Stress-smoothing holes in an elastic plate: From the square lattice to the checkerboard

Minimization of the hoop stresses variation was recently advanced to form a novel and efficient criterion of the stress state optimization in a statically loaded elastic domain with a finite number of free-form holes. As a radical generalization of the well-known equi-stress principle, it offers substantial analytical and numerical advantages over direct minimization of the local stress concentration factor. Here we extend the proposed criterion beyond its primary application to the shape optimization in a regular perforated structure with the checkerboard arrangement of identical traction-free holes. The averaging nature of the stresses variation allows its effective numerical implementation in a wide range of the governing parameters at a modest computational cost. The results obtained describe in depth the elastic response of the optimal structure to applied loads.