A computational three-dimensional elasticity theory for bending and frequency analysis of the axisymmetric circular/annular plates via machine learning and discrete singular convolution integration methods

Abstract

The present study deals with the frequency and bending behavior of annular/circular nanocomposite plates. The nanocomposite is made of three-phase materials of graphene oxide (nanoscale) and carbon fibers (microscale), and epoxy matrix (macro-scale) in multiple layers of different orientations. The governing equation extracted to investigate the multiscale hybrid laminated nanocomposite reinforced (MHLNR) is a three-dimensional elasticity theory. Furthermore, the whole structure is on the elastic substrate, which takes into account the horizontal forces in the calculations. The displacement compatibility and equilibrium condition are considered in the interlayers of the three, five, and seven layers of the composite structure. The bulk material properties at each layer are evaluated utilizing fiber micromechanics and Halpin–Tsai equations. The discrete singular convolution method is employed to transform the equations and solve equations. The obtained results are further verified using several references in this field. In addition, an adaptively tuned deep neural network model is designed based on the data of the current study to predict the results. Finally, a comprehensive parametric study is carried out to demonstrate the influences of different parameters on the internal stress field and frequency responses of the current sandwich structure.