Shape Optimisation of Holes in Loaded Plates by Minimisation of Multiple Stress Peaks

Abstract : A new method has been developed for simultaneously minimising the peak tangential stresses on multiple segments around the boundary of a hole in a uniaxially-loaded or biaxially-loaded plate. It is based upon iterative finite element analysis. The efficacy of this new multi-peak method is demonstrated by 2D and 3D numerical examples, some of which include significant geometric constraints. A comprehensive series of benchmarks is explored in some detail and sets of useful transferable coordinates of optimised hole shapes for selected load and geometry cases are provided. It is shown that, when the optimal shape is achieved, the separate tensile and compressive stress segments around the hole boundary converge to constant stress regions of different values. The optimal hole shapes produce significant reductions in peak stress for all regions around the hole boundary, as compared to typical non-optimal circular holes. As the most fatigue critical location in a structure may not necessarily be the one with the biggest active tensile peak, it is desirable to be able to minimise these other stress peaks around the hole boundary. Hence, optimal shapes computed using the multi-peak method are useful for critical structural regions where it is desirable to substantially increase or maximise the fatigue life.