Optimal free-form shapes for shoulder fillets in flat plates under tension and bending

In engineering practice, section transitioning fillets in plates have typically consisted of circular profiles. However, these profiles are not optimal and can result in significant stress concentrations. Also, there is a paucity of transferable data available in the literature relating to optimal fillets, which could offer an alternative option. This paper presents useful design data defining optimal free-form fillet shapes for use under tension and bending loading conditions for a key range of fillet geometries, notably the relative fillet length. These results have been obtained to a high fidelity using an iterative 2D finite element gradientless shape optimisation procedure. The true optimal shapes that are given here offer the lowest possible stress concentration, subject to the bounding geometric constraints, and are presented in a tabular form that allows them to be easily used by designers.