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Peer-reviewedCC BY 4.0Journal of Fractal Geometry

Membrane Deformation – Finite Elements – Parametric Shape Optimization on the Koch Snowflake

  • Nizar Riane
  • Claire David
  • François Vigneron
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Abstract

We introduce the finite element method to analyze a membrane with a Koch snowflake-shaped boundary. The fractal nature of this domain presents unique challenges due to its intricate boundary structure. Our approach involves discretizing the domain, estimating the error, and proving convergence. With these aspects addressed, we solve a shape optimization problem to determine the optimal thickness of the membrane. These findings provide valuable insights into how fractal boundaries affect structural performance and optimization.

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Cite

BibTeXRIS
BibTeX
@article{riane2026membrane,
  title = {{Membrane Deformation – Finite Elements – Parametric Shape Optimization on the Koch Snowflake}},
  author = {Nizar Riane and Claire David and François Vigneron},
  journal = {Journal of Fractal Geometry},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-04960644v6},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Membrane Deformation – Finite Elements – Parametric Shape Optimization on the Koch Snowflake
AU  - Nizar Riane
AU  - Claire David
AU  - François Vigneron
PY  - 2026
DA  - 2026/09/27
JO  - Journal of Fractal Geometry
UR  - https://hal.science/hal-04960644v6
AB  - We introduce the finite element method to analyze a membrane with a Koch snowflake-shaped boundary. The fractal nature of this domain presents unique challenges due to its intricate boundary structure. Our approach involves discretizing the domain, estimating the error, and proving convergence. With these aspects addressed, we solve a shape optimization problem to determine the optimal thickness of the membrane. These findings provide valuable insights into how fractal boundaries affect structural performance and optimization.
SN  - 2308-1317
ER  -