I'm interested in buckling, having recently renewed my contact with Dr Frank Mirtsch of Berlin. For some years he has been stiffening thin shells by controlled in-plane buckling, producing very nice hexagonal buckles if he confines or supports the shell so that it won't collapse due to local failure. Biruta Kresling also worked with buckling in tubes and other shapes, such as cones. The technique that Frank has developed requires that the shell have some curvature (he started with tubes) and has produced stiffened structures of architectural dimensions. Part of his inspiration is the work of Paul Green who has shown that local buckling can be a significant factor in the initiation of morphology of plants at the meristem and elsewhere. Indeed the buckling one sees in bits of plants inside buds is really quite remarkable in its regularity - think of a poppy petal which shows a beautiful Miura folding. Hands-off origami! All folding in nature HAS to be auto-generated (tell me otherwise!). So buckling can generate morphology or be the initial phase of development followed by deployment.
This got me thinking, since many plant structures are stiffened by buckling. Think of leaves such as maize or Pittosporum where the buckling of the edge of the leaf essentially applies a prestrain to the leaf (edge in compression/bending, centre in tension). How would you get a metal plate to buckle like that? So I started to look through the literature, and all the examples I could find were of rectangular plates under some sort of uniform strain. What happens if a plate of irregular shape (e.g. a trapezoid) is uniaxially compressed in-plane in the direction where one side is longer than the other so that its final projected outline is rectangular? The longer side will end up buckled. Or you could have a plate with 'ears' at the end so that both edges buckle like a leaf? Would this be a cheaper way of stiffening a plate than (for instance) turning over the edge?
Answers, please, on a buckled postcard . . .
Julian Vincent
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