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

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 represent...

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Bibliographic Details
Published in:Computational mechanics 2018-10, Vol.62 (4), p.701-723
Main Authors: Marco, Onofre, Ródenas, Juan José, Fuenmayor, Francisco Javier, Tur, Manuel
Format: Article
Language:English
Subjects:
Algorithms
Cartesian coordinates
Classical and Continuum Physics
Computational Science and Engineering
Design optimization
Engineering
Mathematical analysis
Mechanical components
Original Paper
Sensitivity analysis
Shape optimization
Splines
Theoretical and Applied Mechanics
Velocity distribution
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Summary: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.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-017-1522-0