wave. The internal and external fluids are different and there is uniform airflow in the external fluid medium. An explicit expression of transmission loss is derived in terms of modal impedance of the fluids and the shell. The results show the effects of (a) the incident angles of the plane wave; (b) the flight conditions of Mach number and altitude of the aircraft; (c) the ratios between the core thickness and the total thickness of the shell; and (d) the structural loss factors on the transmission loss. Comparisons of the transmission loss are made among different shell constructions and different shell theories.