Numerical Optimization of CNT Distribution in Functionally Graded CNT-Reinforced Composite Beams

This paper is concerned with the numerical optimization of the thickness-wise CNT (carbon nanotube) distribution in functionally graded CNT-reinforced composite (FG-CNTRC) beams to secure the structural safety. The FG-CNTRC in which CNTs are inserted according to the specific thickness-wise distribution pattern are extensively investigated for high-performance engineering applications. The mechanical behaviors of FG-CNTRC structures are definitely affected by the distribution pattern of CNTs through the thickness. Hence, the tailoring of suitable CNT distribution pattern is an essential subject in the design of FG-CNTRC structure for a given boundary and loading conditions. Nevertheless, the thickness-wise CNT distribution pattern has been assumed by several linear functions so that these assumed primitive patterns cannot appropriately respond to arbitrary loading and boundary conditions. In this context, this paper aims to introduce a numerical method for optimally tailoring the CNT distribution pattern of FG-CNTRC beams. As a preliminary stage, the effective stress is defined as the objective function and the layer-wise CNT volume fractions are chosen as the design variables. The exterior penalty-function method and golden section method are adopted for the optimization formulation, together with finite difference scheme for the design sensitivity analysis. The proposed optimization method is illustrated and validated through the benchmark experiments, such that it successfully provides an optimum CNT distribution which can significantly minimize the effective stress, with a stable and rapid convergence in the iterative optimization process.