An elastic plate with two closely spaced identical holes of fixed area is taken
as a two-dimensional sample geometry to find the interface shape which
minimizes the energy increment in a homogeneous shear stress field given
at infinity. This is a transient model between a single energy-minimizing
hole and a regularly perforated plate, both numerically solved by a genetic
optimization algorithm together with a fast and accurate fitness evaluation
scheme using the complex-valued elastic potentials which are specifically
arranged to incorporate a traction-free hole boundary. Here the scheme is
further enhanced by a novel shape-encoding procedure through a conformal
mapping of a
single hole rather than
both holes simultaneously as is done
in standard practice. The optimized shapes appear to be slightly rounded
elongated quadrangles aligned with the principal load axes. Compared to
the single (square-like) optimal hole, they induce up to 12% less energy
depending on the hole spacing. Qualitatively, it is also shown that the local
stresses, computed along the optimal shapes as a less accurate by-product of
the optimization, exhibit a tendency to be
piecewise constant with no local
concentration.
