Nonlinear dynamic investigation of plates: Considering seismic loads, strain rate, material, and geometrical nonlinearities

Abstract This study presented a nonlinear dynamic approach to investigate dynamic responses of the plated structures taking into account the strain rate, material, and geometrical nonlinearities. The higher-order shear deformation theory was employed together with Hamilton’s principle to obtain governing equations of motion. The inclusion of material and geometrical nonlinearities as well as considering the effects of strain rate resulted in a very strong and accurate approach for analyzing the plated structures, especially, under severe dynamic loads such as seismic load. This approach was designed such that it can be employed for all types of rectangular plates such as isotropic, sandwich, composite, and functionally graded material (FGM) plates. The set of equations of motion were reduced in the form of nonlinear dynamic equations to enable solving them, which was carried out using the Runge-Kutta method through the mathematical model Maple. Besides, the governing equations of stress along with the plate thickness were derived, and the calculated stresses were plotted concerning the variation of thickness. The validity of the method was evaluated through two types of analysis: static and dynamic such that the results obtained from the presented method were compared with those of literature and those obtained from a numerical model employing ABAQUS. The small discrepancy among the results proved the accuracy and validity of the method of this study. Thereafter, to examine the application of the presented method of this study two example problems were defined: one dealing with a sandwich plate with FGM faces and a steel core and the other considering a composite laminate of four layers. The aim was to investigate dynamic responses of the plates and stress distribution through the plate thickness, subject to a real seismic load resulted from a Vrancea earthquake that occurred in Romania.