A smooth single-variable-based interpolation function for multi-material topology optimization

This article presents a novel single-variable-based material interpolation scheme for multi-material density-based topology optimization. In the proposed scheme, no additional variables are needed to deal with the multiple materials, i.e., the number of design variables is independent of the number of material candidates, thus it makes the multi-material topology optimization computationally efficient. Moreover, the proposed interpolation function and its first-order derivative are continuous, which is tractable for gradient-based optimization algorithms. Additionally, we also address some weaknesses of single-variable-based interpolation schemes for multimaterial and tailor a new filtering technique to alleviate them. In the optimization process, the method of moving asymptotes is used with the sensitivity analysis obtained from the adjoint method. The proposed multimaterial interpolation scheme and its dedicated filtering technique are employed to find the materials distribution in different two-dimensional structures such that the compliance is minimized under the mass and cost constraints. The obtained results from our proposed method consistently outperform other state-of-the-art methods available in the literature.