Abstract
Topology optimization is a powerful computational design tool that has led to discovery of highly efficient structures. The optimization process for lattice structures, such as frames, usually begins with a dense mesh of interconnected elements. An iterative process then allows for simultaneous resizing and removing of elements throughout the design domain. In recent years there has been a surge in the number of studies that include stochastic variabilities, e.g. uncertainty in external forces, material properties, and geometric imperfections, in the optimization process to avoid sub-optimal or impractical designs under real-world engineering conditions. This study focuses on the topology optimization of frame structures under geometric imperfections in the form of elemental crookedness. To handle the stochastic nature of the problem, an uncertainty quantification method must be implemented. The brute-force Monte Carlo approach is a highly accurate, yet extremely costly method, and is not desirable within an optimization routine. To allow for immensely improved computational burden without great sacrifice to accuracy, an efficient uncertainty quantification engine based on stochastic perturbation expansion is used to approximate statistical moments up to second order. A robust design optimization formulation is created via the inclusion of variance(to control the variability of performance). To avoid complex topologies and hair-like elements that often emerge as a result of robust topology optimization, manufacturability constraints are enforced through a SIMP-like method to push the outcome toward a more manufacturable yet efficient structure. The effects of the uncertainties are illustrated by comparing the performance of optimized topologies to that of their deterministic counterpart. The functionality of the manufacturability constraints is also examined.