Structure-material integrated design by level sets

This paper proposes a structure-material integrated design method in the framework of level sets. A two-scale optimization is performed, where not only is the structural configuration optimized, but the effective properties of the constituent material are also designed by optimizing the configuration of the periodically-arranged microstructures. In this way, the approach can simultaneously generate optimized material distribution patterns as well as optimized materials. Due to the fact that the level set method produces material-void solutions only, the obtained material is uniformly distributed over the material regions of the structure in a strict sense. Three numerical examples are presented to validate the proposed method. The obtained optimal solutions illustrate that whether to design material cells or to optimize structural configurations to achieve the best structural performance would be problem dependent, and thus further demonstrate the necessity and validity of the integrated design scheme.