Geometrical optimization of an opening near a fixed hole in an elastic plate

Abstract

Perforated plates under external loads produce stress concentration around the holes which endangers the operation of structures. Various measures are used to enhance the holes, wherein hole shape optimization is a more economical method that remarkably adjusts the stress state. The optimization of an opening near a fixed circular hole, which minimizes the stress concentration along its boundary, in an elastic plate subjected to uniform infinite stresses and boundary traction is discussed in this paper. The direct solver of stress is based on the complex potential theory and the differential evolution algorithm is applied to acquire the optimal hole shapes in which the hole shape is parameterized by a proper mapping function. Optimal hole shapes and the stress distributions on the optimal boundaries for different distances, surface traction, horizontal stress, and area ratio are presented.