Robust Optimum Designs of Fiber-reinforced Composites Using Constraints with Sensitivity

Abstract

An efficient method of optimization considering manufacturing uncertainties is proposed in this article. By including the sensitivities and uncertainties in the modified constraints, a robust optimum design problem is formulated, which analytically deals with the effects of manufacturing uncertainties by a maximizing procedure. Although the maximizing procedure utilizes the similar concept of anti-optimization technique, and a numerical method is still needed for the optimization sub-problem, the anti-optimization sub-problem is analytically, rather than numerically, solved in the proposed method. It is therefore more efficient in computing time than traditional anti-optimization technique where both optimization and anti-optimization sub-problems are solved numerically. The proposed method is used for the robust optimum design of fiber-reinforced composites, which have wide scatters of stiffness, stress, and factor of safety due to the inherent manufacturing uncertainties of ply-thickness and ply-orientation. The accuracy of the new method for robust optimum design is demonstrated by verifying examples with analytical solution. The effects of ply orientation and ply thickness uncertainties on optimum weight of composite plate are studied in the illustrated examples. It is found that the optimum weight increases with ply orientation and ply thickness uncertainties, and uncertainties have strong effect on the optimal weight in all analysis cases.