Robust topology optimization accounting for misplacement of material

Topology optimization is a method to find the best distribution of material in a given design domain. The use of topology optimization for structural design often leads to slender structures which are sensitive to geometric imperfections such as the misplacement or misalignment of material. A robust approach to topology optimization is therefore presented which takes into account these geometric imperfections. An Eulerian approach is followed as the imperfections are modeled on the same finite element grid used in the deterministic topology optimization problem. Translation of material is obtained by adding a small perturbation to the center of the density filter kernel. The spatial variation of the geometric imperfections is modeled by means of a vector valued Gaussian random field. The random field is conditioned in order to incorporate supports in the design where no misplacement of material occurs. In the robust optimization problem, the objective function is defined as a weighted sum of the mean value and the standard deviation of the performance of the structure under uncertainty. A sampling method is used to estimate these statistics and the sensitivities thereof in the optimization algorithm. The solutions obtained by the robust approach are verified by means of an extensive Monte Carlo simulation. Keywords— Topology optimization, Geometric imperfections, Random fields, Robust optimization