The plastic bending of clamped polygonal plates with an application to radial buckling in milk bottle tops

Solutions for the plastic bending of clamped polygonal plates are investigated. For an isosceles triangular plate, and for a truncated isosceles triangular plate, minima exist for plastic work of formation with respect to angles of the triangle, and location of the apex of the deformed pyramid shape. A characteristic number of radial buckles is formed when the foil circular top of British one-pint milk bottles is pushed in and material drawn over the rim of the bottle on opening. The plastic bending analysis provides an approximate means of predicting the number of buckles.