Topology optimization of imperfect frame structures with improved manufacturability

We present a framework for robust topology optimization of frame structures under uncertainty in member geometry. Imperfect geometry is defined as a general out-of-straightness. The uncertainty in response is quantified using a second-order stochastic perturbation that allows for accurate estimation of first and second-order response statistics in the presence of geometric random imperfections. The adjoint method is employed to compute the sensitivities, allowing for the use of gradient-based optimizers. A novel approach based on the augmentation of the set of physical design variables with an "indicator set" and a SIMP-like strategy is utilized to control the complexity of the final design and arrive at optimized topologies with improved manufacturability. Numerical examples are provided to demonstrate the performance of the proposed framework where comparison is made with the deterministic designs to highlight the improvements and differences both in terms of overall topology, e.g., load path diversification, and volume re-distribution and the impact of the manufacturability considerations on the topology of the final design.