A single hole in an infinite elastic plate is used as the simplest setup to find the hole
shape which induces the maximum energy increment in a homogeneous stress field
given at infinity. In order to avoid the energy unboundedness trivially caused by
jagged shapes with an arbitrarily large number of sharp notches, we restrict our
attention to only fully concave shapes with everywhere negative curvature. It goes in
parallel with the well-known fact that the energy-minimizing hole shapes are
invariably convex. Though rather empirical, this easily verified condition allows us
to obtain finite and stable energy maxima at moderate computation cost
using the same flexible scheme as in the first author’s previous research on
optimal shaping of the single energy-minimizing hole. The scheme combines
a standard genetic algorithm optimization with an efficient semianalytic
direct solver and with an economic shape parametrization, both formulated
in complex-variable terms. The results obtained are detailed in tables and
graphs. They may stimulate further studies in both theoretical and practical
directions.
