Robust Topology Optimization of Transient Dynamics Considering Geometric Uncertainty

To address the efficiency and modeling challenges in transient dynamic topology optimization arising from geometric uncertainties, a data-driven robust topology optimization method is proposed. Firstly, the mate-rial field is parameterized using compactly supported radial basis functions, with the support radius treated as a random variable to describe geometric uncertainties. Secondly, an arbitrary polynomial chaos expan-sion method is employed to efficiently calculate the mean and standard deviation of the maximum dynamic compliance. To alleviate the computational burden of finite element analysis and sensitivity analysis in dynamic optimization, a model order reduction technique based on modified Gram-Schmidt orthonormali-zation is introduced, significantly enhancing optimization efficiency. An optimization model is then estab-lished to minimize the weighted sum of the mean and standard deviation of the maximum dynamic compli-ance under volume constraints. Numerical examples demonstrate that the statistical moments of dynamic compliance calculated by the proposed method are in good agreement with Monte Carlo simulation results, with a maximum error of less than 0.01. While maintaining accuracy, the average single-step computation time is reduced by approximately 90% compared to the full analysis method, indicating a significant im-provement in computational efficiency. Therefore, the proposed method is well-suited for robust transient dynamic design problems considering geometric uncertainties.