Shape and topology optimization based on the convected level set method
Shape and topology optimization based on the convected level set method
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DOI：
10.1007/s00158-016-1444-z
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发表时间：
2016-04
影响因子：
3.9
通讯作者：
K. Yaji;M. Otomori;T. Yamada;K. Izui;S. Nishiwaki;O. Pironneau
中科院分区：
文献类型：
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作者：
K. Yaji;M. Otomori;T. Yamada;K. Izui;S. Nishiwaki;O. Pironneau
本研究的目的是构建一种基于对流水平集方法的形状优化方法，其中水平集函数被定义为使用基于双曲正切函数的正弦滤波器获得的截断光滑函数。双曲正切函数的局部性质显著地减少了双曲正切函数的指定轮廓与使用时间演化方程更新的水平集函数之间的误差的产生。此外，小尺寸的误差有利于使用对流重新初始化，其基本思想是，重新初始化嵌入在时间演化方程，而这样的治疗通常是在一个单独的计算在传统的水平集方法进行。在进行重新初始化时，对流水平集方法可以完全避免额外的计算。通过一个平均柔度最小化问题和一个柔顺机构的设计问题验证了该方法的有效性。
The aim of this research is to construct a shape optimization method based on the convected level set method, in which the level set function is defined as a truncated smooth function obtained by using a sinus filter based on a hyperbolic tangent function. The local property of the hyperbolic tangent function dramatically reduces the generation of red the error between the specified profile of the hyperbolic tangent function and the level set function that is updated using a time evolution equation. In addition, the small size of the error facilitates the use of convective reinitialization, whose basic idea is that the reinitialization is embedded in the time evolution equation, whereas such treatment is typically conducted in a separate calculation in conventional level set methods. The convected level set method can completely avoid the need for additional calculations when performing reinitialization. The validity and effectiveness of our presented method are tested with a mean compliance minimization problem and a problem for the design of a compliant mechanism.