Stabilized time-series moving morphable components method for topology optimization

The moving morphable components (MMC) method has been widely used for topology optimization due to its ability to provide an explicit description of topology. However, the MMC method may encounter the instability issue during iteration. Specifically, the iteration history is highly sensitive to parameters of the optimizer, that is, the move limits in the method of moving asymptotes (MMA). Additionally, the final topology obtained from the MMC method usually depends on the initial values. To address these issues and improve the stability of the MMC method in practical applications, this article introduces two strategies. The first strategy is based on the time-series MMC (TSMMC) method, which proposes a unified description of curved components. However, the use of control-points-based design variables may introduce instability into the iteration process due to the strong locality associated with these variables. To mitigate this, global design variables have been incorporated into the formulation. Numerical examples demonstrate that this mixed formulation, combining global and local design variables, can enhance stability significantly. To further enhance stability, the second strategy involves using the trust region-based moving asymptotes (TRMA) method as the optimizer instead of MMA. The TRMA method incorporates an accuracy control mechanism, resulting in stable and fast convergence behavior, as demonstrated in the numerical examples.