The paper is devoted to a non-typical shape of a shell of revolution with positive Gaussian curvature. The meridian of the shell is a plane curve composed of a clothoid and a circular arc. Geometrical properties of the middle surface of the shell of revolution are presented. Pre-buckling state of the shell under uniform pressure is described analytically. The critical pressure and buckling modes for the shell are calculated with the use of the FEM (the ANSYS system). Post-buckling behaviour of the shells is shown. Results of analytical and numerical investigations are presented in tables and figures.

Elastic buckling of clothoidal–spherical shells under external pressure – theoretical study

The subject of the present paper is a family of egg-shaped shells. The meridian of these shells resembles that of a goose egg. The capacity and mass of the shell were maintained constant. The ratio of the minor B to the major L axis of the shell was determined according to the experimental results of the analysis of 333 goose eggs. Fourteen B/L ratios were determined as follows: 0.4, 0.5, 0.6, 0.65, 0.66, 0.67, 0.68, 0.69, 0.70, 0.71, 0.72, 0.8, 0.9 and 1.0. The effect of the ratio on the buckling behavior of the egg-shaped shell was numerically and analytically analyzed.

Buckling of egg-shaped shells subjected to external pressure

The paper is devoted to shells of revolution with positive and negative Gaussian curvature. The meridian of shells is a plane curve in the Cassini oval form. Geometrical properties of the middle surface of the shell of revolution based on this curve are presented. The membrane state of stress of a family of shells with constant capacity and mass under uniform pressure is described analytically and numerically with the use of the FEM (the ANSYS system). The critical pressure, buckling modes and equilibrium paths of analysed shells are calculated numerically. The advantages of a pressure vessel made in the form of Cassini ovaloidal shell, such as the lack of edge effect and a stable post-buckling behaviour, are pointed out. The results of the analytical and numerical investigations are compared and presented in tables and figures.

http://am.ippt.pan.pl/am/article/viewFile/v67p179/pdf

Elastic buckling of Cassini ovaloidal shells under external pressure - theoretical study

Materials with negative Poisson's ratio (auxetic) exhibit an unusual property of expanding when stretched in the direction normal to an applied uniaxial tension and vice versa when compressed, a phenomenon which is known to result in many beneficial effects in the performance of materials in various practical situations. In particular, it has long been suggested that spherical shells made from isotropic materials having Poisson's ratio less than -0.5 exhibit enhanced resistance to buckling as a result of externally applied normal pressure. This work uses finite elements (FEs) modelling to assess the behaviour of various spherical, torispherical and ellipsoidal shells when they are subjected to external (in all cases) or internal (in the case of torispherical and ellipsoidal shells) pressures. We find that to a first approximation, the critical buckling pressures scale linearly with (1 - ν 2 ) -112 thus suggesting that the critical buckling pressures tends to infinity as ν tends to -1, this being in accordance to what was known for spherical shells. We also find that the Poisson's ratio has an effect on the amplitude and the number of buckling wavelengths that occur when the shells buckle.

On the effect of the Poisson's ratio (positive and negative) on the stability of pressure vessel heads

This study investigated the free hydroforming of a stainless-steel egg-shaped shell. An egg-shaped shell is a promising geometry for deep pressure hulls. The length and width of the egg-shaped shel...

Theoretical and experimental study of the free hydroforming of egg-shaped shell

This article is concerned with the elastic buckling of super ellipsoidal shells under external uniform pressure. The middle surface of a super ellipsoidal shell is defined by the following equation: (x/a)2n +(y/b)2n + (z/c)2n  = 1 where n is an integer varying from unity to infinity. It is clear from the equation that the range of shell shapes covered sphere (n = 1, a = b = c) to cube (n = ∞, a = b = c) and ellipsoid (n = 1) to cuboid (n = ∞). By adopting a recently proposed solid shell element for the buckling analysis, the critical buckling pressures of thin to thick super ellipsoidal shells are obtained and tabulated for engineers. The shell element allows for the effect of transverse shear deformation, which becomes significant in thick shells. Their buckling shapes are also examined. In addition, a simple approximate formula for predicting the critical buckling pressure of thick spherical shells is proposed.

Y.Q. Ma

Papers

Buckling of super ellipsoidal shells under uniform pressure