Implementation of Penalty Method for Optimization of FGM Beams

In this study, optimization of four-parameter power-law distribution of functionally graded (FG) beams resting on elastic foundations for the density with constraint on the frequency parameter is presented. To perform optimization, Genetic Algorithm (GA) is used to find the optimal solution. Genetic Algorithms is most directly suited to unconstrained optimization. Thus, penalty method is implemented for handling the existing constraints. A proper artificial neural network (ANN) is trained by training data sets obtained from generalized differential quadrature (GDQ) method and then is applied to reproduce the behavior of the structure both in free vibration and density for improving the speed of the optimization process.