Robust topology optimization of isogeometric Kirchhoff--Love shells by the Speed Method
Abstract
This paper presents a framework for robust topology optimization of Kirchhoff-Love (KL) multi-patch shells using isogeometric analysis and non-matching meshes and provides a CAD-compatible method. The material distribution is optimized via a NURBS-based level set method, enabling accurate boundary representation and seamless export to standard CAD/CAM workflows. The shape derivative is computed using the speed method, yielding a volume-based formulation that avoids boundary approximations and aligns with the isogeometric principle of coarse, high-order discretizations. This eliminates the need for local refinement, adaptive quadrature, or trimming as the descent direction for the compliance and volume objectives are obtained through a biharmonic equation. The framework is extended to robust optimization under uncertainty, accounting for stochastic loading and material properties via Monte Carlo sampling and Gaussian Random Fields. Numerical examples demonstrate the method's efficiency and robustness across single- and multi-patch shells, reproducing literature results with fewer elements than traditional FEM or refined IGA approaches. The developed methods and tools can be directly extended to problems involving stress-based optimization and risk-averse metrics. The numerical implementations are open-source and available on GitHub.
Related
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BibTeX
@misc{eisenhardt2026robust,
title = {{Robust topology optimization of isogeometric Kirchhoff--Love shells by the Speed Method}},
author = {Philipp Eisenhardt and Fernando Hübner Scherer and Barbara Wohlmuth and Andrei Constantinescu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30389},
eprint = {2610.30389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30389},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Robust topology optimization of isogeometric Kirchhoff--Love shells by the Speed Method
AU - Philipp Eisenhardt
AU - Fernando Hübner Scherer
AU - Barbara Wohlmuth
AU - Andrei Constantinescu
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30389
UR - https://arxiv.org/abs/2610.30389
AB - This paper presents a framework for robust topology optimization of Kirchhoff-Love (KL) multi-patch shells using isogeometric analysis and non-matching meshes and provides a CAD-compatible method. The material distribution is optimized via a NURBS-based level set method, enabling accurate boundary representation and seamless export to standard CAD/CAM workflows. The shape derivative is computed using the speed method, yielding a volume-based formulation that avoids boundary approximations and aligns with the isogeometric principle of coarse, high-order discretizations. This eliminates the need for local refinement, adaptive quadrature, or trimming as the descent direction for the compliance and volume objectives are obtained through a biharmonic equation. The framework is extended to robust optimization under uncertainty, accounting for stochastic loading and material properties via Monte Carlo sampling and Gaussian Random Fields. Numerical examples demonstrate the method's efficiency and robustness across single- and multi-patch shells, reproducing literature results with fewer elements than traditional FEM or refined IGA approaches. The developed methods and tools can be directly extended to problems involving stress-based optimization and risk-averse metrics. The numerical implementations are open-source and available on GitHub.
ER -