This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same numerical technique. This leads to a scheme that is comparatively easy to differentiate, allowing for a fully symbolic derivation of the gradient and subsequent gradient-based optimization. To improve the efficiency and robustness of the scheme, the basis is re-selected during each optimization iteration and adjusted to the current needs. The scheme is validated in two test cases.
|Number of pages||19|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Publication status||Published - 2021|
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- Adjoint-based optimization
- Elliptic Grid Generation
- Isogeometric Analysis
- Parameterization techniques
- Shape optimization