Combination of FEM-DQM for nonlinear mechanics of porous GPL-reinforced sandwich nanoplates based on various theories

In this novel work, applying boundary shape function differential quadrature hierarchical finite element method (DQHFEM) will be employed to analyze frequency, damping, bending, and buckling of an embedded sandwich nanoplate using different plate theories such as refined zigzag theory (RZT), sinusoidal shear deformation theory (SSDT), first-order shear deformation theory (FSDT) and classical plate theory (CPT). The face sheets as well as the core layer of the sandwich structure respectively are formed by porous material and nanocomposites reinforced with graphene platelets (GPLs) considering various dispersion. According to the Halpin-Tsai micromechanics model, Young's modulus, as well as the rule of mixture for density as well as Poisson's ratio related to the face sheets, can be obtained. Further, for modeling the mentioned sandwich structure much more realistic, Kelvin-Voigt model is applied. In order to gain motion of equations, D'Alembert's principle is utilized where size influences can be contemplated as well using higher-order strain gradient nonlocal theory. In this comprehensive research, diverse parameters featuring the influences of structural damping, strain gradient parameters, GPL volume percent, dispersion, viscoelastic medium, porosity, boundary edges, and geometric variables upon vibration, buckling, and bending behaviors correlative to this structure. It is ascertained that RZT is the most accurate theory among other mentioned theories in estimating the static and dynamic response of structure which needs no shear correction factors. Moreover, the presence of GPLs can make the entire sandwich structure stiffer and dispersion patterns of pores, as well as GPLs, can affect the vibration, buckling, and bending of the structure.