This paper studies free vibrational behavior of porous nanocomposite shells reinforced with graphene platelets (GPLs). GPLs are uniformly and nonuniformly distributed thorough the thickness direction. Different porosity distributions called uniform, symmetric, and asymmetric are considered. The elastic properties of the nanocomposite are obtained by employing Halpin–Tsai micromechanics model. The GPL-reinforced shell is modeled via first order shear deformation theory and Galerkin's method is implemented to obtain vibration frequencies. New results show the importance of porosity coefficient, porosity distribution, GPL distribution, GPL weight fraction, and geometrical and foundation parameters on vibration behavior of porous nanocomposite shells.

A refined trigonometric higher-order plate theory is presented for bending analysis of simply supported functionally graded ceramic–metal sandwich plates. The effects of transverse shear strains as well as the transverse normal strain are taken into account. The number of unknown functions involved in the present theory is only four as against six or more in case of other shear and normal deformations theories. Several types of the present symmetric and non-symmetric sandwich plates are used. The faces are assumed to be functionally graded through the thickness, while the core layer is still homogeneous and made of an isotropic material. The present refined plate theory is used to derive the field equations of the functionally graded sandwich plates. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.

Here, free vibration analysis of functionally graded piezoelectric (FGP) plates with porosities is carried out based on refined four-unknown plate theory. The present plate theory captures shear deformation impacts needless of shear correction factor. A modified power-law model is adopted to describe the graded material properties of a functionally graded piezoelectric plate. Implementing an analytical approach, which satisfies different boundary conditions, governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in the literature. The impacts of applied voltage, porosity distribution, material graduation, plate geometrical parameters, and boundary conditions on vibration of porous FGP plate are discussed.

A simplified three-unknown shear and normal deformations nonlocal beam theory for thermo-electro-magneto mechanical bending analysis of a nanobeam with a functionally graded material core and two functionally piezomagnetic layers is studied in this paper. The assumed structure is subjected to mechanical, thermal, electrical, and magnetic loads. An initial applied voltage and magnetic load is considered on the functionally graded piezomagnetic material layers. Eringen’s nonlocal constitutive equations are considered in the analysis. Governing equations are derived according to the present refined theory using the principle of virtual displacements. The numerical results including the deflection, electric, and magnetic potential distribution are calculated in terms of important parameters of the problem such as applied electric and magnetic potentials, two parameters of temperature distribution, and nonlocal parameter. The numerical results indicate that increase in applied electric potential increases the deflection unlike the applied magnetic potential that decreases the deflection. Furthermore, it can be concluded that increasing the nonlocal parameter leads to increase in the deflection.

This research is concerned with the analysis of post-buckling of a nano-composite beam reinforced by graphene plateletes (GPLs) having geometrical imperfection. GPLs are uniformly and nonuniformly distributed thorough the thickness direction. Different porosity distributions are considered. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The postbuckling load-deflection relation is obtained by solving the governing equations having cubic nonlinearity applying Galerkin's method needless of any iteration process. New results show the importance of porosity coefficient, porosity distribution, GPL distribution, GPL weight fraction, geometrical imperfection, and foundation parameters on nonlinear buckling behavior of porous nanoscale beams. Specially, porosities and GPL reinforcement have a great impact on postbuckling configuration of both ideal and imperfect nanocomposite beams.