Shape and topology optimization based on the convected level set method

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.