A rigid inclusion perfectly embedded in a thin plate is considered as a two-dimensional
elastostatic composite structure to solve the inverse problem of finding the
inclusion shape around which the local maximum of the von Mises equivalent
stresses attain the global minimum under shear loading at infinity. Absent
optimality preconditions such as the equistress principle for bulk-type loading, a
fast and accurate assessment of a given shape is developed by combining
complex-valued series expansions with a new infinite summation scheme.
This approach to solving the direct problem is then included into a genetic
algorithm optimization over the set of shapes obtained from a circle by a
finite-term conformal mapping with square symmetry. Compared to a circular
inclusion, the stresses may thus be lowered by 15–25%, depending on the
Poisson’s ratio of the plate. The numerical results presented allow us to
conjecture that the von Mises stresses around the optimal shape are
uniform. The
inclusion that minimizes the induced energy increment is also identified
by the same approach. Both shapes appear to be very similar, though not
identical.
