The stress-minimizing hole in a shear-loaded elastic plate at a given energy increment

Minimization of the peak tangential stresses around a single hole in an infinite 2D elastic plate under remote pure shear and a given hole-induced strain energy level is considered as a free-shape optimization problem under a physical constraint. It is solved by combining a genetic algorithm with the almost analytical, and hence highly accurate stress-strain solver for any finitely parameterized family of closed curves. The results obtained in wide ranges of the governing parameters are detailed and discussed. They may be applicable to the optimal holes design in constructive elements and dilute perforated structures. The current analysis extends the author’s previous publications, which were focused on the unconstrained shape optimization within the same setup.