Robust Structural Topology Optimization Considering Boundary Uncertainties

Traditionally, topology optimizations are often carried out in a deterministic framework, where it is assumed that the boundary involved in the problem can be determined exactly. However, boundary uncertainties are unavoidable in real-world applications due to incomplete information, observation errors and manufacturing imperfections, etc. Furthermore, it is also well known that solutions to optimization problems may exhibit remarkable sensitivity to boundary perturbations. This may lead to the performance of the actual structure far from optimal or cannot meet the design requirements. Therefore it is of great importance to take the effect of boundary uncertainty into consideration for optimal topology designs of structures.In the present paper, we proposed a approach for structural topology optimization considering the uncertainty of boundary variations via level set approach. First, in order to make the optimal design less sensitive to the possible boundary variations, we choose the response of structure enduring the worst case perturbation as the objective function for ensuring the robustness of the optimal solution. Second, 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. Then the corresponding optimization problem formulated as a worst case design problem. Last, numerical examples demonstrate the effectiveness of the proposed approach.