Multi-material topology optimization of structures using an ordered ersatz material model

This paper proposes a new element-based multi-material topology optimization algorithm using a single variable for minimizing compliance subject to a mass constraint. A single variable based on the normalized elemental density is used to overcome the occurrence of meaningless design variables and save computational cost. Different from the traditional material penalization scheme, the algorithm is established on the ordered ersatz material model, which linearly interpolates Young’s modulus for relaxed design variables. To achieve a multi-material design, the multiple floating projection constraints are adopted to gradually push elemental design variables to multiple discrete values. For the convergent element-based solution, the multiple level-set functions are constructed to tentatively extract the smooth interface between two adjacent materials. Some 2D and 3D numerical examples are presented to demonstrate the effectiveness of the proposed algorithm and the possible advantage of the multi-material designs over the traditional solid-void designs.