Optimal notch shapes for loaded plates

Abstract

This paper presents design data defining optimal freeform notch shapes for use in tensile loading conditions for a range of geometries, notably the notch aspect ratio and plate widths. Here, an iterative two-dimensional finite element gradientless shape optimization procedure was used to obtain the optimal shapes, which offer the lowest possible stress concentration, subject to the geometric constraints. Precise non-dimensional coordinates are given, for a range of notch aspect ratios and plate widths, and are presented in a tabular form that allows them to be easily used by designers. All cases have been solved with a minimum radius of curvature constraint, which results in a ‘robust’ optimal shape that has no sharp corners. The optimal shapes were found to provide up to a 26 per cent reduction in local peak stress over circular shapes of the same aspect ratio. Optimal geometries are also given for limiting notches that provide a net section stress equal to unity, at a finite notch aspect ratio. The results obtained are applicable to both the initial design of notched components and the shape reworking of existing components to remove damage.