Regularization of shape optimization problems using FE-based parametrization
Regularization of shape optimization problems using FE-based parametrization
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DOI：
10.1007/s00158-012-0843-z
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发表时间：
2013-04
影响因子：
3.9
通讯作者：
M. Firl;R. Wüchner;K. Bletzinger
中科院分区：
文献类型：
--
作者：
M. Firl;R. Wüchner;K. Bletzinger
本文介绍了一种通用的基于完全稳定网格的形状优化策略，它允许基于有限元参数化的机械问题的形状优化。通过应用滤波器方法和网格正则化策略，避免了众所周知的网格依赖性结果。过滤方法在基于SIMP（Solid Isotropic Material with Penalization）的拓扑优化中得到了成功的应用。这里介绍的滤波器方法使用基于卷积积分的特定公式。它表明，过滤器的方法，确保网格独立的最优设计。此外，它们提供了一个简单而强大的工具，以探索整个设计空间与类似的机械性能的最佳设计。基于有限元参数化的优化策略的成功应用需要将滤波方法与网格正则化策略相结合。后者确保了有限元解的可靠结果，这对灵敏度分析至关重要。本演示介绍了一种新的网格正则化策略，该策略基于更新的参考策略（URS）。结果表明，在此机械基础上制定的方法在快速和强大的网格正则化方法的结果。得到的网格显示出最小的网格变形，即使网格边界的大移动。所提出的正则化方法的性能证明了几个示例。
This paper introduces a general fully stabilized mesh based shape optimization strategy, which allows for shape optimization of mechanical problems on FE-based parametrization. The well-known mesh dependent results are avoided by application of filter methods and mesh regularization strategies. Filter methods are successfully applied to SIMP (Solid Isotropic Material with Penalization) based topology optimization for many years. The filter method presented here uses a specific formulation that is based on convolution integrals. It is shown that the filter methods ensure mesh independency of the optimal designs. Furthermore they provide an easy and robust tool to explore the whole design space with respect to optimal designs with similar mechanical properties. A successful application of optimization strategies with FE-based parametrization requires the combination of filter methods with mesh regularization strategies. The latter ones ensure reliable results of the finite element solutions that are crucial for the sensitivity analysis. This presentation introduces a new mesh regularization strategy that is based on the Updated Reference Strategy (URS). It is shown that the methods formulated on this mechanical basis result in fast and robust mesh regularization methods. The resulting grids show a minimum mesh distortion even for large movements of the mesh boundary. The performance of the proposed regularization methods is demonstrated by several illustrative examples.