Robust topology optimization of structures with uncertainties in stiffness – Application to truss structures

A computational strategy is proposed for robust structural topology optimization in the presence of uncertainties with known second order statistics. The strategy combines deterministic topology optimization techniques with a perturbation method for the quantification of uncertainties associated with structural stiffness, such as uncertain material properties and/or structure geometry. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. This in turn leads to significant computational savings when compared with Monte Carlo-based optimization algorithms which involve multiple formations and inversions of the global stiffness matrix. Examples from truss structures are presented to show the importance of including the effect of controlling the variability in the final design. It is also shown that results obtained from the proposed method are in excellent agreement with those obtained from a Monte Carlo-based optimization algorithm.