Abstract A method for isogeometric structural shape optimization using a multilevel approach and automated sensitivity analysis is presented in this work. The analysis mesh is obtained after carrying out successive refinements using the knot insertion and/or degree elevation algorithms, while retaining the coarse geometry for the domain design. Even though analytical sensitivities can be derived and implemented, they are prone to implementation errors and time consuming to derive. To circumvent the complication, we propose to use an automatic differentiation toolbox to perform the sensitivity analysis. This facilitates the computation of the gradients of the objective function with respect to the design variables defined over the coarse design domain with accuracy up to machine precision. Both forward and reverse modes of automatic differentiation are implemented. The accuracy, numerical efficiency and memory requirements are studied for analytical, numerical and automatic sensitivities in order to show the benefits and limitations of using automated gradients. Finally, numerical examples for two-dimensional and solid-shell shape optimization problems are presented to show the efficiency of the automatic sensitivities.

中文翻译：

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使用自动灵敏度分析的等几何结构形状优化

摘要 在这项工作中提出了一种使用多级方法和自动灵敏度分析的等几何结构形状优化方法。分析网格是在使用结插入和/或度数提升算法执行连续细化后获得的，同时保留域设计的粗略几何形状。即使可以导出和实施分析敏感性，它们也容易出现实施错误并且导出耗时。为了避免并发症，我们建议使用自动微分工具箱来执行敏感性分析。这有助于以高达机器精度的精度计算目标函数相对于在粗设计域上定义的设计变量的梯度。实现了自动微分的正向和反向模式。研究了分析、数值和自动灵敏度的准确性、数值效率和内存要求，以显示使用自动梯度的好处和局限性。最后，给出了二维和实体壳形状优化问题的数值例子，以显示自动灵敏度的效率。