Student Paper: Introducing Uncertainty in Direction of Loading for Topology Optimization.

Uncertainty is an important consideration in structural design and optimization to produce robust and reliable solutions. Existing methods that include loading direction uncertainty in structural topology optimization may not represent realistic uncertainties or employ a discrete sampling approach that approximates the effect of the uncertainty. The sampling approach can become computationally expensive when an accurate approximation is required. An efficient and accurate approach is developed in this paper when solving the minimization of expected compliance problem with uncertain direction of applied loading. This new approach is analogous to a multiple load case problem where load cases and weights are derived explicitly to compute exactly the expected compliance and sensitivities. The approach is then broadened to include uncertainty in magnitude of loading without penalizing efficiency. Illustrative examples using a level set based topology optimization method are then used to demonstrate the proposed approach. I