Optimal Tailoring of CNT Distribution in Functionally Graded Porous CNTRC Beams

This paper is concerned with the multi-objective optimization of thickness-wise CNT distribution in functionally graded porous CNT-reinforced composite (FG-porous CNTRC) beams. The mechanical behaviors of FG-porous CNTRC structures are strongly influenced by the thickness-wise distributions of CNTs and porosity. Nevertheless, several linear functions were simply adopted to represent the thickness-wise CNT distribution without considering the porosity distribution, so these assumed linear primitive CNT distribution patterns are not sufficient to respond to arbitrary loading and boundary conditions. In this context, this study presents the multi-objective optimization of thickness-wise CNT distribution in FG-CNTRC porous beams to simultaneously minimize the peak effective stress and the peak deflection. The multi-objective function is defined by the larger value between two normalized quantities and the design variable vector is composed of the layer-wise CNT volume fractions. The constrained multi-objective optimization problem is formulated by making use of the exterior penalty-function method and the aspiration-level adjustment. The proposed optimization method is demonstrated through the numerical experiments, and the optimization solutions are investigated with respect to the porosity distribution and the combination of aspiration levels for two single-objective functions. It is found from the numerical results that the optimum CNT distribution is significantly affected by the porosity distribution. Furthermore, the proposed method can be successfully used to seek an optimum CNT distribution within FG-porous CNTRC structures which simultaneously enhances the multi-objective functions.