In recent years, the functionally graded materials (FGM) with cellular structure have become a hot spot in the field of materials research. For the continuously varying cellular structure in the layer-wise FGM, the connection of gradient cellular structures has become the main problem. Unfortunately, the effect of gradient connection method on the overall structural performance lacks attention, and the boundary mismatch has enormous implications. Using the homogenization theory and the level set method, this article presents an efficient topology optimization method to solve the connection issue. Firstly, a simple but efficient hybrid level set scheme is developed to generate a new level set surface that has the partial features of two candidate level sets. Then, when the new level set surface is formed by considering the level set functions of two gradient base cells, a special transitional cell can be constructed by finding the zero level set of this generated level set surface. Since the transitional cell has the geometric features of two gradient base cells, the shape of the transitional cell fits perfectly with its connected gradient cells on both sides. Thus, the design of FGM can have a smooth connectivity with C1 continuity without any complex numerical treatments during the optimization. A number of examples on both 2D and 3D are provided to demonstrate the characteristics of the proposed method. Finite element simulation has also been employed to calculate the mechanical properties of the designs. The simulation results show that the FGM devised by the proposed method exhibits better mechanical performances than conventional FGM with only C0 continuity.
Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints
