Robust topology optimization for structures under bounded random loads and material uncertainties

Abstract Design optimization considering uncertainties arising from different sources has been one of the hotspots in the area of structural optimization. This paper presents a robust topology optimization method for structures with bounded loads and spatially correlated material uncertainties. We first develop a new model for random structural loads with bounded nature, in which the uncertain load components are assumed to be uniformly distributed within a convex set represented by an ellipsoid model. This model is then combined with the random field discretized by means of the expansion optimized linear estimation to provide uncertainty modelling of structures exhibiting both load and material uncertainties. The robust topological design problem is formulated as a bi-criteria optimization problem for minimizing the mean value and standard deviation of the structural compliance under these uncertainties. The polynomial chaos expansion, in conjunction with the sparse grid quadrature rule, is employed for calculating the statistical moments of the structural responses. The adjoint sensitivity analysis scheme is derived, and a gradient based optimizer is employed for updating the design variables. Numerical examples show that the structural designs obtained by the proposed robust topology optimization method exhibit higher robustness against uncertainties as compared with their deterministic counterpart.