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Structural and Multidisciplinary Optimization

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24.12.2016 | RESEARCH PAPER

On shape sensitivities with heaviside-enriched XFEM

verfasst von: Ashesh Sharma, Hernan Villanueva, Kurt Maute

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 2/2017

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Abstract

This paper investigates the behavior of shape sensitivities within the context of the eXtended Finite Element Method (XFEM) using a Heaviside enrichment strategy, wherein the shape derivative is computed by the adjoint method. The Heaviside function is discontinuous by construction. This feature of the enrichment function presents advantages as well as challenges in the computation of shape sensitivities, both of which are discussed in detail in this paper. Using continuum and discrete approaches, we present the derivation of analytical shape sensitivities with respect to the design variables which define the design geometry. We propose a robust semi-analytical approach to computing the shape sensitivities, which provides great ease of implementation as compared to fully analytical approaches. The behavior of the XFEM-based shape sensitivities is analyzed using linear heat diffusion examples in 2D, and an incompressible fluid flow example in 3D. We compare XFEM-based shape sensitivities against shape sensitivities obtained through the classical approach of using a body-fitted mesh. It is found that the former are not as smooth as those obtained using a comparable body-fitted mesh. This discrepancy is shown to be an outcome of the discretization error of the design geometry on a background mesh and is not a consequence of the approach by which the XFEM-based shape sensitivities are computed.

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Titel: On shape sensitivities with heaviside-enriched XFEM
verfasst von: Ashesh Sharma
Hernan Villanueva
Kurt Maute
Publikationsdatum: 24.12.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Structural and Multidisciplinary Optimization / Ausgabe 2/2017
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-016-1640-x

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