Robust Topology Optimization for Structures Considering Spatially Bounded Geometric Uncertainties

In structural topology optimization design, considering the uncertainties related to material properties and working loads in practical engineering structures, a series of robust topology optimization methods have been developed in recent years. At present, most robust topology optimization methods are based on deterministic geometry boundary of structures. In fact, manufacturing errors or measurement errors often lead to the uncertainty of structure boundaries. The structural design may be very sensitive to the small fluctuation of the boundary if ignoring the geometric uncertainty. Considering the spatially bounded characteristic of the boundary uncertainty, the interval field is used to measure the geometric uncertainty, and an efficient robust topology optimization method based on Chebyshev polynomial expansion is developed. Firstly, the boundary disturbance of the structure is described by modelling the projection threshold variable in the Heaviside filter as an interval field, and a robust topology optimization model under the worst case is then constructed. Secondly, based on the interval KL (Karhunen-Loève) expansion, the interval field is approximately discretized into finite interval variables, and the robust objective function and constraint are evaluated using the Chebyshev polynomial expansion method. Thirdly, the sensitivities of the robust objective function and constraint with respect to the design variables are derived, and the gradient-based optimization algorithm is used to update the topology design variables. Finally, several numerical examples are provided to verify the effectiveness of the proposed method. The analysis results of numerical examples show that the geometric uncertainty fluctuation of the structural boundary has an important impact on the structural performance. Compared with the topology optimization design under the deterministic boundary, the robust topology optimization design considering uncertainty has better robustness when considering the fluctuation of the structural boundary. © 2023 Editorial Office of Chinese Journal of Mechanical Engineering. All rights reserved.