A novel finite element model in nonlocal transient analysis of viscoelastic functionally graded porous nanoplates resting on viscoelastic medium

Abstract

The transient analysis of viscoelastic functionally graded porous (FGP) nanoplate resting on the viscoelastic medium using the finite element method (FEM) is studied in this work. The nanoplate is made from a material that varies in thickness and has mechanical qualities that change depending on the porosity. The whole of the mechanical system rests on a Pasternak medium, which is modeled in accordance with a Kelvin–Voigt viscoelastic model. The general plate motion balance equations are developed by the application of the higher‐order shear plate theory (HSDT) with a new inverse hyperbolic function, the nonlocal hypothesis, and Hamilton's principle. In order to develop a four‐node quadrilateral element, Lagrangian and Hermitian interpolation functions are used. These functions are employed to define the main variables that correspond to the in‐plane displacements and the transverse displacements, respectively. The direct integration method developed by Newmark is used to calculate the dynamic responses of the plate. The outcomes that were anticipated by the essay have been confirmed by reputable sources. The dynamic response characteristics of a viscoelastic FGP nanoplates that is placed on a viscoelastic medium are explored, and a number of factors that influence these features are discovered and explained.