Stress-smoothing holes in an elastic plate: The triangular checkerboard lattice of low symmetry

Abstract

The shape optimization problem for a linearly elastic perforated plate with the triangular checkerboard of identical holes is considered with respect to the recently advanced criterion of minimizing the hoop stress variation. The paper continues the author’s previous research on optimizing the square-symmetric checkerboard and extends the results obtained to the non-symmetric lattice of the holes which are varied not only in their shapes, but also in their location. This novelty is resolved by enhancing the same three-component algorithm as before. It combines a genetic algorithm (GA) optimization with an efficient direct solver and with an economic shape parametrization, both formulated in the complex variable terms. The averaging nature of the stress variation criterion permits its effective numerical implementation for a wide range of the holes volume fraction at reasonable computational efforts. For an engineering audience, the elastic behaviour of the optimal structures is detailed in a graphics set.