Showing papers on "Spherical shell published in 1986"

Poloidal and toroidal fields in geomagnetic field modeling

Abstract: The theory of surface operators is described and applied to four surface operators on spheres: the dimensionless surface gradient, ▽1=r▽-r∂r; the dimensionless surface curl, Λ1=rˆ×▽1; the dimensionless surface Laplacian, ▽1²=▽1 · ▽1; and the Funk-Hecke operators, integral operators with axisymmetric kernels. Three methods are given for solving ▽1²g=f as g=▽1−2f; one method works numerically when f has a rapidly convergent expansion in spherical harmonics, the second works when f is smooth in longitude but not latitude, and the third (a Funk-Hecke operation) works when f is rough in all directions. With this apparatus, a complete proof is given of the Helmholtz representation of an arbitrary vector field v S (r), the spherical surface of radius r centered on the origin: there are unique scalar fields f, g, h on S(r) such that v=rˆf+▽1g+Λ1h and 〈g〉r=〈h〉r=0. Here 〈g〉r is the average value of g on S (r). From the Helmholtz representation on spherical surfaces, the Mie or poloidal-toroidal representation in spherical shells is deduced. Suppose S(a,c) is the spherical shell whose inner and outer boundaries are S(a) and S(c). Suppose B is solenoidal in S (a,c), i.e., ▽·B=0 and 〈Br〉a=0. Then there are unique scalar fields P and Q in S(a,c) such that B=▽ × Λ1P + Λ1Q and 〈P〉r=〈Q〉r=0 for a ⪕ r ⪕ c. The fields P = ▽ × Λ1P and Q=Λ1Q are the poloidal and toroidal parts of B. Applications of this formalism to geomagnetic field modeling are discussed. Gauss's resolution of the geomagnetic field B on S(b) into internal and external parts is generalized; if the radial current Jr does not vanish on S (b), then to Gauss's expression must be added a toroidal field on S(b) due entirely to Jr on S(b). A simple proof is given of Runcorn's theorem that to first order in susceptibility no external magnetic field results from magnetization in a horizontally homogeneous spherical shell polarized by sources inside the shell. A Funk-Hecke-based method of modeling ionospheric currents is described, which may be more accurate than truncated spherical harmonic expansions and easier to use than Biot-Savart integrals. Finally, the formalism makes possible the modeling of satellite samples of the geomagnetic field in a spherical shell S (a,c) where electric currents cannot be neglected. Two approximation schemes are described. One is a truncated power series expansion in (c-a)/H, where H is the radial length scale of the currents. The other assumes that most of B in S(a,c) is not due to the currents between S (a) and S(c), and that the currents in S(a,c) are field-aligned. Then the collection of physically possible magnetic fields in S(a,c) is only 50% larger, in a well-defined sense, than the collection of vacuum fields there. Methods of calculation are given explicitly.

Spherical shell tectonics: Effects of sphericity and inextensibility on the geometry of the descending lithosphere

Abstract: The shape of a deep seismic zone is thought to represent that of the descending slab of lithosphere. The lithosphere before subduction is a spherical shell, and the shape of the descending slab is the result of the deformation of the spherical lithosphere at the subduction zone. Upon bending a spherical shell often deforms in a very different way from a simple plate. We examine whether the actual shape of the descending slab can be explained by a simple bending of an inextensible spherical shell, which shows little surface deformation under moderate stress. This examination is made region by region for most of the subduction zones in the world by means of an analogue method. The lithosphere is simulated by an inextensible spherical shell made of polyvinyl chloride resin. The Wadati-Benioff zone is shaped by plaster by referring to the reliable hypocentral data selected from the International Seismological Centre (ISC) bulletins. The spherical shell is forced to fit the miniature of the Wadati-Benioff zone. Fitting is first attempted only by bending. If a good fit is not attainable and if a discontinuity or gap in seismic activity is observed in the relevant region, the spherical shell is torn along this discontinuity or gap, and the goodness of fit is reexamined. The results of the analysis are summarized as follows: (1) The shape of the Wadati-Benioff zone can be simulated largely by a simple bending of a spherical shell without surface deformation. (2) In almost all of the regions of poor fit with bending, a good fit can be achieved by tearing the spherical shell along the trace of low seismicity. The sphericity of the lithosphere and the inextensibility upon deformation are the two essential factors in controlling the slab shape. This means that the lateral constraint is most important for understanding the geometry of the downgoing slab of lithosphere and the stress state within it. Further, several problems related to the deformational characteristics of the spherical lithosphere are also reviewed and discussed in connection with subduction tectonics.

Time lag in diffusion

Abstract: Adsorption and desorption diffusion time lags are given for some homogeneous hollow cylinder and spherical shell membrane systems. The treatment relates to a constant diffusion coefficient with solution or sorption obeying Henry's law. Time lags for both “forward” and “reverse” flow have been determined and identities between them derived. For the hollow cylinder and spherical shell membrane systems considered here, there are only three distinguishable time lags.

High pressure fluid-driven tension actuators and method for constructing them

Abstract: High pressure, fluid-driven tension actuators, axially contractible upon inflation by a suitable fluid such as compressed air to convert fluid pressure energy into linear contraction displacement, employ nearly spherical shell surfaces when inflated constrained by meridian and parallel elements. The inflatable shells are formed of elastomeric resilient material, and the constraining elements in certain embodiments of the invention comprise a reinforcing, tubular, knitted, fabric sleeve that axially encompasses, conforms to, and is bonded to a resilient, hollow bladder which defines a fluid chamber having at least one conduit connected at a polar location to bladder and sleeve for inflating and deflating the chamber. The parallel and meridian elements for constraining the elastomeric resilient shell include a generally square constraining pattern extending in an equatorial band around the shell upon inflation of the nearly spherical shell. The constraining elements serve to define an outer limit to spherical expansion of the bladder or shell and reinforce the bladder against rupture upon inflation by high pressure fluid, and the energy for the actuator to return to its initial formed shape is derived from the shear of each region of the shell and the bending of the elastomeric material.

The onset of time‐dependent convection in spherical shells as a clue to chaotic convection in the Earth's mantle

Abstract: This work presents a detailed numerical study of the dynamical behavior of convection in a spherical shell, as applied to mantle convection. From both two-dimensional (120 radial and 360 tangential points) and three-dimensional (60 radial levels and spherical harmonics up to order and degree L = 33, m = 33), it is shown that for a spherical shell (with inner-to-outer radii ratio eta = 0.62) convection becomes time-dependent, with l = 2 dominating, at a Rayleigh number of about 31 times supercritical for a constant-viscosity, base-heated configuration. This secondary instability is characterized by oscillatory time dependence, with higher frequencies involved, at slightly higher Rayleigh numbers. In illustrating the onset of time dependence, the analysis is extended to show that the onset of weak turbulence in spherical-shell convection takes place at about 60 times the critical Rayleigh number via a quasi-periodic mode.

Analysis of Large Plastic Deformations in Shell Structures

Abstract: Four specific problems of large plastic deformation in shell structures are analysed and discussed. They are:- inversion of a spherical shell; formation of “flaps” in long-running ductile fracture of a high-pressure pipeline; inversion of a tube; and propagating collapse of a confined tube under external pressure. All of these examples involve travelling plastic hinges; and indeed such hinges seem to be a recurrent feature of large plastic deformations of shells. Two different kinds of travelling hinge are encountered, and analysed in simple ways. The first is a sort of rolling crease, while the second is almost purely extensional in character.

Method of forming spherical shells

Abstract: A process for manufacturing a spherical shell from a blank utilizing dies, comprising the steps of forming and clamping a flange portion of the blank by pressing with the dies and applying fluid pressure to an elastic diaphragm or flat metal sheet to cause the diaphragm or sheet to bulge the blank so as to form a curved shell surface.

Particle packings and the computation of pore size distributions from capillary condensation hysteresis

Abstract: Many porous materials are made up of particulate buildings blocks, and the pores are voids between the particles. This fact is important when one computes pore size distributions for such materials. Their results show that the preferred model for packed-particle pore structures is either a simple cubic or body-centered cubic model. The desorption process can be viewed as a Kelvin-type (hemispherical) mechanism operating in the minimum dimensions of the void structure, while adsorption can be viewed as a Kelvin mechanism operating in the largest dimensions of the void structure. Contact zone coalescence (assistance filling) seems to be delayed with respect to this instability. This delayed coalescence is associated with a strong dependence of multilayer adsorption on particle size as well as the surface energy barrier for expansion of a spherical shell. Furthermore, the desorption results are consistent with the additional effect of a pore-blocking or network mechanism.

Non-linear studies of orthotropic shallow spherical shells on elastic foundation

Abstract: Governing non-linear integro-differential equations for cylindrically orthotropic shallow spherical shells resting on linear Winkler-Pasternak elastic foundations, undergoing moderately large deformations are presented. Three problems, namely, non-linear static deflection response, non-linear dynamic deflection response and dynamic snap-through buckling of orthotropic shells have been investigated. The influences of material orthotropy, foundation parameters and shell-material damping on the deflection response are determined for the clamped and the simply- supported immovable edge conditions accurately. Orthotropy, foundation interaction and material damping play significant roles in improving the load carrying capacity of the shell structures.

Large Amplitude Free Vibrations of Shells of Variable Thickness—A New Approach

Abstract: Large-amplitude free vibrations of thin elastic shallow spherical and cylindrical shells of nonuniform thickness have been investigated following a new approach. Numerical results for movable as well as for immovable edge conditions are given in tabular forms and compared with other results. Nomenclature A = nondimensional amplitude D = modulus of rigidity E = Young's modulus e,e2 = first and second strain invariants of the middle surface el9e2 = newly defined strain invariants h - shell thickness k = curvature at the middle surface, in case of cylindrical shell R = radius of the base of the spherical shell R0 = radius of the spherical shell r,0 = polar coordinates T - kinetic energy V, V{ = potential energy of spherical and cylindrical shells, respectively w0(/) = unspecified function of time x,y - Cartesian coordinates a = normalized constant of integration ex,ey,yxy = strain components in Cartesian coordinates in middle surface p = density of the shell material v - Poisson's ratio of the shell material

Rotative electrical connector

Abstract: A rotative electrical connector is provided that allows connection of wires to a movable member so that the member can be moved without disturbing the electrical connection or fatiguing the electrical wire. The connector includes a spherical conductive member attached to the electrical wire and a spherical shell encasing the spherical member, which, in turn, is connected to a second electrical lead. Preferably, a conductive lubricant, such as a conductive grease is inserted into the space between the outer surface of the spherical member and the interior surface of the spherical shell so that there is an electrical connection between the spherical member and the shell. More than one electrical lead can be accommodated by using additional spherical members attached to the additional electrical leads, each of them encompassed in a separate conductive shell, the spherical members and spherical shells being insulated from one another but mechanically connected to one another.

Energy streamlines for a spherical shell scattering plane waves

Abstract: Plane sound waves are incident on an elastic spherical shell, submerged in water. Theoretical plots of the flow of sound energy around the shell, based on a thin‐shell analysis, are given for the case where the n=2 mode is excited. The shell is made lossy, and the water is lossless. Four conditions are treated: two thicknesses of shell, each with the interior either empty or full of water. It is found that significant amounts of energy are held in ring‐shaped vortices centered on or near the shells. Values for the absorption cross sections are calculated.

A mixed pseudospectral/finite difference method for the axisymmetric flow in a heated, rotating spherical shell. [for experimental atmospheric simulation

Abstract: Abstract A numerical solution technique for the axisymmetric flow in a differentially heated, rotating spherical annulus is developed. This method, based on the incompressible Navier-Stokes equations, simulates the Atmospheric General Circulation Experiment (AGCE) proposed for a future Shuttle mission. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This pseudospectral/finite difference (PS/FD) method is applied to a hierarchy of cases of varying difficulty. The difficult cases are characterized by thinner Ekman layers resulting from higher rotation rates, larger difference in boundary temperatures, and stronger body forces. Comparison of the results establishes the higher accuracy and efficiency of the PS/FD method over the pure second-order accurate finite difference (FD) method. This paper discusses the development and performance of a mixed PS/FD model for the AGCE which has been modelled in the past only by pure FD formulations.

Transmission of fast neutrons through an iron sphere

Abstract: Integral experiments have been performed using a homogeneous iron spherical shell to test neutron cross-section data. Neutron leakage spectra from the shell were measured using 252Cf-fission and (d...

Stress analysis of filament wound tanks using three-dimensional finite elements

Abstract: Application a la flexion d'une coque spherique stratifiee renforcee de fibres, sous une charge uniformement repartie

Geometrically Nonlinear Analysis of Shallow Spherical Shell Using an Integral Equation Method

Abstract: Recently, numerical solution techniques have been developed and widely used in various fields of natural science and engineering.

Large Deflection Analysis of Shallow Spherical Shell Using an Integral Equation Method

Abstract: Geometrically nonlinear analysis of shallow spherical shell using an integral equation method is presented. An integral equation formulation of shell bending problems is based on the stress function approach which is the one of previously proposed two formulations. Nonlinear algebraic equations obtained by the discretization of the derived nonlinear integral equation set are solved effectively by using of the Riks-Wempner method. Numerical results indicate the versatility and effectiveness of the new method for nonlinear bending problems of shallow shells.

The ablative implosion of spherical shells

Abstract: An analytic model is developed to describe the final state reached by a gas‐filled spherical shell compressed by a constant ablation pressure. The model takes into account the solid compressibility and the mass loss by ablation, and gives the magnitudes that characterize the state of the gas and solid when the implosion stagnates. The model provides an adequate physics interpretation and an extension of a recently reported model [B. Ahlborn, M. H. Key, and A. R. Bell, Phys. Fluids 25, 541 (1982)]. The restrictions of the model imposed by the approximations adopted are discussed. The results are compared with available numerical simulation data and with the previous model already mentioned, and the main differences between them are discussed.

Assessment of Fiber Strength in a Urinary Bladder by Using Experimental Pressure Volume Curves: An Analytical Method

Abstract: In the present study, an analytical method is developed to deduce the constitutive equations of fibers embedded in a thick shell from the time-variant pressure volume curves obtained by experimental procedures. It is assumed that the spherical shell under consideration is composed of a fiber reinforced material and undergoes radial deflection, modeling the behavior of some biological shells such as urinary bladder. The fiber stress is expressed as a function of fiber strain, rate of strain and the degree of biochemical activation. The function form is chosen such that equations of mechanical equilibrium can be integrated analytically to yield chamber pressure as a function of chamber volume, time rate of change of volume and activation. Arbitrary coefficients appearing in the fiber stress-equation are also present in the resultant time-variant pressure-volume relation. These coefficients can be determined by curve-fitting commonly used clinical data such as cystometry measurements.

Three axes driving unit

Abstract: PURPOSE:To permit the correct position control by connecting an outer spherical shell on the fixed side and the inner spherical shell on the driven side through a gimbal mechanism and installing actuators which revolve around three axes on the inner spherical shell. CONSTITUTION:An inner spherical shell 5 installed onto the shaft lever 2 on the driven side is accommodated into an outer spherical shell 4 installed onto the shaft lever 1 on the fixed side so as to be revolved relatively. The outer and inner spherical shells 4 and 5 are connected through a gimbal mechanism 6 so as to be revolved around three axes crossing at right angles each other. Rotary actuators 14-16 consisting of three motors, etc. for deceleration- revolving the inner spherical shell 5 through a frictional wheel 17 around three axes are installed onto the outer spherical shell 4 side, and said frictional wheel 17 is attached onto the inner spherical shell 5 through a hole 18 formed onto the outer spherical shell 4.