Efficient robust topology optimization of large-scale continuum structures under load uncertainty
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With the increasing complexity of structural design problems, robust topology optimization (RTO) faces increasingly severe computational efficiency challenges. The huge cost of large-scale structural analysis, compounded by repeated analyses required for uncertainty quantification, substantially increases the overall computational burden of RTO. To address this issue, this study proposes an efficient robust topology optimization framework based on discrete variable (RDVTO). The framework first applies direct probability integration (DPIM) with an iterative sequence sampling strategy to quantify uncertainties, enabling accurate statistics with minimal structural analyses. Subsequently, improvements are introduced to the multigrid preconditioned conjugate gradient method based on extended multiscale finite elements (EMsFEM-MGPCG), further enhancing structural analysis efficiency. For load uncertainty issues, the improved method employs matrix representation of load vectors, enabling the calculation of displacements for all representative points in a single computation. Finally, sequential approximate integer programming with trust region (SAIP-TR) is adopted to solve RDVTO problems, producing clear topology configurations. For 3D examples involving millions of degrees of freedom, the proposed method still achieves efficient solutions on a single computer, highlighting its strong potential for engineering applications.
