Topology optimization of continuum structures under hybrid uncertainties

The aim of this paper is to study the topology optimization for mechanical systems with hybrid material and geometric uncertainties. The random variations are modeled by a memory-less transformation of random fields which ensures their physical admissibility. The stochastic collocation method combined with the proposed material and geometry uncertainty models provides robust designs by utilizing already developed deterministic solvers. The computational cost is decreased by using of sparse grids and discretization refinement that are proposed and demonstrated as well. The method is utilized in the design of minimum compliance structure. The proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling by using adaptive sparse grids method.