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.

等几何形状优化现已研究了十多年。该贡献旨在在这个有前途的框架内汇编关键要素，并特别关注敏感性分析。基于与等几何形状优化相关的所有研究，我们介绍了已出现的过程的全局概述。主要特征是使用两个具有相同几何形状的细化级别：执行形状更新的粗略级别和执行分析的精细级别。我们将说明在优化过程中，尤其是在灵敏度分析过程中，这两个模型如何相互作用。我们提出了新的理论发展，算法和定量结果有关基于离散伴随的灵敏度的分析计算。为了强调这种灵敏度分析方法的多功能性，我们执行了8个基准优化示例，这些示例具有不同类型的目标函数（顺应性，位移场，应力场和固有频率），不同类型的等几何元素（2D和3D标准实体，以及Kirchhoff-Love壳）和不同类型的结构分析（静态和振动）。将分析灵敏度的数值性能与近似灵敏度进行比较。结果的准确性和数值成本使我们相信，所提出的方法是为形状优化建立鲁棒框架的可行策略。不同类型的等几何元素（2D和3D标准实体，以及Kirchhoff-Love壳），以及不同类型的结构分析（静态和振动）。将分析灵敏度的数值性能与近似灵敏度进行比较。结果的准确性和数值成本使我们相信，所提出的方法是为形状优化建立鲁棒框架的可行策略。不同类型的等几何元素（2D和3D标准实体，以及Kirchhoff-Love壳），以及不同类型的结构分析（静态和振动）。将分析灵敏度的数值性能与近似灵敏度进行比较。结果的准确性和数值成本使我们相信，所提出的方法是为形状优化建立鲁棒框架的可行策略。