A thin elastic plate with a square lattice of traction-free holes is considered
as a setup for the optimization problem of finding the hole shapes which
minimize the (nonnegative) variation of the hoop stresses (MSV) induced
by unit bulk load at given perforation rate and effective bulk modulus
of the
structure. In this context, there is the well-known correspondence between the
local and the averaged stress-strain field. The starting point of this study is
the analytically proven existence of the specially shaped (equistress) holes
which together provide the global maximum of the structure’s bulk modulus
and a zero-variation (constant) stress distribution around the hole’s face.
Here, using an effective optimization scheme we numerically analyze the
-to-MSV relation
for nonoptimal
and hence nonzero MSV across certain representative intervals of their values
depending on the structure’s porosity. This is performed by explicitly finding the
optimal hole shapes and the attendant stress distributions. The results obtained are
detailed in tables and graphs.
