Ellipsoidal Heads Research Articles

Stress analysis of two-arc approximate ellipsoidal pressure vessel heads and parameter optimization

By studying the stresses of a two-arc approximate ellipsoidal head and comparing those of a standard ellipsoidal head of the same dimensions the paper concludes that the bearing capacities of the two kinds of heads are not the same. The maximum stresses on the inside surface and outside surface of the two-arc approximate ellipsoidal head are much greater than those of the standard one. The maximum latitudinal stresses of the former are 1·15 times and 1·53 times the latter, inside and outside; the longitudinal stresses are 1·78 times and 1·49 times those of the latter, respectively. Firstly, the paper gives the best parameters of two-arc approximate ellipsoidal heads which could make the smallest volume difference of the two kinds of heads.

Numerical analysis of the elastic-plastic behaviour of pressure vessels with ellipsoidal and torispherical heads

The purpose of this study is to investigate the elastic-plastic behaviour of pressure vessels with ellipsoidal and torispherical heads. The investigation was carried out by finite element analysis and lower bound limit analysis. First yield pressures, limit pressures and shakedown pressures are obtained for various geometric parameters and compared with previous results.

Dose Homogeneity in Boron Neutron Capture Therapy Using an Epithermal Neutron Beam

Simulation models based on the neutron and photon Monte Carlo code MCNP were used to study the therapeutic possibilities of the HB11 epithermal neutron beam at the High Flux Reactor in Petten. Irradiations were simulated in two types of phantoms filled with water or tissue-equivalent material for benchmark treatment planning calculations. In a cuboid phantom the influence of different field sizes on the thermal-neutron-induced dose distribution was investigated. Various shapes of collimators were studied to test their efficacy in optimizing the thermal-neutron distribution over a planning target volume and healthy tissues. Using circular collimators of 8, 12 and 15 cm diameter it was shown that with the 15-cm field a relatively larger volume within 85% of the maximum neutron-induced dose was obtained than with the 8- or 12-cm-diameter field. However, even for this large field the maximum diameter of this volume was 7.5 cm. In an ellipsoid head phantom the neutron-induced dose was calculated assuming the skull to contain 10 ppm 10B, the brain 5 ppm 10B and the tumor 30 ppm 10B. It was found that with a single 15-cm-diameter circular beam a very inhomogenous dose distribution in a typical target volume was obtained. Applying two equally weighted opposing 15-cm-diameter fields, however, a dose homogeneity within +/- 10% in this planning target volume was obtained. The dose in the surrounding healthy brain tissue is 30% at maximum of the dose in the center of the target volume. Contrary to the situation for the 8-cm field, combining four fields of 15 cm diameter gave no large improvement of the dose homogeneity over the target volume or a lower maximum dose in the healthy brain. Dose-volume histograms were evaluated for the planning target volume as well as for the healthy brain to compare different irradiation techniques, yielding a graphical confirmation of the above conclusions. Therapy with BNCT on brain tumors must be performed either with an 8-cm four-field irradiation or with two opposing 15- or 12-cm fields to obtain an optimal dose distribution.

Enhancement of the epithermal neutron beam used for boron neutron capture therapy

Purpose: This report describes a study to enhance the epithermal neutron beam at the Brookhaven Medical Research Reactor by increasing the epithermal neutron flux and/or reducing contamination by fast neutrons. Methods and Materials: The beam was reevaluated using Monte Carlo calculations and flux and dose measurements in air and in an ellipsoidal head phantom at the patient irradiation port. Changes in its geometry and materials were considered, including rearranging the fuel elements in the reactor core and redesigning the moderator and the patient irradiation port. Results: Calculations of the new fluxes and doses at the patient irradiation port showed that the epithermal neutron flux can be increased by 100%, while the fast neutron dose per epithermal neutron can be reduced by 38%. In 1992, some of the proposed changes were made. In June 1992, measurements were made after one additional fuel element was added to replace a graphite spacer block on the epithermal beam side of the reactor core. The results show that the epithermal neutron flux increased by 18%, as predicted by the Monte Carlo calculations. In October 1992, the fuel elements in the reactor core were rearranged by placing four new fuel elements in the first row facing the epithermal port; the intensity of the epithermal neutron beam increased by 50% and the fast neutron and gamma doses per epithermal neutron may have decreased slightly. Conclusion: The epithermal neutron beam at the Brookhaven Medical Research Reactor has gained a 50% increase in the epithermal neutron flux and the fast neutron and gamma doses per epithermal neutron are reduced slightly after the rearrangement of the fuel elements in the core.

Stress analysis of ellipsoidal vessel head with large-diameter flush radial nozzle and comparison of reinforcement types

The membrane solution and the asymptotic solution of the edge problem of thin shells of revolution were employed to solve analytically the stress analysis for an ellipsoidal vessel head with a large-diameter flush radial nozzle and its reinforcement structures under internal pressure.A comparison of several reinforcement types is given. Results are presented for the stress distributions and stress concentration factors.

Stress concentration and flexibility factor of nozzles in ellipsoidal pressure vessel heads subject to external moment

Ellipsoidal heads are commonly used as end closures for cylindrical pressure vessels in chemical and process industries. In the design of nozzles in pressure vessels, stress and flexibility of the nozzle-vessel structure are important factors to be considered. In this paper, a parametric study of radial nozzles in ellipsoidal vessel heads, when the nozzles are subjected to overturning moments, is presented. The computer program KSHEL, which is based on elastic thin shell theory, was utilized. Stress concentration factors and flexibility factors were determined and are presented as graphs of dimensionless nozzle-vessel parameters.

On the estimation of stress concentration and flexibility at nozzles in ellipsoidal vessel heads

The US Welding Research Council Bulletin Number 107 (WRC-107) is currently being used by many designers in the estimation of stress concentrations at nozzle-vessel junctures. The validity of the application of this design document to the case of nozzles in ellipsoidal vessel heads is studied in this paper. A number of comparisons of the stress intensity and flexibility at the nozzles between approximate approaches and the exact situation were made and discussed.

Thrust load on welded-pad reinforced nozzle in an ellipsoidal pressure vessel head

A thin shell analysis is performed to investigate the stress distribution of welded-pad reinforced nozzles in ellipsoidal pressure vessel heads. A comparison of the structural behavior of such a nozzle to an integrally reinforced nozzle shows that a sixty percent higher stress is present in a typical nozzle-vessel geometry. A parametric study is performed for welded-pad reinforced nozzles in ASME 2:1 pressure vessel heads. Results are presented as stress concentration factors and shear stress concentration factors as functions of nondimensional nozzle-vessel geometries.

Radial flexibility of welded-pad reinforced nozzles in ellipsoidal pressure vessel heads

A thin shell analysis was performed to investigate the radial flexibility of welded-pad reinforced nozzles in ellipsoidal pressure vessel heads. A comparison of the flexibility of such a nozzle to that of an integrally reinforced nozzle was made. The effect of size and thickness on flexibility was studied. A parametric study was performed for welded-pad reinforced nozzles in ASME 2:1 pressure vessel heads. Results are presented as flexibility factors which are functions of nondimensional nozzle-vessel geometries.

A computer program for nonlinear analysis of pressure vessels

This paper describes the nonlinear analysis of pressure vessels necessary for taking into account the large deformations that take place at the junctions of shells of different geometries. Specifically, a computer program has been developed, based on both the linear and nonlinear theories of shells, which obtains numerical solutions for the most commonly used types of pressure vessels, namely those with spherical, ellipsoidal or conical heads and also flat-end pressure vessels. A multisegment integration technique has been used to obtain the solutions of the governing equations. The computed solutions are found to be highly accurate when compared with the known results of simple shells, as no nonlinear analysis is reported in the literature on the shell junctions in pressure vessels.

Large deformation analysis of ellipsoidal head pressure vessels

Among the most common pressure vessels, the elliptical head pressure vessel stands out to be the second best in order of preferable stress distribution at the head-cylinder junction—the best being hemispherical head. But, like others, the deformation at the head-cylinder junction of this pressure vessel is so large that the stress distribution obtained from linear shell theory is far off from reality. The nonlinear shell equations of ellipsoidal head pressure vessels are solved here using the multisegment method of integration, developed by Kalnins and Lestingi[11]. Reissner's nonlinear equations for the axisymmetric deformation of shells of revolution, after specialization for ellipsoidal shells and further necessary modification for avoiding geometrical singularity at the apex of the head are used in this analysis. It is shown that the linear theory consistently over estimates the stresses at the head-cylinder junction of ellipsoidal head pressure vessels.

Radial flexibility factors of nozzles in pressure vessel heads

An analytical study is performed to investigate the flexibility of nozzless in pressure vessel heads. Classical thin shell theory is employed. Radial flexibility factors for nozzles in hemispherical and ellipsoidal pressure vessel heads are presented as graphs of non-dimensional shell parameters.

The Uniformly Valid Asymptotic Solution of Ellipsoidal Shell Heads in Pressure Vessels

In this paper, the complex equation is derived for the ellipsoidal shell heads in pressure vessels and uniformly valid asymptotic solution is given.

Stress analysis of ellipsoidal shell with radial nozzle

The thin shell equations of equilibrium in Love-Meissner form for an internally pressurized ellipsoidal vessel head with intersecting radial nozzle (flush or protruding) are solved numerically to obtain the stress distribution in both the ellipsoidal head and the nozzle. The results are presented graphically using appropriate non-dimensional parameters, as stress concentration factors at the point of intersection.

On asymptotic solutions for thin-walled ellipsoidal shell heads in pressure vessels with a circular hole under transverse force [formula omitted] and moment [formula omitted

According to the classical shell theory based on the Love-Kirchhoff assumptions, the second-order asymptotic solutions are given for thin-walled ellipsoidal shell heads in pressure vessels with a circular hole under transverse force P 0 and moment M 0 . The errors that result are within the margins allowed in the classical shell theory based on the Love-Kirchhoff assumptions.

Stress concentration factors for nozzles in ellipsoidal pressure vessel heads due to thrust loads

A theoretical elastic analysis of the stresses due to a thrust applied to a radial nozzle in an ellipsoidal pressure vessel head has been carried out. The nozzle can be either flush or protruding. The results, in the form of stress concentration factors and shear stress concentration factors in the ellipsoidal shells, are presented as graphs of non-dimensional shell parameters.

Structure and assembly of haptoglobin polymers by electron microscopy

Haptoglobin (Hp) consists of light (L) and heavy (H) chains, the latter of which combine with hemoglobin αβ dimers to form a highly stable complex. Human haptoglobin assembles as HL units that occur in two allelic forms; HL 1, which is monovalent, and HL 2, which is divalent. As a result, three phenotypic forms exist in the human population: Hp1-1, the homozygous form in which the monovalent HL 1 unit occurs as a dimer; Hp2-2, the homozygous form of the divalent HL 2 unit, which gives a series of polymers; and the heterozygous Hp2-1 form, which gives a different series of polymers. We have investigated the structures and assembly properties of these two haptoglobin polymeric series in their complexes with hemoglobin using high-resolution scanning transmission electron microscopy. Polymers of complex are composed of ellipsoidal or bilobal head groups, which are the Hαβ subunits connected by thin filament-like structures, which are the L chains. Polymers of size up to pentamers can be identified easily by counting the number of head groups in the molecule. Complex 2-1 and complex 2-2 trimers were studied extensively. The differences in detailed morphology show that while the 2-1 trimer is a linear polymer, the 2-2 trimer is a closed circular molecule. The micrograph images suggest that complex 2-2 tetramers and pentamers, and perhaps higher forms may also be cyclic. The structure of the L 2 subunit of haptoglobin is shown to be composed of two domains, which may be similar in structure to the single domain of the monovalent L 1 chain. The two L 2 domains are connected by a hinge that has quite limited flexibility. Using these structural models, assembly characteristics and structural properties of the trimers and tetramers of complex 2-1 and complex 2-2 are described.

Plastic Buckling of Various Shells

The phenomenon of plastic buckling is first illustrated by the behavior of a fairly thick cylindrical shell, which under axial compression deforms at first axisymmetrically and later nonaxisymmetrically. Plastic buckling encompasses two modes of behavior, nonlinear collapse at the maximum point in a load versus deflection curve and bifurcation buckling. Accurate prediction of critical loads corresponding to either mode in the plastic range requires a simultaneous accounting for moderately large deflections and nonlinear, irreversible, path-dependent material behavior. A thumbnail survey is given of plastic buckling which spans three areas: asymptotic analysis of postbifurcation behavior of perfect and imperfect simple structures, general nonlinear analysis of arbitrary structures, and nonlinear analysis for collapse and bifurcation buckling of shells and bodies of revolution. Comparisons between test and theory are presented for elastic-plastic buckling of axially compressed unstiffened and ring-stiffened cylindrical shells, internally pressurized torispherical and ellipsoidal pressure vessel heads, and pipes under combined external pressure and bending. The effect on buckling of fabrication processes such as cold forming and welding is discussed for the case of ring-stiffened cylindrical shells. Two examples are given of rather complex shell structures in which considerations of plastic buckling affect the design.

Quasielastic light scattering from solutions of lollipop‐shaped particles

AbstractAn expression is derived for the field correlation function of the light scattered from a solution of lollipop‐shaped particles. Such particles are a tractable model of certain bacteriophages. They are assumed to consist of an ellipsoidal head containing optically anisotropic scattering material and a tail which does not scatter. Because of the tail, Brownian rotational movement occurs around a center of rotational friction which is at a distance r0 from the center of the head. The dependence of the field correlation function C(τ) on the rotational diffusion coefficient DR is given by the factor ΣlBl exp[−l(l + 1)DRτ]. It is shown that the tail causes the coefficients Bl to be different from zero for all values of l. Therefore, C(τ) contains a term proportional to exp(−2DRτ), which is not present when r0 = 0. We give plots of Bl for various combinations of parameters. It turns out that dynamic light scattering may be used to measure r0.

Equivalent torispherical pressure vessel heads

Lower bounds to limit pressures for ellipsoidal and torispherical heads of cylindrical shells have been calculated using a numerical optimisation technique. These have been used to explore the ideas of equivalence between torispherical and ellipsoidal heads. The geometrical proportions of torispherical heads which have optimum limit pressures have been found and these are compared with the results of three geometrical criteria of ‘equivalence’.