Robust topology optimization of thin plate structure under concentrated load with uncertain load position

Abstract

This study investigates the robust topology optimization of a thin plate structure under a concentrated load with load position uncertainty. The effect of uncertain load direction, load magnitude, and load distribution in topology optimization problems has been investigated in previous research, but few studies have dealt with robust topology optimization considering load position uncertainty. In this study, load position uncertainty is modeled using the convex hull model, in which the load position uncertainty is confined within a circular area whose center is at the nominal load position. The worst load condition is defined as that when the applied load is at a position in the convex hull that gives the worst value of the mean compliance. Here, the robust objective function is formulated as a weighted sum of the mean compliance obtained from the mean load condition and the worst compliance obtained from the worst load condition, with a plate model based on Reissner-Mindlin plate theory. The robust topology optimization problem is formulated using a level set-based topology optimization method. Through numerical examples, robust optimum configurations are compared with deterministic optimum configurations and the validity of the proposed robust design method is then discussed.