Keywords: buckling, shells, welding, initial geometric imperfections, finite element method, analysis of variance.

Thin shells are such common structural elements: silos, boilers, containers, tanks, etc. No manufacturing process exists that can be used to produce these structures without suffering from various kinds of initial geometric imperfections. Control of the manufacturing processes of shells and their optimisation makes it possible to decrease the degree of these imperfections, but they can never be completely removed. Large thin shells are often constructed from plates which are rolled to obtain the correct curvature and subsequently welded together to form strakes. The strakes are then welded to build the complete shell structure. At the circumferential welds localised geometric imperfections develop. The welding profile can vary from one shell to another but a common feature of welds is that their geometry can be characterised by a small number of parameters that consist essentially of the amplitude and wavelength of the weld prints. Measurements have revealed that mostly axisymmetric imperfections occur in shell structures assembled by welding. For axially compressed circular cylindrical shells made from isotropic and homogeneous elastic material, axisymmetric localized geometric imperfections such as those resulting from the welding of strakes were found to constitute the most adverse issues. Various axisymmetric familiar shapes of single localised defects were investigated. Since multiple localized defects can arise in the same shell structure and interact mutually, studying their global effect on the buckling strength is required to assess a safer shell design. In this paper two interacting localised imperfections were considered. They were both assumed to have an entering triangular shape. This simple geometric imperfection (a peak of the geometric imperfection directed inwards the shell) was recognised to constitute the most unfavourable case with regard to shell buckling strength.

An investigation of the relative effect on buckling arising from each factor describing the imperfect shell having two triangular defects were performed following two stages. At first, a single triangular geometric imperfection is considered when two similar defects of this form were present on the shell structure. In this last case, the distance separating the defects is an additional parameter. To the previous three parameters one should add the shell aspect ratios: radius over thickness and length over thickness. The relative influence of all the intervening factors was quantified in order to estimate the most adverse shell configuration: that one yielding the least shell buckling resistance. Modelling was performed by means of the finite element method. A special software package dedicated to buckling analysis of quasi axisymmetric shells was used. It enabled computing the buckling load either using the linear Euler buckling analysis or through a full non linear iterative procedure. It was shown by comparison with the single imperfection case that further diminution of the critical stress would be obtained if two defects were present on the shell structure. In the investigated range of parameters, the shell buckling load was found to be more sensitive to the distance separating defects while imperfection amplitude and wavelength were identified to have limited effect.

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