Keywords: buckling, external pressure, carbon-fibre reinforced polymer, imperfections, repair, pressure vessels.

The paper examines the load carrying capacity of externally pressurised and geometrically imperfect steel hemispherical shell. First, the concept of a 'lower bound' response curve is introduced. Its practical significance, backed by experiments, is outlined. Relevance of this approach is contrasted with the recently postulated drive to substitute imperfection sensitive components by imperfection insensitive variants obtained as a result of structural optimization [1].

In practice, once an imperfect area is identified, the following two options are favoured: (i) lower the external pressure to a safe level, or (ii) cut out the imperfect or damaged area and replace it with a perfect segment. The second option is particularly inconvenient as it requires emptying the vessel and if the vessel contains chemicals, the flame cutting can be dangerous.

The paper explores the possibility of restoring the buckling strength of a locally imperfect hemisphere through the use of fibre reinforced plastics. It is proposed to apply an external patch of composite material to the imperfect area in order to increase the buckling strength, and ideally to bring it to the undamaged level. Initially parameters of the most dangerous imperfection, having the shape of local flattening, are calculated. They are then used as the basis for restoration of the original buckling strength. It is assumed that an axisymmetric flattening in a steel hemisphere is positioned at the apex, and that the profile of the patch is uniquely described by the amplitude of flattening and radius of curvature of the imperfect patch. Next, the whole area of the imperfect patch is covered, on the outer (external) surface of the steel shell, by a multi-ply composite material. Covering the composite layer extends into the perfect area by a small, overlapping meridional distance. The length of the overlapping contributes to the restoration of the buckling strength. Numerical results are provided for a clamped steel hemisphere typically found in petrochemical industries. The composite patch is taken in the form of six plies with the quasi-isotropic stacking sequence. The elastic constants of the patch correspond to a woven carbon fibre cloth.

The thicknesses of the composite layer which, for given amplitude of flattening and the most unfavourable radius of curvature, restore the buckling strength are given in the paper. Three different values of overlapping length were considered in detailed calculations. Response curves have been obtained for the amplitude of the imperfection varying between 0 and the wall thickness of the master shell. Details about modelling and computing, together with discussion of results are provided in the paper. This is an entirely numerical study and the background information can be found in [2,3].

1

H.A. Mang, G. Höfinger, X. Jia, "Sensitivity Analysis of the Postbuckling Behavior of Elastic Structures", Computational Technology Reviews, 2, 1-22, 2010. doi:10.4203/ctr.2.1

2

J. Blachut, K. Magnucki, "Strength, stability and optimisation of pressure vessels - review of selected problems", Applied Mechanics Reviews, Transactions of the ASME, 61(6), 060801-1 - 0608-1-33, 2008.

3

J. Blachut, O.R. Jaiwal, "On the choice of initial geometric imperfections in externally pressurized shells", J. Pressure Vessel Technology, Transactions of the ASME, 121, 71-76, 1999. doi:10.1115/1.2883670

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