Robust topology optimization with non-Gaussian material fields using polygonal finite elements
Abstract
We present a computational framework for robust topology optimization that integrates polygonal finite-element discretizations, spatially correlated non-Gaussian material modeling, and non-intrusive polynomial-chaos surrogates. Spatial uncertainty in Young's modulus is represented as a homogeneous non-Gaussian random field obtained via a memoryless transformation of a truncated Karhunen-Loève expansion, ensuring physical admissibility through positivity of stiffness while preserving the prescribed autocovariance. Polygonal finite elements provide a stable discretization for density-based optimization on unstructured meshes and mitigate checkerboard artefacts and mesh bias, while the sparse polynomial-chaos expansion enables efficient estimation of low-order statistical moments required by the robust objective at a fraction of the cost of intrusive or Monte Carlo approaches. Numerical studies on a cantilever and a curved beam show that introducing non-Gaussian material variability leads to systematic load-path redistribution and a reallocation of 6-12% of the structural volume, together with a reduction in compliance scatter. The non-intrusive surrogate reproduces intrusive reference results within 3% using an order of magnitude fewer full finite-element analyses. These results demonstrate that the proposed framework offers a physically consistent and computationally efficient route to topology-optimized designs that remain reliable under realistic material uncertainty.
Versions
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BibTeX
@misc{cuellar2026robust,
title = {{Robust topology optimization with non-Gaussian material fields using polygonal finite elements}},
author = {Nilton Cuellar and Anderson Pereira and Ivan F. M. Menezes and Americo Cunha Jr},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05466},
eprint = {2609.05466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05466},
}
RIS
TY - UNPB
TI - Robust topology optimization with non-Gaussian material fields using polygonal finite elements
AU - Nilton Cuellar
AU - Anderson Pereira
AU - Ivan F. M. Menezes
AU - Americo Cunha Jr
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.05466
UR - https://arxiv.org/abs/2609.05466
AB - We present a computational framework for robust topology optimization that integrates polygonal finite-element discretizations, spatially correlated non-Gaussian material modeling, and non-intrusive polynomial-chaos surrogates. Spatial uncertainty in Young's modulus is represented as a homogeneous non-Gaussian random field obtained via a memoryless transformation of a truncated Karhunen-Loève expansion, ensuring physical admissibility through positivity of stiffness while preserving the prescribed autocovariance. Polygonal finite elements provide a stable discretization for density-based optimization on unstructured meshes and mitigate checkerboard artefacts and mesh bias, while the sparse polynomial-chaos expansion enables efficient estimation of low-order statistical moments required by the robust objective at a fraction of the cost of intrusive or Monte Carlo approaches. Numerical studies on a cantilever and a curved beam show that introducing non-Gaussian material variability leads to systematic load-path redistribution and a reallocation of 6-12% of the structural volume, together with a reduction in compliance scatter. The non-intrusive surrogate reproduces intrusive reference results within 3% using an order of magnitude fewer full finite-element analyses. These results demonstrate that the proposed framework offers a physically consistent and computationally efficient route to topology-optimized designs that remain reliable under realistic material uncertainty.
ER -