Stankiewicz G, Dev C, Steinmann P (2026)
Publication Type: Journal article
Publication year: 2026
Book Volume: 262
Article Number: 104657
DOI: 10.1016/j.finel.2026.104657
Variable thickness topology optimization (VTTO) provides a highly effective approach to generating sheet-like structures with superior structural performance. However, integrating stress constraints into VTTO introduces severe numerical challenges, particularly the “singularity trap”, which is further amplified by the presence of low thickness regions and blurred structural boundaries. In this work, we present a comprehensive framework to incorporate a stress constraint directly into the variable thickness topology optimization problem. To mitigate the numerical instabilities, we first employ a compound regularization strategy consisting of a SIMP-based penalization and a density-gradient-informed (DGI) projection to effectively eliminate low thickness densities and sharpen the structural edges. We then introduce a smooth hybrid ϵ-relaxation formulation that guarantees physical consistency in the feasible thickness regime while preventing singular stress calculations near zero density. Furthermore, we apply an automated exponential continuation scheme for the stress relaxation parameter to stabilize the design evolution. The calculation of elemental stresses is enhanced utilizing a solid-domain Helmholtz-type PDE filter to suppress jagged boundary artifacts. The proposed methodology is validated on standard L-beam and cracked domain benchmarks under varying stress limits and target relaxation parameters. Our numerical tests confirm that the algorithm robustly identifies optimal sheet-like topologies, effectively alleviating stress concentrations with acceptable constraint violations.
APA:
Stankiewicz, G., Dev, C., & Steinmann, P. (2026). Stress-constrained variable thickness topology optimization for improved fracture resistance of sheet structures. Finite Elements in Analysis and Design, 262. https://doi.org/10.1016/j.finel.2026.104657
MLA:
Stankiewicz, Gabriel, Chaitanya Dev, and Paul Steinmann. "Stress-constrained variable thickness topology optimization for improved fracture resistance of sheet structures." Finite Elements in Analysis and Design 262 (2026).
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