Simply and doubly periodic arrangements of the equi-stress holes in a perforated elastic plane: The single-layer potential approach

The layer potentials of two-dimensional linear elastostatics are applied as a novel building block for the semi-analytical design of non-standard arrangements of the equi-stress holes in an infinite plate under a given bulk-type loading. Thematically, this paper begins where our previous work left off with the main attention being focused on periodic structures of low rotational symmetry which are hard to tackle by the more customary conformal mapping technique. The analytical derivations are backed up by numerical simulations, in which a genetic algorithm is utilized to identify the optimal interface shapes for different geometries and a wide range of the governing parameters.