A Novel 3-D Topology Optimization Methodology Based on the Min-Cut Theorem

Abstract

Topology optimization (TO) has become a new paradigm to provide a quantitative design methodology for modern devices. In the two categories, the discrete-variable-based one and the continuous-variable-based one, of the existing TO methodologies, the on/off method - a typical method of the former - outperforms the latter in terms of an intuitive representation of the optimized results. Moreover, the existing TO techniques or procedures are generally 2-D. To address the aforementioned issues of existing methodologies, a new 3-D TO method based on the min-cut theorem is proposed. Three types of element connectivity are defined and used to transform a 3-D mesh grid to a 2-D network, providing equivalent quantities to perform the 3-D TO under the same implementation as in 2-D with no additional cost. Furthermore, the mechanism of the parameter selection is explored to provide rules for parameter tuning in engineering applications. As demonstrated by the reported numerical results, the proposed methodology is characterized by straightforward policy of parameter tuning and can find the optimized checkerboard-free topology with significant performance improvements.