Robust topology optimization of multi-material structures based on the material-field series-expansion method

The performance of composite structures can be dramatically improved through the synergy between different constituent materials. However, the topology optimization of multi-material structures poses a heavy computational burden, which becomes more significant when load uncertainty is considered. This article proposes an efficient method to address the problem of robust topology optimization of multi-material structures. Employing the property that the material-field series-expansion method can significantly reduce the number of design variables, the proposed method improves the computational efficiency of the robust optimization problem. Meanwhile, the modification of the original multi-material interpolation model improves the quality of the optimized designs. Monte Carlo simulation is used to treat the load uncertainty, but it is decoupled from the optimization process based on linear elasticity theory to reduce computation cost. The effectiveness of the proposed method is demonstrated by numerical examples, which show that robust design results can be efficiently generated by this method.