A New Lighting on Analytical Discrete Sensitivities in the Context of IsoGeometric Shape Optimization
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ORIGINAL PAPER
A New Lighting on Analytical Discrete Sensitivities in the Context of IsoGeometric Shape Optimization T. Hirschler1,2 · R. Bouclier3,4 · A. Duval1 · T. Elguedj1 · J. Morlier4 Received: 22 May 2020 / Accepted: 29 June 2020 © CIMNE, Barcelona, Spain 2020
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.
1 Introduction Structural shape optimization has been one of the early application of IsoGeometric Analysis whose seminal paper is Hughes et al.[42]. Wall et al.[87] have rapidly highlighted its benefit for shape optimization because IGA uses models that combine an accurate geometrical description and great analysis capabilities. Indeed, IGA employs spline-based geometric models to perform the analysis. More precisely, IGA is a Finite Element Method that uses a spline model to describe the domain geometry but also to represent the numerical solution of the problem using the isoparametric * T. Hirschler [email protected] 1
Univ Lyon, INSA-Lyon, CNRS, LaMCoS UMR 5259, 69621 Villeurbanne Cedex, France
2
École Polytechnique Fédérale de Lausanne, MATH, MNS, 1015 Lausanne, Switzerland
3
Univ Toulouse, INSA-Toulouse, IMT UMR CNRS 5219, 31077 Toulouse Cedex 04, France
4
Univ Toulouse, ISAE Supaero-INSA-Mines Albi-UPS, CNRS UMR5312, Institut Clément Ader, 31055 Toulouse Cedex 04, France
paradigm[19, 42]. Even in its original version, IGA draws on advanced and well-known technologies coming from the field of Computer-Aided Design, as for instance NURBS models. Nowadays, a large panel of spline technologies (T-Splines, LR B-Splines, etc.) is available for simulation[28, 69]. Th
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