Truss topology optimization under uncertain nodal locations with proportional topology optimization method

This paper presents an approach to solving truss topology optimization problem with small uncertainty in the locations of the structural nodes. The nodal locations in the truss are assumed to be random, and the probabilistic method is used here to deal with the uncertainty. The objective of the optimization problem is to minimize the mean compliance of the truss structure under nodal location uncertainty. It is a well-acknowledged barrier to compute the inverse of the structural stiffness matrix which involves variations in the optimization problem. In this paper, based on Neumann series expansion, this optimization problem can be recast into a simpler deterministic structural optimization problem. In order to avoid the sensitivity calculations for the objective function, the proportional topology optimization method which shows comparable efficiency and accuracy with gradient-based method is used. The numerical examples demonstrate the effectiveness and high efficiency of the proposed approach, and further illustrate that the optimal truss topology can be dramatically impacted by nodal location uncertainties.