Robust topology optimization of slender structures with geometric imperfections

1. Abstract Structural topology optimization often leads to slender structures which are sensitive to geometric imperfections such as the misplacement of material. A robust approach is therefore presented in order to take into account material misplacement in topology optimization problems. A probabilistic approach to robust optimization is followed. Spatially varying geometric imperfections are modeled by means of a vector-valued Gaussian random field. Both a linear elastic and a nonlinear elastic formulation are considered in order to analyze the importance of geometric nonlinear effects on the design performance and the optimized design. The objective function of the robust optimization problem 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. 2.