Topology-aware stress analysis in shell structures

Abstract

We present a stable and accurate algorithm for tracing principal stress lines (PSLs) in shell structures, applicable to both first- and second-order triangular and quadrilateral elements. The algorithm operates directly in the isoparametric space of the elements, leveraging their inherent shape functions to account for curved geometry without resorting to artificial subdivision. This approach enables, for the first time, a consistent stress topology analysis for shell elements, including a rigorous treatment of stress degeneracies. Our PSL seeding strategy integrates stress topology with the curved shell surface, ensuring a uniform and consistent PSL distribution. We evaluate the algorithm's performance through a series of numerical experiments, demonstrating its utility for advanced stress analysis. Furthermore, we demonstrate the generation of a globally consistent, space-filling PSL structure, which is directly applicable to downstream tasks such as lightweight structural design. To support practical use, we provide a publicly available MATLAB implementation. The implementation features a unified file interface that supports diverse mesh types and is compatible with standard finite element method (FEM) output, offering a versatile tool for stress investigation and design evaluation in computational mechanics. The code is available at https://github.com/PSLer/PSLshell.