Multi-dimensional optimization of functionally graded material composition using polynomial expansion of the volume fraction

The work of this paper proposes a method for multi-dimensional optimization of functionally graded materials (FGMs) composition. The method is based on using polynomial expansion of the volume fraction of the constituent materials. In this approach, the design variables are the coefficients of the polynomial expansion which to be determined through the optimization process. This method provides much more flexibility in the design compared to the methods based on the power-law, or the exponential-law which will in turn lead to more optimal designs. Also it requires much less number of design variables compared to the grid based approaches which is also utilized for two-dimensional optimization of FGMs structures. As an application of the proposed method, the optimization of a simply supported Aluminum plate reinforced with Silicon Carbide nano-particles is considered. Cost plays a very important role for this type of structures, since the cost of the reinforcements such as Silicon Carbide nano-particles, or carbon nano-tubes is too high. So the aim of the optimization process is to minimize the amount of the reinforcement required to satisfy certain performance criteria. Both static, and dynamic cases are considered in this work; a plate under a transverse pressure distribution is considered as the static case, and the panel flutter problem as the dynamic case.