Multi-objective optimization for maximum fundamental frequency and minimum cost of hybrid graphene/fibre-reinforced nanocomposite laminates

Abstract

The present article proposes a multi-objective optimization study aiming at the optimal cost-effective design of nano-reinforced laminates. To maximize the fundamental frequency and minimize the cost, a hybrid laminate is studied, introducing both conventional fibres and graphene nanoplatelets reinforcement. A multi-objective genetic algorithm optimization is adopted to provide the optimal natural frequency and cost for the laminate. Optimization is implemented using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which converges to near-optimal solutions for all scenarios tested. The vibration problem is solved using the finite element method and the first-order shear deformation theory. Effective material properties are derived using micromechanical equations. Different optimization problems are solved using one to four types of design variables, including graphene and fibre distribution along the thickness, layer thickness, and fibre angles. Results indicate that increasing the graphene nanoplatelets content and keeping the minimum fibre content leads to cost-effective design. A drastic increase in the fundamental frequency and decrease in the cost is obtained for the hybrid graphene/fibre-reinforced laminate compared to conventional fibre-reinforced composites.