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An extension of shape sensitivity analysis to an immersed boundary method based on Cartesian grids

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Abstract

Gradient-based shape optimization processes of mechanical components require the gradients (sensitivity) of the magnitudes of interest to be calculated with sufficient accuracy. The aim of this study was to develop algorithms for the calculation of shape sensitivities considering geometric representation by parametric surfaces (i.e. NURBS or T-splines) using 3D Cartesian h-adapted meshes independent of geometry. A formulation of shape sensitivities was developed for an environment based on Cartesian meshes independent of geometry, which implies, for instance, the need to take into account the special treatment of boundary conditions imposed in non body-fitted meshes. The immersed boundary framework required to implement new methods of velocity field generation, which have a primary role in the integration of both the theoretical concepts and the discretization tools in shape design optimization. Examples of elastic problems with three-dimensional components are given to demonstrate the efficiency of the algorithms.

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Acknowledgements

The authors wish to thank the Spanish Ministerio de Economía y Competitividad for the financial support received through the project DPI2013-46317-R and the FPI program (BES-2011-044080), and the Generalitat Valenciana through the Project PROMETEO/2016/007.

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  1. Centro de Investigación en Ingeniería Mecánica (CIIM), Universitat Politècnica de València, 46022, Valencia, Spain

    Onofre Marco, Juan José Ródenas, Francisco Javier Fuenmayor & Manuel Tur

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  1. Onofre Marco
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  3. Francisco Javier Fuenmayor
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  4. Manuel Tur
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Correspondence to Onofre Marco.

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Marco, O., Ródenas, J.J., Fuenmayor, F.J. et al. An extension of shape sensitivity analysis to an immersed boundary method based on Cartesian grids. Comput Mech 62, 701–723 (2018). https://doi.org/10.1007/s00466-017-1522-0

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