M-VCUT level set method for optimizing cellular structures

Abstract

This paper presents a multiple variable cutting (M-VCUT) level set method for the topology optimization of cellular structures. This method first divides the reference design domain into cells, and then in each cell it uses multiple basic level set functions combined with their cutting functions to describe the microstructure. The basic level set functions are used to describe microstructure prototypes that are kept fixed during the course of optimization. Each basic level set function is cut by its own cutting function to achieve shape and topology variation of microstructure. After the cutting operations, multiple virtual microstructures are obtained in each cell, and they are further combined together through a union operation to generate an actual microstructure. Based on the multiple virtual microstructures, multiple combination options are available, thus resulting in an enlarged design space and performance improvement as compared to the VCUT level set method developed in our previous study. Moreover, as a generalization of the VCUT level set method, connections between microstructures in neighboring cells are naturally guaranteed without any extra constraints.