Optimization of in-plane functionally graded panels for buckling strength: Unstiffened, stiffened panels, and panels with cutouts

The work of this paper deals with the in-plane material optimization with the objective of minimizing the amount of the nano-reinforcement required to satisfy the desired buckling constraints. The minimization of the reinforcement is necessary for nano-reinforced composites because the price of the reinforcement is very high. Three types of panels are considered; (1) unstiffened panel, (2) panels with cutouts, and (3) stiffened panels. The in-plane distribution of the reinforcement is represented using the polynomial expansion technique which is also extended to model non-rectangular domains via coordinates transformation. It was found that material grading can saves a very significant amount of the reinforcement up to 200% relative to homogenous panels. The saving of the reinforcement depends on four factors; (1) the problem nature, (2) the boundary conditions, (3) the applied loads, (4) the direction of the material gradings.