Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices

This paper proposes an efficient approach to solving robust topology optimization problem of structures under loading uncertainty. The objective is to minimize a weighted sum of the mean and standard deviation of structural compliance. Loading uncertainties can be in either concentrated loads or uniformly distributed loads. By exploiting of the linear elastic nature of structure, Monte Carlo sampling is completely separated from the topology optimization process, thus accurate calculation of objective function becomes possible. Efficient sensitivity analysis method is developed and its computational cost is only linearly proportional to the number of uncertain loads. The sensitivity analysis is also integrated into the density based topology optimization approach to solve the robust topology optimization problems. The numerical examples demonstrate the effectiveness of the proposed approach. The effect of uncertainty level, probability distribution of uncertainty and different influence of loading magnitude and directional uncertainty on the robust designs are also shown by the numerical examples.