Showing papers on "Shell (structure) published in 1970"

Analysis of thick and thin shell structures by curved finite elements

Abstract: A general formulation for the curved, arbitrary shape of thick shell finite elements is presented in this paper along with a simplified form for axisymmetric situations. A number of examples ranging from thin to thick shell applications are given, which include a cooling tower, water tanks, an idealized arch dam and an actual arch dam with deformable foundation. A new process using curved, thick shell finite elements is developed overcoming the previous approximations to the geometry of the structure and the neglect of shear deformation. A general formulation for a curved, arbitrary shape of shell is developed as well as a simplified form suitable for axisymmetric situations. Several illustrated examples ranging from thin to thick shell applications are given to assess the accuracy of solution attainable. These examples include a cooling tower, tanks, and an idealized dam for which many alternative solutions were used. The usefulness of the development in the context of arch dams, where a ‘thick shell’ situation exists, leads in practice to a fuller discussion of problems of foundation deformation, etc., so that practical application becomes possible and economical.

The stability of elastic equilibrium

Abstract: : A general theory of elastic stability is presented. In contrast to previous works in the field, the present analysis is augmented by an investigation of the behavior of the buckled structure in the immediate neighborhood of the bifurcation point. This investigation explains why some structures, e.g., a flat plate supported along its edges and subjected to thrust in its plane, are capable of carrying loads considerably above the buckling load, while other structures, e.g., an axially loaded cylindrical shell, collapse at loads far below the theoretical critical load.

Uniform Shell Designs

Abstract: Designs are generated which have an equally spaced distribution of points lying on concentric spherical shells. They have uniform space‐filling properties and are tabulated up to ten factors. The designs are shown to be more uniform than familiar experimental designs on the basis of two measures of uniformity. Their use is illustrated by an example with four factors.

Left Ventricular Wall Stress Calculated from One-Plane Cineangiography

Abstract: Left ventricular dimensions from routine clinical one-plane cineangiograms were combined with left ventricular pressure measurements to permit calculation of left ventricular wall stresses. The 25 patients included 12 with normal left ventricular dynamics, 6 with volume overload, 3 with outflow obstruction, and 4 with cardiomyopathy. Average stresses calculated on the basis of an ellipsoid model agreed with average values obtained from the exact solution of a thick-walled elastic ellipsoidal shell. Peak values were 150 to 625 g/cm2 in the circular direction and 75 to 365 g/cm2 in the longitudinal direction. A fiber-corrected stress was defined which represents a force per muscle fiber. The variation in fiber-corrected stress during the cardiac cycle may be considerably different from the variation in simple stress. The force-velocity characteristics of circular fibers for the 25 patients are presented. The data on peak wall stress overlap in the four groups of patients. Peak velocity of circumferential fiber shortening varied from 0.44 to 0.63 lengths/sec in patients with myocardial weakness and varied from 0.74 to 2.56 lengths/sec in the other patients. Contractile element velocity was determined during ventricular ejection when the rate of force change equaled zero. Contractile element velocity of shortening was 0.22 to 0.32 lengths/sec in the cardiomyopathy group and 0.50 to 1.32 lengths/sec in the other patients.

Optimum Geometry of Saddle Shaped Coils for Generating a Uniform Magnetic Field

Abstract: Saddle shaped coils for generating a field perpendicular to the axis of a cylindrical shell to which the coils are confined can be designed in a compact and easily constructed form. The central magnetic field of such a system and its second derivatives with respect to displacements from the center are given as functions of the coil dimensions, and conditions for minimizing these derivatives are discussed. A coil pair with a length‐to‐diameter ratio of 2 and circular arcs of 120° will have no second order central field derivatives in any direction.

Effect of a local axisymmetric imperfection on the buckling behaviorof a circular cylindrical shell under axial compression

Abstract: Local axisymmetric dimple imperfection effects on buckling load of circular cylindrical shell under axial compression

Low Buckling Loads of Axially Compressed Conical Shells

Abstract: : The stability of simply supported conical shells under axial compression is investigated for 4 different sets of in-plane boundary conditions with a linear Donnell type theory. The first two stability equations are solved by the assumed displacement, while the third is solved by a Galerkin procedure. The boundary conditions are satisfied with 4 unknown coefficients in the expressions for u and v. Both circumferential and axial restraints are found to be of primary importance. Buckling loads about half the 'classical' ones are obtained for all but the stiffest simple supports SS4 (v = u = o). The low buckling loads for 'classical' simple supports SS3 are confirmed by two different methods of analysis, a closed form solution in Hankel functions and a finite difference solution. Except for short shells, the effects do not depend on the length of the shell. Buckling under combined axial compression and external or internal pressure is studied and interaction curves were calculated for the 4 sets of in-plane boundary conditions. (Author)

An Exact Analysis of the Transient Interaction of Acoustic Plane Waves With a Cylindrical Elastic Shell

Abstract: The governing system of differential equations for the linear problem of the transient interaction of plane acoustic waves and a submerged elastic cylindrical shell is transformed into a system of Volterra integral equations of the second kind. The integral equations are solved by a step-by-step integration scheme and numerical results to the problem are obtained exactly within the limit of series solution imposed by the Gibb’s phenomenon and within the limit of numerical truncation and roundoff errors. Detailed features of the transient response of the shell were revealed.

Thermally dissipative enclosure for portable high-intensity illuminating device

Abstract: A sealed, thermally dissipative enclosure for a portable highintensity illuminating device is disclosed. The enclosure includes a housing shell having an exterior surface equipped with a plurality of outwardly extending fins and which is configured to form a cavity. A reflector having a specular mirrorlike surface is situated in the cavity of the housing shell. An aperture, extending through the housing shell and the reflector and generally aligned along the longitudinal axis of the enclosure, is provided to accommodate a light source. A cupshaped receptacle is included to provide a lamp socket, or other power connection, and to seal the aperture by having a portion thereof secured to the shell housing. The cavity is sealed by a faceplate which is securely retained in the mouth of the cavity. The dissipation of thermal energy is facilitated by positioning the reflector, in the cavity of the housing shell, to obtain optimal transfer of thermal energy from within the enclosure through the housing shell to the surrounding atmosphere.

Fluid flow directing structure for pressure vessel

Abstract: A light weight filament wound pressure vessel. The vessel includes a central cylindrical shell and a pair of end caps adapted to fit into the opposite ends of the shell. Each of the end caps includes a convex, dome-like upper portion, a cylindrical skirt depending from the upper portion and integrally connected thereto, and an annular land connected to the edge of the cylindrical skirt. The cylindrical skirts are of substantially the same outer diameter as the central shell. The lands have an outer diameter which is slightly less than the inner diameter of the central shell so that the junction between the lands and the skirt forms a shoulder having a radial dimension substantially equal to the thickness of the central shell. Each land has an annular groove therein for carrying a resilient O-ring. The O-rings are of a slightly larger diameter than the outer diameter of the lands so that they sealingly engage the inner wall of the central shell when the lands are inserted into the central shell. The central shell and cylindrical skirts of the end caps form a smooth external junction. The assembly is overwound with a fiberglass filament to provide the desired bursting strength of the vessel. The lands may be integrally connected to the skirts or mounted on a collector ring. In one embodiment of the pressure vessel of this invention a fluid flow directing means is integrally connected to the internal surfaces of one of the end caps for guiding fluids through the vessel and eliminating ''''channeling.'''' This embodiment of the invention is particularly adapted for use as a water conditioning tank.

Vehicle seat having restraint system within trim

Abstract: A self-contained seat and restraint system including a semirigid seat shell having a channel about the rear and sides thereof, a fixed, beltless buckle in one side of the channel, and a retractable lap belt guided through and by the other side of the channel. A shoulder belt system is also carried by the shell. The shell is trimmed both front and back to fully enclose both the shell and the restraint system mounted thereon.

Electrical connector shield

Abstract: A shielding arrangement for eliminating electromagnetic interference in an electrical connector. A first shell member contains a bore portion on its outer surface and an annular groove adjacent to the bore portion. A conductive shielding member having a section contiguous to the bore portion and a first spring portion adjacent one side of the surface snaps into the groove for removably securing the shield to the shell and a second spring portion adjacent the other side of the section. The second spring portion may be formed at an acute angle with respect to the section and yieldable to provide good electrical contact between the first shell member and a second shell member movable with respect to said first shell member. The first shell member may contain a second annular groove opposite the first annular groove, the shield section at junction of the section and the second spring member being insertable into the second annular groove. Further, the spring members may be formed of finger portions.

Concrete structural member

Abstract: A concrete structural member and method of forming same is disclosed. The member, which may be used in forming roadway and bridge guard rails, median barriers and the like, includes a pair of identically shaped, pre-cast, outer face members or shells spaced from each other with their inner faces confronting each other. The outer surface of each shell has a contour which, when the members are together, defines the desired structural shape. A core of solid material, such as concrete, is bast between the shells to thereby form a composite integral structure with the shells.

Vibrations of Elastic Surface Systems Carrying Dynamic Elements

Abstract: The set of problems where shells, plates, or membranes carry discrete dynamic systems at discrete points on their surface is treated in a general manner. Interaction of each discrete dynamic system with the surface system is assumed to be in direction of the normal to the surface only. General solution equations are given. To apply these general equations to a specific problem, the eigenfunctions and eigenvalues of the surface system alone and the displacement impedances of the discrete dynamic systems at their point of attachment are required. The eigenfunction and eigenvalue equations of a system consisting of a circular cylindrical shell carrying a dynamic absorber, which is also connected with a second spring to ground, are obtained as specific examples.

Similitude Approximations for Vibrating Thin Shells

Abstract: True dynamic similitude in the Newtonian sense proves often to be too restrictive in experimental investigations of dynamic characteristics of large shell structures by use of smaller models. Also, design information yielded by true similitude considerations is limited because of the usual requirement of total geometrical scaling. Thus, approximate similitude relationships were derived starting with Love's equations of motion for thin shells. Depending on the relative dominance of bending and membrane stress influences, selection is made between two similitude expressions. This allows the introduction of shell thickness as a parameter independent of the scaled surface geometry. Free as well as forced vibrations are examined. Some of the implications of approximate similitude are illustrated using as an example a simply supported circular cylindrical shell.

A model of the human skull as a poroelastic spherical shell subjected to a quasistatic load

Abstract: Two-phase isotropic homogeneous poroelastic material is taken as a model of the living bone in the sense that the osseous tissue is considered as a linear perfectly elastic solid and the fluid substances filling the cavities as a Newtonian viscous fluid. Using the Heinrich-Desoyer formulation of the consolidation theory of Terzaghi-Biot adapted to the spherical bodies and the Laplace transformation, the pressure head function is determined first. The complimentary solution of the equation for the displacement of the solid phase is then adapted from the classical elastic solution in terms of the Legendre polynomials. For simplicity, only the axisymmetric case is considered. The integration constants are determined from the third governing equation as well as from the boundary and initial conditions. Three illustrative examples are investigated in detail, assuming hydrostatic load: (1) a thick-walled shell if the fluid pressure may be disregarded, (2) a solid poroelastic sphere, (3) a thin-walled poroelastic shell. In case 2, the rheological model describing the behavior of the body seems to correspond to the Kelvin-Voigt model proposed for osseous tissues by Zarek and Edwards.

Origin of laminar-shelled articulate brachiopods

Abstract: The calcareous shell of Billingsella is composed of a primary layer of crystallites commonly disposed vertically or at high angles to the shell surface, and a laminar secondary layer of flat-lying blades which usually amalgamate laterally to form a succession of plates. The succession is unlike that of other billingsellaceans such as Nisusia or contemporaneous orthaceans like Oligomys and Orusia which have a secondary layer composed of fibres. It is, however, closely comparable with the impunctate, laminar secondary layer of the Triplesiacea and early Davidson-iacea. The other pene-contemporaneous laminar-shelled articulates, the Stropho-menacea and Plectambonitacea, differ in being pseudopunctate. These differences in shell structure suggest that the Strophomenida were polyphyletically derived, mainly from the Nisusiidae but also from the Billingsellidae which gave rise to the Davidsoniacea (and Triplesiacea).

Receptacles for the storage of liquefied gases at cryogenic temperatures

Abstract: Tanks for the storage of liquefied gases at cryogenic temperatures are disclosed. The disclosed tanks comprise two concentric shells with dished ends. The internal shell is fabricated from layers of glass fabric with organosiloxane treatment. A layer of high tensile wire fabric is incorporated as one of the integral laminae of the internal and external shells. The internal shell is covered with an insulating layer of flexible and rigid urethane foam. This foam is fabricated in contoured or flat blocks of suitable size and shape to conform to the inner shell. The blocks may be separated from the inner shell by multiple layers of metallized polyethylene terephthalate (Mylar), or other material which will reflect radiant heat.

Transient Interactions of Spherical Acoustic Waves and a Cylindrical Elastic Shell

Abstract: The three‐dimensional transient interaction between spherical acoustic waves with infinitely steep wavefronts and a circular cylindrical elastic shell of infinite length is investigated. The incident spherical wave is transformed into cylindrical partial waves by using the addition theorem for the modified Bessel function. The governing wave equation and equations of motion of the shell are solved by a series expansion‐Laplace‐Fourier transform technique. The transformed solution of the problem is obtained in closed form exact within the limit of series solution imposed by the Gibb's phenomenon. The physical solution is obtained by an accurate numerical scheme for the two‐fold inverse Laplace‐Fourier transforms. Detailed numerical results are obtained for the transient response of the shell and some quantitative effects of the sphericality of the incident waves on the response of the shell are also revealed.

Vehicle body construction

Abstract: The disclosure illustrates a vehicle body comprising a tubular cage-type frame over which a reinforced glass fiber outer shell is secured by means of a polyester adhesive. Rigid urethane foam material fills the recesses formed on the inside of the reinforced glass fiber shell by the tubular frames to structurally interconnect and reinforce the frame and the outer shell. A pair of unitary ceiling panels and a series of vertical sidewall panels are secured to the frame members. The vehicle body is used for a self-propelled vehicle by securing the tubular frame to the vehicle chassis.

The Effect of a Circular Hole on the Buckling of Cylindrical Shells

Abstract: An experimental and theoretical investigation of the effect of a circular hole on the buckling of thin cylindrical shells under axial compression was carried out. The experimental program consisted of tests performed on seamless electroformed copper shells and Mylar shells with a lap joint seam. The copper shells were tested in a controlled displacement testing machine equipped with a noncontacting surface displacement measuring device. Three-dimensional surface plots obtained in this manner showed the changes in the displacement field over the entire shell, including the hole region, as the applied load was increased. The Mylar shells were tested in a controlled load testing machine and demonstrated the effect of increasing the hole radius on the buckling loads of the cylinder. The theoretical solution was based on a Rayleigh-Ritz approximation. The solution provided an upper bound for the buckling stresses of the cylinders tested for hole radii less than ten per cent of the shell radii. The theoretical solution also identified the governing parameter of the problem as being related to the hole radius, the shell radius, and the shell thickness. The theoretical part of the investigation showed that even a small hole should significantly reduce the buckling stresses of circular cylinders. Experimentally, it was found that the effect of a small hole is masked by the effects of initial deformations but, at larger hole radii, the reduction in buckling stress took the form predicted by the theory. The experimental results also showed that the character of the shell buckling was dependent on the hole size. For very small holes the shell buckled into the general collapse configuration and there was no apparent effect of the hole on the buckling mode of the shell. For slightly larger holes the shell still buckled into the general collapse configuration, but the buckling stresses of the shell were sharply reduced as the hole size increased. For still larger holes the buckling stresses did not decrease as sharply as the hole size increased and the shell buckled into a stable local buckling configuration.

Influence of a supersonic flowfield on the elastic stability of cylindrical shells

Abstract: The rather complex interaction problem of shell divergence and panel flutter that may be encountered by an aerospace vehicle during the boost phase of a trajectory is treated theoretically and the results then compared qualitatively with recent experimental observations. The analytical model considers the combined influence of internal pressure and axial compressive loading on a thin-walled cylindrical shell in a supersonic flowfield. Radial edge constraint and initial imperfections also are considered. The formulation employs the nonlinear Donnell shell equations and a linear "piston theory" aerodynamic approximation and utilizes a kinetic stability approach. The aeroelastic stability of the shell is determined about its deformed middle surface using Galerkin's technique in a modal solution. The results of the analysis indicate that the supersonic flowfield has no effect on the critical buckling load or the unstable mode of the shell. Small amounts of axial loading, however, were found to reduce significantly the critical panel flutter speed of the shell. These results were verified, at least qualitatively, in recent wind-tunnel tests on shell models.