Showing papers on "Spherical shell published in 1976"

Effect of thickness inhomogeneities in internally pressurized elastic-plastic spherical shells

Abstract: The behaviour of elastic-plastic spherical shells under internal pressure is investigated numerically for thickness-to-radius ratios ranging from cases of thin shells to very thick shells. The shells under consideration are made of strain-hardening elastic-plastic material with a smooth yield-surface. Attention is restricted to axisymmetric deformations, and results are presented for initial thickness inhomogeneities in various axisymmetric shapes. For smooth thickness-variations in the shape of the critical bifurcation mode, the reduction in maximum pressure is studied together with the distribution of deformations in the final collapse mode. Also, the possibility of flow localization due to more localized, initially thin regions on a spherical shell is investigated.

Dynamo theory and the solar cycle

Abstract: In this paper solutions of the mean field induction equation in a spherical geometry are discussed. In particular, the 22-year solar magnetic cycle is considered to be governed by an axisymmetric, periodic solution which is antisymmetric with respect to the equatorial plane. This solution essentially describes flux tubes travelling as waves from mid-latitudes towards the equator. In a layer of infinite extent the period of such dynamo waves solely depends on the strength of the two induction effects, differential rotation and α-effect (cyclonic turbulence). In a spherical shell, however, mean flux must be destroyed by turbulent diffusion, so the latter process might actually control the time scale of the solar cycle.

Finite element large deflection analysis of shallow shells

Abstract: A finite element formulation is presented to study the non-linear buckling of arbitrary shallow elastic thin shells with general boundary conditions and subjected to conservative pressure loading. Pre and post buckling behaviour of a large number of shallow and semi deep doubly curved shells is studied in detail. Unsymmetrical bifurcation paths of a shallow spherical shell subjected to uniform inward pressure are also investigated.

A complete model of the propagation of solar-flare cosmic rays

Abstract: A two-stage model of the propagation of 1–50 MeV solar-flare cosmic rays is presented. The first stage consists of a thin spherical shell of radius ra near the Sun which feeds particles into interplanetary space (the second stage) where they propagate along the Archimedean mean interplanetary magnetic field under the influences of anisotropic diffusion, convection, and energy changes. To calculate the time dependence at a fixed point in space, account is taken of the corotation of flux tubes past the observer.

Theory of Convection in a Deep Rotating Spherical Shell, and Its Application to the Sun

Abstract: The theory of convection in a rotating spherical shell, when applied to the Sun, should ultimately satisfy at least three broad constraints. The radial heat flux by the convection must not vary significantly with latitude; an equatorial acceleration must be produced; and the convection must give the right dynamo action to produce the gross features of a solar cycle.

Ion beam inertial fusion target designs

Abstract: A class of ion beam fusion targets consisting of a spherical shell of frozen DT surrounded by a low-density, low-Z pusher and a high-density tamper was designed. These designs have a number of advantages over targets with high-density, high-Z pushers.

Rupture protection device for steam generators of substantially cylindrical shape, preferably of pressurized-water nuclear power plants

Abstract: Rupture protection device for a steam generator of substantially cylindrical shape, includes a rupture protection enclosure for surrounding the steam generator, the enclosure including a base, a cover and a jacket formed of tension-resistant and compression-resistant material, and axially stressable connecting means for connecting the base, the cover and the shell to one another, the jacket being formed of substantially cylindrical sections, the cover being formed of a substantially concave divided spherical shell and an undivided bearing ring, the spherical shell having an outer rim surface, the bearing ring being formed with an inner ring surface corresponding to the outer rim surface, the spherical shell being braced as a separate structural member through the outer rim surface thereof against the inner ring surface of the bearing ring, the bearing ring forming part of a bracing assembly including the base, the cover, and the substantially cylindrical jacket through the intermediary of the axially stressable connecting means.

Closed form solutions for small deformations superimposed upon the symmetrical expansion of a spherical shell

Abstract: For small axially symmetric deformations of isotropic incompressible hyperelastic materials which are super-imposed upon the symmetrical expansion of a spherical shell, new closed form solutions are derived without any restrictions on the strain-energy function. These solutions are used to derive the n=1 buckling criterion for thick-walled spherical shells which are subjected to uniform external pressure. They are also used to deduce an upper bound to the force deflection relation for small superimposed translational deflections of bonded pre-compressed spherical rubber bush mountings.

Angle connecting joint for space frameworks - spherical shell has several slots on different diameters and connecting struts

Abstract: The joint is for use on building frameworks, scaffolding and children's toys such as climbing frames. The joint has the advantage of general application being usable for high stress frameworks and also for these with low loading. It is simple to use and can fit various angles of strut. The design is based on a spherical shell (1) with several slots (7, 9, 10) cut on different circumferences. The rod shaped building struts (22, 23) have threaded ends or threaded connectors with the screw heads (17, 28) fitting inside the spherical shell. At least two of the slots (7, 10) are at right angles on the great circles ('equators') of the sphere. A hemispherical joint can be used and a fully spherical connector can be made in two halves.

Acrylic Plastic Spherical Shell Windows Under Point Impact Loading

Abstract: : Acrylic plastic spherical sector windows have been subjected to point impact loading applied to the convex surface at the center of the window. The point impact loading simulated the velocities and kinetic energies encountered in a typical collision between an immovable underwater obstacle and a submersible equipped with a large panoramic bow window. Experimental results show that spherical sector windows with 117 degrees included angle and t/Ro = 0.094 fracture during simulated underwater collisions where the kinetic energy of the impactor was at least 435 foot-pounds. For windows with t/Ro = 0.166 the required kinetic energy to generate fracture is 1750 foot-pounds. The kinetic energy of a submersible required for initiation of fracture in the bow window increased with depth, but only moderately. Protective shields fabricated from 0.375-inch thick acrylic plastic did not provide any significant protection against impact generated fracture of spherical windows. Only a bumper appears to provide adequate protection for the bow window in a submersible colliding with a large underwater object.

On the Final Stage in Pressure Sintering Process

Abstract: The densification rate equation on the final stage in pressure sintering is derived on the basis of a theory of diffusional creep developed by Nabarro and Herring. The stress distribution in a powder compact is regarded to be the same as the stress distribution in a thick walled spherical shell under an external pressure. The resultant densification rate is expressed by dρ/dt=(9/2) (40 DΩ/kTd2)(1-ρ)(p2-p1), where ρ is the relative density and p2-p1 is the pressure difference between outside and inside of the hollow sphere. The rate equations are also obtained taking into consideration the effects of the surface energy and the enclosed gas pressure.

Further study of the model of a human skull as a cupola with a plane base

Abstract: An experimental study of the base deformation of isolated human scull under conditions of scull collision with an obstacle has been carried out. The findings are compared with human cerebrospinal traums phenomena. An earlier suggested continuous scull model is modified on the basis of the data obtained. It is shown that the modified model (a part of spherical shell with the flat base) resembles scull behaviour in statics and dynamics better than the scull model in the form of spherical shell.

The effect of radiation loading on the equivalent circuit for a piezoelectric polymer transducer

Abstract: The equivalent circuit for a transducer using distended piezoelectric polymer sheets has been shown to be similar to that using a thin spherical shell, except that the mechanical impedance is given by a summation, in parallel, of impedances associated with a normal‐mode expansion. The modal impedances are determined by the shape of the sheet boundary, the magnitude of the distension, and the nature of the radiation interaction between modes. The case of a distended circular sheet, fastened at the outer edge, radiating into a circular tube with rigid walls has been analyzed in detail This can be used to approximate the behavior of one transducer in a infinite hexagonal array. The behavior of distended rectangular sheets in an infinite rectangular array in an infinite baffle has also been studied. In both cases, the radiation field is given. [Work supported by ONR.]

Vortex perturbations of the nonstationary motion of a liquid with a free boundary

Abstract: The first studies on the stability of nonstationary motions of a liquid with a free boundary were published relatively recently [1–4]. Investigations were conducted concerning the stability of flow in a spherical cavity [1, 2], a spherical shell [3], a strip, and an annulus of an ideal liquid. In these studies both the fundamental motion and the perturbed motion were assumed to be potential flow. Changing to Lagrangian coordinates considerably simplified the solution of the problem. Ovsyannikov [5], using Lagrangian coordinates, obtained equations for small potential perturbations of an arbitrary potential flow. The resulting equations were used for solving typical examples which showed the degree of difficulty involved in the investigation of the stability of nonstationary motions [5–8]. In all of these studies the stability was characterized by the deviation of the free boundary from its unperturbed state, i.e., by the normal component of the perturbation vector. In the present study we obtain general equations for small perturbations of the nonstationary flow of a liquid with a free boundary in Lagrangian coordinates. We find a simple expression for the normal component of the perturbation vector. In the case of potential mass forces the resulting system reduces to a single equation for some scalar function with an evolutionary condition on the free boundary. We prove an existence and uniqueness theorem for the solution, and, in particular, we answer the question of whether the linear problem concerning small potential perturbations which was formulated in [5] is correct. We investigate two examples for stability: a) the stretching of a strip and b) the compression of a circular cylinder with the condition that the initial perturbation is not of potential type.

Design of efficient stiffened shells of revolution

Abstract: A method to produce efficient piecewise uniform stiffened shells of revolution is presented The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function This allows the general buckling constraint to be included in the design process only when it is violated The self-adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort Results for four conical shells and one spherical shell are given