Level Set-Based Robust Topology Optimization Using Stationary Stochastic Process Model

Abstract

A robust topology optimization approach in consideration with random field uncertainty in loading condition is proposed in this paper. The proposed method integrates the level set-based topology optimization and the robust design method using stochastic process model. The stochastic process model is applied to describe the uncertainty of design parameters with nonuniform distribution in space with a reduced set of random variables. 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. The standard deviation of mean compliance is approximated by the first-order sensitivity with respect to random variables that are described through the assumed spectral distributions from Wiener-Khintchine theorem. As a topology optimization, a level set-based approach incorporating a fictitious interface energy proposed by parts of the authors is applied. The method has several advantages to makes it possible to change structural topology as well as boundary shapes and to control the geometrical complexity of the optimum configuration qualitatively. Through numerical examples, the efficiency of the proposed robust topology optimization approach is demonstrated by comparing between the deterministic and robust optimum configurations.