Stress-related topology optimization based on Isogeometric Analysis and global stress measures

Abstract

This paper presents a robust isogeometric topology optimization (ITO) framework that integrates Isogeometric Analysis (IGA) with global stress measures to enhance both accuracy and stability in stress-related structural optimization. Non-Uniform Rational B-Splines (NURBS)-based IGA is employed to ensure higher-order continuity and refined topology representation, enabling precise stress evaluation. The p-norm stress aggregation approximates maximum stress, while incorporating average stress into ITO mitigates oscillations for large p-norm parameters and further reduces sensitivity to $P$. Notably, this approach eliminates stress concentrations even when $P=3$, and maintains stable convergence as $P$ increases up to 40 or more, thereby extending the feasible range of $P$-values. By examining various weight combinations of p-norm and average stress, we reveal how controlling both amplitude and mean stress leads to more uniform and lower stress levels. Additionally, an adaptive continuous scheme for stress constraints further improves convergence stability by gradually tightening stress limits from a relaxed state to the target value. Numerical results confirm that the proposed method consistently delivers accurate, stable, and efficient solutions for stress-related isogeometric topology optimization, marking a significant advancement in the field.