Optimal plastic design of axisymmetric solid plates with a maximum thickness constraint

Abstract A systematic method for deriving least-weight solutions for plastically designed, axially symmetric solid plates of prescribed maximum thickness is presented. It is shown that the solution in general consists of regions having (a) stiffeners of maximum depth but infinitesimal width running in one direction only, with a plate of vanishing thickness in between the stiffeners or (b) a “smooth” solid plate. It follows that the majority of existing papers on least-weight solid plates, based on smooth thickness variation throughout, have failed to locate the global optimum. The method is illustrated with examples of circular plates. The weight of the optimal solution is compared with that of intuitively selected designs.

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