Optimization of Functionally Graded Beams Resting on Elastic Foundations

In this study, two goals are followed. First, by means of the Generalized Differential Quadrature (GDQ) method, parametric analysis on the vibration characteristics of three-parameter Functionally Graded (FG) beams on variable elastic foundations is studied. These parameters include (a) three parameters of power-law distribution, (b) variable Winkler foundation modulus, (c) two-parameter elastic foundation modulus. Then, volume fraction optimization of FG beam with respect to the fundamental frequency is studied. Since the optimization process is so complicated and time consuming, Genetic Algorithm (GA), a computational algorithm based on Darwinian theories that allow to solve optimization problems without using gradient-based information on the objective functions and the constraints, is performed to obtain the best material profile through the thickness to maximize the first natural frequency. A proper Artificial Neural Network (ANN) is trained by training data sets obtained from GDQ method and then is applied as the objective function in genetic algorithm by reproducing the fundamental frequency for improving the speed of the optimization process. Finally, the optimized material profile for the maximum natural frequency of a FG beam resting on elastic foundations is presented.