Keywords: barrelled shells, buckling analysis, shell of revolution, FEM, bending, horizontal tank, stability.

The present work is devoted to the elastic stability of shells of revolution in the pure bending state. Buckling shapes are presented and the dependency between the shape of a shell and its critical stress is described. The ABAQUS system based on the finite elements method was used to obtain the results.

Examples of works concerning stability of shells under bending can be easily found in the literature. However they are usually limited to cylindrical shells. Brush and Almroth [1] and Volmir [2] present analytical solutions of the problem and a state of the art in this field. In the paper presented here the authors extend the investigation to shells of revolution other than cylindrical ones including a cylinder as a reference point. A family of shells of revolution of the same volume and length is investigated including shells with positive (barrel) and negative Gaussian curvature. The model of a shell is simply supported at both ends. To introduce a pure bending conditions a non-uniform axial load is applied to the edge of the shell.

The results obtained from the analyses confirm the advantages of barrelled shells presented for example by Blachut [3]. A barrelled shell can bear about 75% higher load than a cylinder if pure bending conditions are assumed. The gain in buckling strength grows monotonically with decreasing the meridional radius of curvature R. The buckling shape is of the form of short wrinkles concentrated near the edge of the shell where the load is applied. Shells with negative Gaussian curvature buckle in a global way and the buckling load decreases with decreasing radius R. Since buckling of thin, middle-length bending shells is caused by compressive stresses the buckling analysis under axial compression was also carried out. The results are similar to those obtained for bending load. Critical stresses are slightly higher, up to 5.5%, for bending.

1

D.O. Brush, B.O. Almroth, "Buckling of Bars, Plates, and Shells", McGraw-Hill, New York, 1975.

2

A.S. Volmir, "Stability of deformation systems", Nauka, Moscow, 1967. (in Russian)

3

J. Blachut, P. Wang, "Buckling of barrelled shells subjected to external hydrostatic pressure", JPVT, Trans ASME, 123, 232-239, 2001. doi:10.1115/1.1357160

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