Optimal hole shape for minimum stress concentration using parameterized geometry models

Abstract

The goal of this work is to obtain optimal hole shape for minimum stress concentration in two-dimensional finite plates using parameterized geometry models. The boundary shape for a hole is described by two families of smooth curves: one is a “generalized circular” function \(((x/R )^{\eta_1}+(y/R)^{\eta_2 }=1)\) with powers as two parameters; the other one is a “generalized elliptic” function \(((x/a)^{\eta_1 }+(y/b)^{\eta_2 },\)a and b are ellipse axes) with powers as two parameters and one of the ellipse axes as the third parameter. Special attention is devoted to the practicability of parameterized equations and the corresponding optimal results under the condition with and without the curvature radius constraint. A number of cases were examined to test the effectiveness of the parameterized equations. The numerical examples show that extremely good results can be obtained under the conditions with and without curvature radius constraint, as compared to the known solutions in the literature. The geometries of the optimized holes are presented in a form of compact parametric functions, which are suitable for use and test by designers. It is anticipated that the implementation of the suggested parameterized equations would lead to considerable improvements in optimizing hole shape with high quality.