Robust compliance topology optimization using the first-order second-moment method

A robust topology optimization approach is presented which uses the probabilistic first-order second-moment method for the estimation of mean value and variance of the compliance. The considered sources of uncertainty are the applied load, the spatially varying Young's modulus, and the geometry with focus on the latter two. In difference to similar existing approaches for robust topology optimization, the presented approach requires only one solution of an adjoint system to determine the derivatives of the variance, which keeps the computation time close to the deterministic optimization. For validation, also the second-order fourth-moment method and Monte Carlo simulations are embedded into the optimization. For all approaches, the applicability and impact on the resulting design are demonstrated by application to benchmark examples. For random load, the first-order second-moment approach provides unsatisfying results. For random, Young's modulus and geometry, however, the robust topology optimization using first-order second-moment approach provides robust designs at very little computational cost.