Natural frequency analysis and optimal design of CNT/fiber/polymer hybrid composites plates using mori‐tanaka approach, GDQ technique, and firefly algorithm

Abstract

In the present work, two main goals are followed. First, free vibrations of multiscale nanocomposite plates consist of agglomerated carbon nanotubes (CNTs), E‐glass fibers, and polymer are presented based on first‐order shear deformation theory. Mori‐Tanaka (MT) approach and fiber micromechanics are used to estimate the mechanical properties of CNT/fiber/polymer composite (CNTFPC) plate. For natural frequency analysis of the CNTFPC plate, 2‐D generalized differential quadrature (GDQ) method as an efficient and accurate numerical tool is implemented to solve the governing equations. The accuracy of the MT method and GDQ technique are examined by comparing the present results with the experimental or numerical data available in the literature. A parametric study is carried out to investigate the influences of CNTs volume fraction, CNTs agglomeration, fiber volume fraction, different geometrical parameters such as the thickness‐to‐length ratio, different laminate lay‐up (cross‐ply and angle‐ply) and various boundary conditions on the natural frequencies of CNTFPC plates. As for the second goal of the paper, stacking sequence optimization of CNTFPC plates is presented to maximize the fundamental natural frequency of the structure. The search space of optimization problem is large and consequently the optimization processes becomes too much time consuming. Therefore, a biologically‐inspired meta‐heuristic algorithm called firefly algorithm that solves optimization problems without using gradient‐based information on the objective functions and the constraints is applied to obtain the best stacking sequence of CNTFPC plate. POLYM. COMPOS., 39:1433–1446, 2018. © 2016 Society of Plastics Engineers