Level Set-Based Robust Topology Design Considering Spatial Uncertainty

Abstract

This study extends the authors’ proposed robust topology optimization approach to the design problems with two-dimensional nonuniform spatially-varied random parameters. The robust optimization is formulated to model the nonuniform spatial distribution of random variables by stochastic process model with a reduced set of random variables. The proposed approach integrates the robust optimization formulation and the level set-based topology optimization. The robust optimization is formulated to minimize the robust compliance that is defined as a weighted sum of the expected value and the standard deviation of mean compliance under volume constraint. Through numerical examples, the validity of the proposed robust topology optimization approach is demonstrated. Also, the eects that uncertain random parameters have upon the obtained robust optimum configurations are investigated through the power spectrum of the structural response.