Research project undertaken at The University of Edinburgh as part of Dr Sadowski's PhD thesis during 2007 - 2010.

Background

The most serious loading condition for slender thin-walled metal silos has long been recognised to be the condition of discharge, with eccentric discharge probably causing more catastrophic failures than any other (Fig. 1). Two key reasons for this high failure rate are the great difficulties in characterising the pressure distribution caused by eccentric solids flow, and in understanding the associated unsymmetrical stresses in the silo wall. Few previous studies have addressed either the linear elastic behaviour of such a silo or its buckling failure under eccentric discharge. The nonsymmetric behaviour of shell structures generally under unsymmetrical pressures is not at all well described in the voluminous shell structures literature.

This research project was the first to employ the new characterisation of eccentric discharge of the EN 1991-4 European Standard on silos and tanks to perform an in-depth numerical investigation into the structural behaviour of silos under eccentric discharge, with a focus on nonlinear buckling in particular. The critical effects of geometric nonlinearity, imperfection sensitivity, material nonlinearity, changes of silo aspect ratio and variations of flow channel geometries were all investigated in depth using computational finite element analyses. A deeper understanding of the mechanics of the behaviour of cylindrical shells under unsymmetrical loads has been achieved.

Methodology

The first part of the project consisted of an exhaustive numerical investigation of the effects of the EN 1991-4 eccentric discharge pressure pattern (Fig. 2) on seven different example silos custom-designed according to the EN 1993-1-6 European Standard on the buckling of metal shells. The silos varied according to aspect ratio, wall thickness distributions and assumed nature of the stored granular solid. The variation of the aspect ratio in particular allowed an in-depth comparison of the structural consequences of the assumed pressure pattern, strictly valid for slender silos only, on significantly different geometries.

Fig 1: Illustration of concentric and eccentric discharge patterns in cylindrical silos
Fig 1: Illustration of concentric and eccentric discharge patterns in cylindrical silos
Fig 2: The EN 1991-4 eccentric discharge pressure pattern
Fig 2: The EN 1991-4 eccentric discharge pressure pattern

Amongst other outcomes, it was found that elastic local buckling is critical under eccentric discharge (Fig. 3). Further, cylindrical shells under local axial compression are not nearly as imperfection sensitive as those under uniform compression. Many 'classical' imperfection forms that are very damaging under uniform stress states actually turned out to be greatly beneficial to the buckling strength under eccentric discharge.

Fig. 3 - Illustration of critical buckling locations under eccentric discharge
Fig. 3 - Illustration of critical buckling locations under eccentric discharge

Fig. 4 - Idealised flow channel profiles
Fig. 4 - Idealised flow channel profiles

The second part of the project involved the formulation of a very general theory for the prediction of pressures in silos due to granular solids flows. Known as the 'mixed flow pressure theory', it permitted a wide range of different flow patterns and geometries to be analysed (Fig. 4), and not just the relatively simple one assumed in the EN 1991-4 model (Figs 1 & 2). An extensive computational study was carried out to assess the structural consequences of the different flow regimes.

References

A number of journal papers are still in preparation, and the following have already been published: