EAAI Journal 2026 Journal Article
A solid-spherical neural operator for residual stress inversion of components with varying geometries
- Zhiwei Zhao
- Changqing Liu
- Yi Yang
- Yingguang Li
Residual stress plays a critical role in manufacturing precision and fatigue life, particularly for aerospace structural components. However, reconstructing three-dimensional field functions over varying geometries remains a long-standing challenge in material and manufacturing. Traditional numerical methods suffer from costly re-meshing and re-computation when geometries or boundary conditions change, which significantly undermines their computational efficiency. To address this problem, a solid-spherical neural operator (SSNO) framework for residual stress inversion in solids is proposed, which enables efficient inversion across varying geometries through a unified solid-spherical representation. The method first maps varying geometries onto a unit solid sphere through a diffeomorphic mapping, then learns the operator in the solid sphere domain and projects the residual stress field results back to the original physical geometry to reconstruct full three-dimensional residual stress fields from geometry-indexed observable data. Numerical experiments on structural components with varying geometries and different stress distributions demonstrate that SSNO achieves rapid and accurate full three-dimensional residual stress inversion for different parts, outperforming conventional methods in terms of generalization, robustness, and computational efficiency across varying geometries. The experimental results indicate that the SSNO model achieves a root mean square error of 0. 119 megapascals (MPa), with an inference time of 1. 29 seconds, representing a four order of magnitude improvement in computational efficiency compared with the iterative optimization method.