Optimized Design of Multi-Material Cellular Structures by a Level-Set Method With Guyan Reduction

Owing to their tailorable physical properties, periodic cellular structures are considered promising materials for use in various engineering applications. To fully leverage the potential of such structures, it will be necessary to develop a design method that is capable of producing material layouts that are not only intricate but at the same time, readily manufacturable. This paper presents a topology optimization framework for designing well-connected and exact-sized multi-material cellular structures that are to be subjected to temperature change. In this framework, multi-material layouts within designable unit cells are represented using level-set functions and corresponding Boolean operations. The connectivity between exact-sized cells, advantageous in realizing the optimal designs, is guaranteed because of a common length scale assumed between these unit cells and the macrostructure. Increase in the number of degree-of-freedoms and concomitant storage requirements are minimized by applying the Guyan reduction method, in which the secondary degree-of-freedom is condensed out to reduce the size of the discretized model. The design capabilities of the proposed method were investigated using several numerical models. The optimized material layouts show that the presented method can create innovative designs facilitating the thermal expansion to improve the performance and enhance overall layouts’ stiffness in different ways, especially when the design is constituted of multiple materials.