Size-dependent bending and buckling of two-dimensional functionally graded microplates, an artificial neural network approach

The main goal of the present study is to focus on the application of artificial neural network (ANN) in predicting the bending and buckling behaviors of size-dependent small-scale micro-plates. To this end, the recently introduced thick microplates made of two-dimensional functionally graded materials (2D-FGM) with simply supported boundary conditions are considered. Adopting the modified couple stress and third-order shear deformation theories together with the Ritz method, the bending and buckling ANN models, including nine and ten input variables, are trained by two databases containing 8842 and 9980 random data for each of these two analyses, respectively. The selected network has six hidden layers, each of them contains 32 nodes. Employing the present ANN model, whose determination coefficient is 98.6%, the variation of microplate deflection and its buckling load versus the input variables are investigated. It is observed that despite the long run-time and the complexities involved in the solution procedures associated with the governing equilibrium and eigenvalue equations, the ANN models enjoy fast and accurate predictions. The rest of the present work is devoted to optimizing the geometric and material variables of a 2D-FGM microplate with respect to the buckling load via the genetic algorithm (GA) method whose fitness function is evaluated by the trained ANN. The results reveal that the combination of the ANN and GA can be treated as a promising tool for optimizing the geometric and material parameters of a 2D-FGM microplate regarding its buckling load.