An Efficient Robust Optimization Method for Two-Bar Structures under Uncertain Loading

Abstract

Uncertainty is omnipresent in manufacturing and engineering community. This paper develops an efficient robust optimization framework for a two-bar structural model under uncertain loading, which includes magnitude and direction uncertainty following Gaussian distribution. This framework aims to simultaneously minimize the expectancy and standard deviation of structural compliance with volume constraints. A reasonable and efficient estimation of the statistical moment of structural compliance is recognized the critical to the probability-based RTO problem. To address the computational challenges associated with high dimensionality in traditional surrogate models, a decoupling technique based on non-intrusive polynomial chaos expansion is developed. Such a numerical evaluation tool is generic for different types of structures. In addition, an analytical expression based on a two-bar structure is derived as a standard reference. The cross-sectional area and angle with horizontal direction of each bar are taken as design variables and optimization is achieved using the optimality criteria. Numerical examples demonstrate that the accuracy and efficiency of the reported algorithm are significantly improved compared to conventional methods such as polynomial chaos expansion and Monte Carlo simulation. The optimized designs prove a better robust performance than their counterparts.