A statistical decomposition of geometric imperfections applied to robust topology optimisation

The present paper deals with the integration of geometric imperfections due to the additive manufacturing process in the framework of a density-based topology optimisation method. Specifically, the model presented in this work splits the geometric imperfections into modes using a strategy based on a statistical decomposition of local geometric patterns. The aleatory uncertainty related to the lack of repeatability of the manufacturing process is propagated through the Monte Carlo method and a robust topology optimisation problem formulation is proposed. The method is applied to the classic problem of the minimisation of a cost function formulated as a weighted sum of the mean and the standard deviation of the structural compliance subject to a constraint on the volume. The effectiveness of the approach is tested on 2D benchmark problems taken from the literature and complemented by a sensitivity analysis on the convergence and accuracy of Monte Carlo estimates. Moreover, a modification of cost function weights allows to support decision-making depending on uncertainty fearfulness. The proposed method has proven effective in mitigating uncertainties arising from geometric imperfections during the design activity.