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Isogeometric shape optimization of vibrating membranes

机译：振动膜的等几何形状优化

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摘要

We consider a model problem of isogeometric shape optimization of vibrating membranes whose shapes are allowed to vary freely. The main obstacle we face is the need for robust and inexpensive extension of a B-spline parametrization from the boundary of a domain onto its interior, a task which has to be performed in every optimization iteration. We experiment with two numerical methods (one is based on the idea of constructing a quasi-conformal mapping, whereas the other is based on a spring-based mesh model) for carrying out this task, which turn out to work sufficiently well in the present situation. We perform a number of numerical experiments with our isogeometric shape optimization algorithm and present smooth, optimized membrane shapes. Our conclusion is that isogeometric analysis fits well with shape optimization.
机译：我们考虑了振动膜的等几何形状优化的模型问题，其形状可以自由变化。我们面临的主要障碍是需要对B样条参数化进行稳健且廉价的扩展，将其从域的边界扩展到域的内部，此任务必须在每次优化迭代中执行。我们尝试了两种数值方法（一种基于构造准保形映射的思想，而另一种基于基于弹簧的网格模型）来执行此任务，结果证明在目前的应用中效果很好情况。我们用等几何形状优化算法进行了许多数值实验，并给出了平滑，优化的膜形状。我们的结论是，等几何分析非常适合形状优化。

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