Numerical and physical robustness with respect to nodewise geometrical uncertainty in topology optimization

Deterministic optimization applied to non-parametric optimization, such as topology, sizing, or shape optimization, may result in optimized designs that are highly mesh-dependent or correspond to a local minimum. Previous robust design optimization methods that consider global geometrical perturbations demonstrate the ability to suppress many local minima in the response function, and thereby, yield improved optimized designs. However, different mesh discretizations sometimes yield fundamentally different optimized designs that cannot be suppressed using global uncertainty formulations. Hence, a novel uncertainty measure is proposed, based on nodewise uncorrelated local geometric distributions. Firstly, the proposed approach employs a computationally efficient generalized first-order method, ensuring improved numerical mesh-independence of optimized designs. Secondly, the proposed method allows for a semi-intrusive implementation independent of the number of design variables and the design variable type. The proposed method is applied as a local uncertainty measure to various numerical examples addressing both numerical and physical geometrical robustness including the design of compliant hinge mechanisms, as well as stiffness- and stress-based optimization formulations.