Volume fraction optimization of four-parameter FGM beams resting on elastic foundation

Abstract

This paper deals with volume fraction optimization of Functionally Graded (FG) beams resting on elastic foundation for maximizing the first natural frequency. The two-constituent functionally graded beam consists of ceramic and metal. These constituents are graded through the thickness of beam according to a generalized power-law distribution. One of the advantages of using generalized power- law distribution is the ability of controlling the materials volume fraction of FG structures for considered applications. The primary optimization variables are the four parameters in the power-law distribution. Since the search space is large, the optimization processes becomes so complicated and too much time consuming. Thus a novel meta–heuristic called Imperialist Competitive Algorithm (ICA) which is a socio-politically motivated global search strategy is applied to find the optimal solution. A proper and accurate Artificial Neural Network (ANN) is trained by training data sets obtained from generalized differential quadrature (GDQ) method to reproduce the behavior of the structure in free vibration. The ANN improves the speed of optimization process by a considerable amount. The performance of ICA is evaluated in comparison with other nature inspired technique Genetic Algorithm (GA). Comparison shows the success of combination of ANN and ICA for design of material profile of FG beam. Finally the optimized material profile for the optimization problem is presented.