Shell Segments Research Articles

Stiffness of thin pressurized shells of revolution

A quasi-linear approach is developed. The strains and rotations are assumed to be small, but the equilibrium conditions are fulfilled on the deformed shell. In the resulting differential equation, bending and appear side by side. The asymptotic form of this equation is discussed for the case of the circular torus. Considered separately, the two effects are fairly similar. Suitable superposition of the two limit solutions yields a close approximation to the composite solution. As a sample application, the transverse of torus shells is derived and is presented as a function of internal p and shell thickness h. It is found in particular that membrane theory remains correct for h small but finite. Linear shell theory, on the other hand, involves an error that is proportional to p if p is small. I. Introduction T HIS paper is concerned with the rotationally symmetric deformations that pressurized, thin elastic shells of revolution experience under axisymmetric external loads. The approach to this problem presented here is a quasilinear approach: the shell strains and rotations are assumed to be small, but, contrary to the approach of linear shell theory, the shell equilibrium conditions will be fulfilled on the deformed shell. Thereby, the stiffening that a shell experiences when it is pressurized is taken into account. This pressure stiffness is neglected in linear shell theory. This deficiency of linear theory has two aspects. Both are illustrated by the model, one half of which is shown in Fig. 1, a pressurized, complete circular torus shell $ subject to an axisymmetric system P of external loads. Consider the equilibrium of the vertical forces on either one of the two toroidal shell segments that connect the two crowns of S. If we assume that S is a membrane shell, then the only vertical forces are P and the vertical components of p. These are

On the Solution of Nonlinear Snap Buckling by the Progressive Approximation Method : Snap Buckling of Spherical Shells under Uniform External Pressure

A set of nonlinear differential equations based on the finite deformation theory in the two-dimensional shells has been solved by assuming a specified deflection mode because of the difficulty to obtain their exact solution;however, the particular deflection mode assumed has a great effect on the buckling load, giving considerably higher theoretical values than experimental values, as noted in the previous paper. From the above circumstances, the progressive approximation method was applied to the snap buckling problem under uniform pressure of a shallow spherical shell segment having a small value of α=aβ2/t (a : radius, t : thickness, 2β : angle of opening) and a more precise and reasonable solution could be obtained by means of a comparatively simple mathematical treatment. That is, much smaller initial buckling loads were obtained with the deflection mode which varied reasonably with the variations of load and deflection, verifying the suitability of this method.

On the Initial Response of a Spherical Shell to a Concentrated Force

This paper is concerned with the initial response of a restricted class of thin elastic shells to localized transient loadings. Attention is restricted to those shells which are essentially spherical and shallow in a neighborhood of the loading. The initial response within this neighborhood can be approximated by the response of a (shallow) spherical shell segment to a concentrated force within the framework of a modified shallow-shell theory.

On the Influence of Uniform Stress States on the Natural Frequencies of Spherical Shells

The influence of uniform tensile and compressive stress states on the natural frequencies of transverse vibrations for shallow spherical shell segments is determined from the general equations for elastokinetic shallow shell problems with longitudinal inertia terms neglected. General frequency determinants are derived and detailed numerical results obtained for a range of shell geometries and stress states.

Permeability of the Egg Shell as Influenced by Washing, Ambient Temperature Changes, and Environmental Temperature and Humidity

USING a subjective dye penetration method, Almquist and Hoist (1931) found that ambient temperature affected permeability of the egg shell and Kraft et al. (1958) reported that the effects of temperature produced similar results employing the same technique. Romanoff (1943) used small segments of shells to determine egg shell permeability and showed that the rate of gas transmission through the shell portions was influenced by environmental temperature and humidity. Hypotheses by other workers are found in additional studies but lack specific and direct information regarding the influence of environmental conditions on permeability of the whole egg shell. The purpose of this report is to evaluate the influences of some common handling practices employed during the marketing operation on egg shell permeability by utilizing the objective colorimetric method of Fromm (1959).EXPERIMENTALGeneral. All eggs used in these studies were laid by a flock of S. C. White Leghorns in their …

Axisymmetric Vibrations of Shallow Elastic Spherical Shells

This paper contains an exact solution within the scope of the bending theory of shells for axisymmetric vibrations of thin shallow elastic spherical shells. Specifically, the solution is applied to an investigation of the natural frequencies of the free axisymmetric vibrations of spherical shell segments with various edge conditions. Comparison drawn with previously known results for transverse vibrations of shallow spherical shells, where the effect of longitudinal inertia is neglected.

Stability limits for a clamped spherical shell segment under uniform pressure

An integration procedure for the differential equations for the finite deflections of clamped shallow spherical shells under uniform pressure is developed. Stability limits for the clamped shell are obtained for a range of the central height to thickness ratio from about 1 to 35. This serves to correct and extend previously known stability limits for this problem.

外圧に因る球形殻の挫屈

The buckling of spherical shells by the external pressure known as the so-called Durchschlag phenomenon was investigated in this paper. Especially the spherical shell segment is practically important as a pressure switch for automatic control besides as a part of structures. In the first chapter, some buckling processes were considered from the view point of static energy taking into account the energy barrier. In the second chapter, the depression of the buckling load observed in experiments was explained theoretically by introducing an initial deflection as a cause of jumping over the energy barrier.

On Vibrations of Shallow Spherical Shells

The problem of the axi-symmetrical vibrations of a shallow spherical shell is reduced to two simultaneous differential equations for the tangential and normal components of displacement. The solution of these equations is obtained in terms of Bessel functions. With this solution the third-order determinant for the frequencies of a shell segment with clamped edge is given but not evaluated. Instead, an approximate value for the lowest frequency is calculated by means of the Rayleigh-Ritz procedure [Eq. (40)]. It is found that very little curvature is needed to modify appreciably the corresponding flat-plate frequency. The approximations which are made are those customary for shallow shells: (1) omission of the transverse shear term in the tangential force equilibrium equation, and (2) relations between couples and changes of curvatures as in the theory of flat plates.