Thin Shell Model Research Articles

A statically determinate truss model for thin shells: Two‐surface analysis (bending theory)

AbstractThis paper presents a simple scheme for analysing shells subject to the Kirchhoff–Love hypothesis. The method combines a previously developed, statically determinate truss model with the static‐geometric analogy of elastic thin shell theory. In this way, both in‐plane and flexural mid‐surface actions are obtained by simply repeating the elementary computations performed on an essentially ‘membrane’ truss.

Dynamo currents representing geomagnetic L variation demonstrated by a multi-layer ionospheric model

A multi-layer ionospheric model and lunar (2,2) tidal mode have been used to calculate dynamo current systems representing lunar geomagnetic semidiurnal variations. Since both the height variation of the ionospheric conductivities and latitudinal dependence of the height of the conductivity peaks have been taken into account, the dynamo current systems agree with equivalent ones (estimated from geomagnetic data) better than those for a thin shell model of the ionospheric conductivity, especially in the polar region.

Dynamic response of pipelines to moving loads

AbstractVibration of buried pipelines induced by moving axial and radial loads has been studied in this paper. A thin shell model has been used for the pipeline, which is assumed to be lying in an infinite isotropic homogeneous elastic medium. In order to allow for the possible motion of the pipe out of phase with the surrounding ground a very thin layer of viscoelastic material is assumed to separate the pipe from the ground. Calculations indicate the presence of the interfacial viscoelastic layer does not influence the pipe response in a significant manner. So all the numerical results presented here are for the case when the pipe is assumed to be perfectly bonded. These show that the maximum pipewall displacements and stresses occur in a soft soil at long wavelengths.

Application of a two-dimensional ballooning model to out-pile and in-pile simulation experiments

The FRETA-B code which has thermal and mechanical models for the fuel behavior during a postulated Loss of Coolant Accident was applied to out-pile tube ballooning experiments and an in-pile integral simulation experiment MT-1 in the NRU reactor. From the analysis of the out-pile experiments, the ballooning model based on the thin-shell model together with an empirical rupture criterion was found effective in predicting the cladding deformation kinetics and the average strain left after rod rupture. The mechanical analysis of the MT-1 experiment was based on the calculation of the temperature history and its transverse distribution under reflooding which were consistent with the limited experimental data. The analysis indicated that the restriction of flow channel blockage to 70% in MT-1 was a result of an azimuthal cladding temperature difference of up to 60 K due mainly to eccentric relocation of pellet fragments.

A sequel to: Nonlinear finite element analysis of elastic systems under nonconservative loading—Natural formulation. Part I. Quasistatic problems

The present paper addresses a weak form quadrature element formulation for the geometrically exact thin shell model in which the Kirchhoff-Love hypothesis is adopted. The displacement derivative continuity conditions are enforced by the reconstruction of rotation variables at the edges of elements. By the utilization of rotation quaternions, a total Lagrange updating scheme is implemented for edge constraint director rotations. Several numerical examples are presented to illustrate the effectiveness of the proposed formulation and the significant reduction in the number of degrees of freedom in geometrically nonlinear thin shell analysis with large displacements and rotations.

The finite bending of curved pipes

Using a thin shell theory developed by Reissner, a nonlinear model for the in-plane bending of a curved pipe is described. It is shown how classical thin shell models of this component can be deduced on making certain simplifying assumptions concerning the mode of deformation. By way of a numerical nonlinear analysis the problem of Brazier buckling of the curved pipe in pure bending is examined and compared to previous simplified solutions.

Study of the structure of the TYCHO SNR with the HEAO 1 scanning modulation collimator experiment

The Tycho SNR was observed with the scanning modulation collimator experiment on board the HEAO 1 satellite. A soft extended source was detected. The extended X-ray source is best fitted with a thin spherical shell model of approximately 3.8 arc minute radius. The presence of a brighter, less extended structure in the western side of the remnant is suggested by our data.

A Shell Model of a Buried Pipe in a Seismic Environment

In a number of recent investigations, a buried pipe undergoing seismic excitation was modelled as a beam on a visco-elastic foundation. However, it is known that two of the observed failure modes in the buried pipelines under seismic loads are buckling and fracture. Therefore, in this paper, a thin circular cylindrical shell model in a resisting soil medium is used for a buried pipe. The coupled equilibrium equations arising from this model are modified to yield three decoupled equations which somewhat simplify the analysis. Then, an application for a long buried pipe is presented and the results are discussed and compared with those of the beam model.

VLBI aperture synthesis observations of H2O masers associated with molecular clouds

A system of programs for aperture synthesis mapping of spectral line VLBI data was developed and applied to data from a five-station experiment. The interferometer phase is derived from the phase of a modeled reference feature. Synthesis maps of the H/sub 2/O maser emission in W51, ON 2, and CRL 2591 are presented. Fringe rate maps are presented of W3 (OH) and W3(C) H/sub 2/O, for which synthesis maps could not be made. The maps are used to identify characteristic scale sizes in H/sub 2/O sources and to discuss the state of saturation, the density, and the minimum size of masers. Pairs of knots with emission over a wide velocity range, which are seen in the maps of W51 and CRL 2591, are discussed in terms of collapsing-cloud and thin-shell models. A model for H/sub 2/O maser sources involving dust shells around newly formed, massive stars is used to explain the general features of the maps. 19 figures, 2 tables.

A kinematic analysis of uterine deformation during labor

A thin shell model of the uterus is proposed and a kinematic solution of uterine deformation during labor derived. In vivo multi-point strain measurements performed during the various stages of labor up to delivery form boundary conditions for the numerical solution, which yields curvature and local obliqueness variations of the uterus during a contraction. The results are discussed in the light of their clinical applications.

A hydromagnetic dynamo of the atmosphere

Conventional dynamo theories start from wind fields which are considered as external forces independent of the ionospheric plasma. These dynamos are called kinematic dynamos. Coupling between the neutral wind and the ionospheric plasma in a self‐consistent manner results in a hydromagnetic dynamo. In this paper a theory of a hydromagnetic dynamo of the geomagnetic Sq current is developed assuming a thin shell model with constant elements of the electric conductivity tensor. Coupling between neutral gas and plasma is described by the Ampere force j × Bo (j being electric current density and Bo geomagnetic field) which depends not only on the velocity difference between neutrals and plasma (ion drag) but also on the electric polarization field. The electric polarization field includes a source free component which is not negligibly small at dynamo layer heights, so that the electric field cannot be represented by an electric potential. This theory leads to a modified Laplace equation of tidal theory which can be solved numerically. Calculations are presented for the diurnal and the semidiurnal tidal wave modes. Their equivallent depths, their vertical wavelengths, and their attenuation factors are discussed as functions of a plasma parameter δ which is proportional to a Cowling conductivity. The horizontal structures of pressure and electric current of the dominant symmetric tidal waves are determined for different values of δ representing the lower atmosphere (δ = 0), the dynamo region (δ ≃ 1), and F layer heights (δ ≃ 10). It is shown that waves with positive equivalent depths at δ = 0 are heavily attenuated at δ > 1 and drastically change their horizontal structure there. On the other hand, waves with negative equivalent depths at δ = 0 are only weakly affected by the Ampere force. From our calculations we suggest that tidal wave theory at thermospheric heights should be reconsidered taking into account electric coupling between the modes. In particular, we predict that the semidiurnal (2, 2) wave so far considered as the dominant semidiurnal mode above about 200 km height may have lost its significance and may in fact be replaced by the symmetric (2, ‐3) wave.

Stress concentrations in conventional shaped metal and unidirectional composite compliant tubes

The design of compliant tube gratings for acoustic decoupling in water requires considerable detailed modeling of tube elastodynamics, array acoustics, grating resonant frequency, resonant bandwidth, elastomer loading, and tube stresses induced by uncompensated hydrostatic loading. Since the stresses depend on the same tube parameters as the acoustic characteristics it becomes necessary to simultaneously consider all grating factors including weight, thickness, and cost. For obvious reasons, however, tube strength must be given top priority in any design, and fundamental to estimating strength is a knowledge of stress risers in uniformly loaded oval shells. For conventional shaped tubes, such as those used by NUSC, the maximum stress is compression on the inside at the center of the curved ring segment. For very thick curved ends the ordinary thin shallow shell model is inappropriate and should be replaced by a more precise model. This paper presents the theoretical and emperical highlights of a detailed stress analysis of compliant tubes, including the flexural stress at the tube ends as well as the ring stresses.

The Flexibility of Curved Pipes in Creep

The redistribution of stress in a linear, thin shell model of a curved pipe creeping under the action of a constant applied in-plane bending moment is represented by an equation of evolution in time. Using finite differences, this continuous system is reduced to a finite set of initial value problems which are numerically integrated using a fifth order Runge-Kutta method. The flexibility of the curved pipe is compared to that of a similar elastic, and a similarly creeping, straight pipe. Results are compared with two simple approximate methods and with a previous-steady state analysis.

Atmospheric solar tides and their electrodynamic effects—II. The equatorial electrojet

The global-scale dynamo solution in Part I is used to determine a full three-dimensional solution within the equatorial electrojet. Inclusion of vertical currents near the magnetic equator nearly doubles the magnetic variation obtained from the thin-shell dynamo model, relaxing the need for E-region diurnal wind speeds as large as those required by previous workers to reproduce the S q current system. This occurs because the electrojet is broadened both vertically and in its north-south extent when three-dimensional current flow is permitted. The underlying physics of this enhancement of the electrojet intensity over that predicted by the thin-shell approximation is discussed. The three-dimensional electrojet structure confirms salient features of simpler noontime meriodional-plane electrojet models, if these are extended to couple with local time variations of the polarization field generated by global dynamo action. By including local winds in our electrojet model, we are able to simulate the double-peaked structures observed near the magnetic equator by rocket-borne magnetometers. The model is also utilized as an aid in elucidating other electrojet phenomena, including the occurrence of plasma instabilities and the counter-electrojet.

A comparison of approximate methods for estimation of the creep relaxation of a curved pipe

The relaxation of stress in a linear, thin shell model of a curved pipe constrained to have a fixed rotation and expanding inelastically due to creep is represented by an equation of evolution in time. Using finite differences this continuous system is reduced to a finite set of initial value problems which are numerically integrated using a second order Runge-Kutta method. Thus the relaxation of the resultant in-plane bending moment can be deduced. Results are compared with two simple approximate methods with important repercussions on high temperature pipework design.

Axisymmetric thermoelastic stress perturbations in a fuel can due to localized variations in internal heat generation and boundary conditions

An exact thermal analysis of a free-standing fuel can subject to axially symmetric localized variations in internal heat generation, internal surface heat flux and external surface heat transfer coefficient has been developed, and used for a comparative study of surface stresses predicted by both exact three-dimensional thermoelasticity theory and thin shell theory. It is concluded that the thin shell model is justified for stresses, but for thermal analysis a shell conduction model should include an adequate treatment of conjugate heat transfer and axial conduction.

Circumstellar dust shell models for alpha Ori.

We present the results from some simple calculations of optically thin dust shell models for a Ori. We show that (1) the mass in the shell is large, 3 x 10- - 1 x 10-2 M0, but compatible with the current picture of mass-loss; and (2) photometry at wavelengths greater than 20 can help to distinguish among various density distributions in `the shell. Subject headings: circumstellar shells - infrared - stars, individual

Shielding Properties of Thick Conducting Cylindrical Shells

The shielding properties of a thick cylindrical shell of finite conductivity is presented. The analysis uses straightforward separation of variables methods via cylindrical harmonic functions. The results show that significant attenuation of the incident fields are achieved for thick cylindrical shields thus demonstrating that the resonances noted in earlier work using thin shell models can be alleviated.

Stability of the thin elastic shell model of the red blood cell

Fung and Tong have recently explained the sphering of red blood cells in hypotonic solution by showing that a thin-walled elastic membrane with the right extensional stiffness and surface tension distribution will swell into a sphere under internal pressure. In this report we investigate the stability of the spherical state of Fung and Tong's model by applying the static energy criterion, which requires a determination of the sign of the quadratic terms in the potential energy functional. It turns out that a spherical cell model with radius less than that of the equatorial radius of the original undeformed cell is indeed stable, if and only if the supposedly arbitrary elastic parameters in the model are restricted in their possble range of values.

Construction of complex photoelastic models using thin molded-epoxy sheets

The construction and analysis of complex thin-shell photoelastic models are discussed. Examples of both two- and three-dimensional applications are presented. The first example concerns an investigation of the structural supports of a new and unique blastfurnace design. The second example is directly related to the design and analysis of complex thin-shell pressure vessels and manifolds.