Shape optimization of the fillet under a bolt’s head

The stress concentration in the fillet under a bolt’s head is a critical issue for the fatigue life of this component. Remembering the variable notch radius solution observed in many biological structures to lower stress concentrations due to normal loads, this work proposes, examines and optimizes a double circular arc fillet, not re-entering the head. The work implements an ad hoc shape optimization procedure that combines a genetic algorithm (the particle swarm optimization) and a parametric, axisymmetric finite-element model of the bolt: by focusing on an M12 bolt, the analysis focuses on two issues: first, the optimization of the radius of each arc in the fillet; second, the optimization of the bolt’s head height and head’s diameter in combination with the fillet radiuses. By comparing the proposed solution with the fillet geometries for the bolt’s heads from the literature, it appears a noticeable stress reduction, about 14% lower than the standard circular fillet, combined with an easy manufacturing.