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A New Lighting on Analytical Discrete Sensitivities in the Context of IsoGeometric Shape Optimization

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Abstract

Isogeometric shape optimization has been now studied for over a decade. This contribution aims at compiling the key ingredients within this promising framework, with a particular attention to sensitivity analysis. Based on all the researches related to isogeometric shape optimization, we present a global overview of the process which has emerged. The principal feature is the use of two refinement levels of the same geometry: a coarse level where the shape updates are imposed and a fine level where the analysis is performed. We explain how these two models interact during the optimization, and especially during the sensitivity analysis. We present new theoretical developments, algorithms, and quantitative results regarding the analytical calculation of discrete adjoint-based sensitivities. In order to highlight the versatility of this sensitivity analysis method, we perform eight benchmark optimization examples with different types of objective functions (compliance, displacement field, stress field, and natural frequencies), different types of isogeometric element (2D and 3D standard solids, and a Kirchhoff–Love shell), and different types of structural analysis (static and vibration). The numerical performances of the analytical sensitivities are compared with approximate sensitivities. The results in terms of accuracy and numerical cost make us believe that the presented method is a viable strategy to build a robust framework for shape optimization.

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Authors and Affiliations

  1. Univ Lyon, INSA-Lyon, CNRS, LaMCoS UMR 5259, 69621, Villeurbanne Cedex, France

    T. Hirschler, A. Duval & T. Elguedj

  2. École Polytechnique Fédérale de Lausanne, MATH, MNS, 1015, Lausanne, Switzerland

    T. Hirschler

  3. Univ Toulouse, INSA-Toulouse, IMT UMR CNRS 5219, 31077, Toulouse Cedex 04, France

    R. Bouclier

  4. Univ Toulouse, ISAE Supaero-INSA-Mines Albi-UPS, CNRS UMR5312, Institut Clément Ader, 31055, Toulouse Cedex 04, France

    R. Bouclier & J. Morlier

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  1. T. Hirschler
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Hirschler, T., Bouclier, R., Duval, A. et al. A New Lighting on Analytical Discrete Sensitivities in the Context of IsoGeometric Shape Optimization. Arch Computat Methods Eng 28, 2371–2408 (2021). https://doi.org/10.1007/s11831-020-09458-6

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