Topology optimization under uncertainty poses extreme difficulty to the already challenging topology optimization problem. This paper presents a new computational method for calculating topological sensitivities of statistical moments of high-dimensional complex systems subject to random inputs. The proposed method, capable of evaluating stochastic sensitivities for large-scale, robust topology optimization (RTO) problems, integrates a polynomial dimensional decomposition (PDD) of multivariate stochastic response functions and deterministic topology derivatives. In addition, the statistical moments and their topology sensitivities are both determined concurrently from a single stochastic analysis. When applied in collaboration with the gradient based optimization algorithm, the proposed method affords the ability of solving industrial-scale RTO design problems. Numerical examples indicate that the new method developed provides computationally efficient solutions.
Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Multi. Optim. 16(1), 68–75 (1998)CrossRefGoogle Scholar
Sui, Y.K., Yang, D.Q.: A new method for structural topological optimization based on the concept of independent continuous variables and smooth model. Acta Mech. Sinica 14(2), 179–185 (1998)CrossRefGoogle Scholar
Wang, H., Kim, N.H.: Robust design using stochastic response surface and sensitivities. In: 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (2006)Google Scholar
Wang, M.Y., Wang, X.M.: Color level sets: a multi-phase method for structural topology optimization with multiple materials. Comput. Methods Appl. Mech. Eng. 193(6), 469–496 (2004)MathSciNetCrossRefzbMATHGoogle Scholar