Design optimization of continuous fiber composites with thermo-mechanical coupling and load uncertainties

Abstract

This paper introduces a theoretical framework for the design optimization of continuous fiber composites reinforced with continuous fiber trajectories subject to thermo-mechanical coupling and load uncertainties. Different uniform temperature variations are applied in the structure to investigate the influence of ambient temperature change on the structural performance. To consider the external load uncertainties, a robust design optimization model is proposed where the loads are modeled as hybrid variables, namely magnitudes as random variables and directions as interval variables, with the robust objective determined through a hybrid orthogonal polynomial expansion method. Furthermore, we use a level-set function to represent the structural boundary, with its evolution driven by shape derivatives calculated based on uncertainty analysis. The continuous fiber paths are subsequently determined by the level-set isoline extracted from the structural boundary, which in turn influences the structural mechanical performance due to the material anisotropy of composites. The continuity of continuous fiber and the equal space between adjacent trajectories largely ensure the additive manufacturability of the composites. Three numerical examples are presented to demonstrate the effectiveness of the developed framework. The results show that the ambient temperature variations and load uncertainties largely impact the optimized topology and fiber infill patterns of composites, thus are important to be considered in the design stage. Moreover, the optimized structure can have a 5-fold stiffness per unit mass compared with the initial design thus largely increasing the material efficiency in carrying external uncertain loads.