Topology optimization of continuum structures under uncertainty – A Polynomial Chaos approach

A computational method for topology optimization in the presence of uncertainty is proposed. The method combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The idea in spectral stochastic formulations is to add an extra dimension, a random dimension, to the problem where the stochastic variability of the input parameters (and outputs of interest) can be modeled. The resulting compact representations for the response quantities allow for efficient and accurate calculation of sensitivities of response statistics with respect to the design variables which are then fed into a gradient-based optimizer that searches for the optimum design. From a variety of frameworks for uncertainty-informed optimization, robust topology optimization is chosen to demonstrate the applicability of the method. Examples from continuum topology optimization under uncertainty in material properties are presented. 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.