Keywords:
Forschungsbericht
Description / Table of Contents:
A fuzzy arithmetic framework for the efficient possibilistic propagation of shape uncertainties based on a novel fuzzy edge detection method is introduced. The shape uncertainties stem from a blurred image that encodes the distribution of two phases in a composite material. The proposed framework employs computational homogenisation to upscale the shape uncertainty to a fuzzy effective material. For this, many samples of a linear elasticity problem have to be computed, which is significantly sped up by a highly accurate low-rank tensor surrogate. To ensure the continuity of the underlying mapping from shape parametrisation to the upscaled material behaviour, a diffeomorphism is constructed by generating an appropriate family of meshes via transformation of a reference mesh. The shape uncertainty is then propagated to measure the distance of the upscaled material to the isotropic and orthotropic material class. Finally, the fuzzy effective material is used to compute bounds for the average displacement of a non-homogenized material with uncertain star-shaped inclusion shapes.
Type of Medium:
Online Resource
Pages:
1 Online-Ressource (36 Seiten, 2,32 MB)
,
Illustrationen, Diagramme
Series Statement:
Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik no. 2907
URL:
https://doi.org/10.20347/WIAS.PREPRINT.2907
DOI:
10.20347/WIAS.PREPRINT.2907
Language:
English
Note:
Literaturverzeichnis: Seite 30-34
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