The actual elastostatic problem of optimizing the stress state in a two-dimensional
perforated domain by proper shaping of holes is considered with respect to
minimization of the global variations of the boundary hoop stresses. This new
criterion radically extends the rather restrictive equistress principle introduced by
Cherepanov and results in a favorable response of the structure to an external load,
with neither local stress concentrations nor underloading of other parts of the
boundary. Mathematically, the variations provide an integral-type assessment
of the local stresses which requires less computational effort than direct
minimization of the stress concentration factor. The proposed criterion can
thus be easily incorporated in the numerical optimization scheme previously
developed by the author in the closely related context of energy optimization. It
includes an efficient complex-valued direct solver and a standard evolutionary
optimization algorithm enhanced with an economical shape parametrization tool.
The effectiveness of the proposed scheme is illustrated through numerical
simulations.
