Material optimization of functionally graded plates using deep neural network and modified symbiotic organisms search for eigenvalue problems

The paper is aimed at improving computational cost enhanced by a new combination of deep neural network (DNN) and modified symbiotic organisms search (mSOS) algorithm for optimal material distribution of functionally graded (FG) plates. The material distribution is described by control points, in which coordinates of these points are located along the plate thickness using B-spline basis functions. In addition, DNN is used as an analysis tool to supersede finite element analysis (FEA). By using DNN, solutions can directly be predicted by an optimal mapping which is defined by learning relationship between input and output data of a dataset in training process. Each of dataset is randomly created from analysis through iterations by using isogeometric analysis (IGA). The mSOS being a robust metaheuristic algorithm is employed to solve two optimization problems: buckling and free vibration with various volume constraints. Moreover, the power of mSOS is verified by comparing to other algorithms in the open literature. Finally, optimal results in all examples generated by the proposed method are compared to those of a combination of IGA and mSOS to demonstrate its effectiveness and robustness.