Robust topology optimisation for expected compliance and variance using level-set method

This paper introduces variance into the robust compliance topology optimization problem where there is uncertainty in loading magnitude. An analytical formulation for compliance variance is derived and shape sensitivities for the level set optimization method are obtained using the adjoint method. Variance is combined with expected compliance to pose a robust optimization problem that aims to minimize a weighted combination of average and variability of compliance. The proposed approach is demonstrated and investigated using two examples that display contrasting behavior.