Robust structural topology optimization considering boundary uncertainties

In classical deterministic topology optimization, the effect of the possible boundary variations on the performance of the structure is not taken into account, which may lead to designs that are very sensitive to manufacturing errors. As a consequence, the performance of the real structure may be far from optimal and even not meet the design requirements. In the present paper, structural topology optimization considering the uncertainty of boundary variations is considered via level set approach. In order to make the optimal designs less sensitive to the possible boundary variations, we choose the compliance and fundamental frequency of structure enduring the worst case perturbation as the objective function for ensuring the robustness of the optimal solution. With use of the Schwarz inequality, the original Bi-level optimization problem is transformed to a single-level optimization problem, which can be solved efficiently. Numerical examples demonstrate the effectiveness of the proposed approach.