Numerical optimization of volume fraction distributions in FGM sandwich beams with FG-CNTRC facesheets

This paper presents a numerical method for the optimal tailoring of volume fraction distributions of reinforcement materials (pillars) within FGM (functionally graded material) sandwich beams with FG-CNTRC (functionally graded CNT-reinforced composite) facesheets. Since the mechanical behaviors of sandwich beams vary depending on the distribution pattern of reinforcement materials (CNT and ceramic in this paper) through the thickness, the tailoring of these distribution patterns is important to enhance the mechanical performance. In the present study, the thickness-wise distributions of CNT in the facesheets and ceramic in the core are optimized to maximize the fundamental natural frequency of sandwich beams, based on the exterior penalty-function method and the golden section method. The developed optimization method is verified and the resulting optimum distributions of CNT and ceramic are compared with the primitive functionally graded distribution patterns which are widely adopted in the literature. Moreover, the volume fraction distributions of CNT and ceramic are also individually optimized, and the optimum results between simultaneous (SO) and individual optimizations (IO) are compared.