## 1 Introduction  
In the last decades, an increased interest in porous materials has arisen among scientists and designers regarding engineering materials and structures due to their remarkable mechanical properties, electrical conductivity and high permeability. Besides, porous materials can be used in the aerospace industry and sea structures because of their very low density, but also in submarines, reformers and catalysts owing to their high specific surfaces. Thus, many investigations on the mechanical behavior of functionally graded (FG) porous plate and shell structures have been increasingly conducted in the literature from a theoretical, experimental and computational standpoint. [PERSON] [1] was one of the pioneers who investigated the buckling response of a fluid-saturated porous slab under an axial compression, and checked for the sensitivity of the buckling load to pore compressibility. Similarly, [PERSON] and [PERSON] [2] suggested an analytical determination of the critical buckling load of a compressed porous beam based on a broken-line hypothesis and the principle of stationary action for the total potential energy. A shear deformation theory was applied in [3] for the buckling study of porous beams with varying material properties, and in [4] for the bending and buckling of rectangular plates made of a foam material with a nonlinear symmetric porosity distribution. In the further work by [PERSON] et al. [5], the elastic buckling behavior of shear deformable FG porous beams was studied systematically to check for the effect of different porosity distributions on the mechanical response. A multiple analytical, numerical and experimental approach was proposed by [PERSON] et al. [6] for the buckling study of plates and beams, with a foam core and external layers of perfect material. In the last decades, different higher-order assumptions have been integrated with high-performance computational methods to treat buckling problems of perfect and/or porous composite structures. A nonlinear dynamic buckling of FG porous beams was performed by [PERSON] et al. [7]. The Galerkin method was applied by the authors to determine the governing equations of the problem, which was then solved numerically by means of a fourth-order Runge-Kutta method. A different approach based on a generalized differential quadrature (GDQ) method was applied by [PERSON] et al. [8] to analyze the nonlinear and linear buckling behavior of FG porous Euler-Bernoulli beams. A refined theory was also proposed by [PERSON] and [PERSON] [9] to treat the buckling problem of smart magneto-electro-elastic-FG porous plates, accounting for two different FG distributions. Hyperbolic higher-order shear deformation theory (HSDT) was combined with a mesh-free approach in [10] to investigate the buckling and free vibration behavior of porous FG plates resting on an elastic foundation. Among coupled problems, [PERSON] et al. [11] focused on the nonlinear thermomechanical buckling and post-buckling of porous FG plates with two poro/nonlinear symmetric and non-symmetric distributions, by using the [PERSON]'s HSDT and Galerkin method. Further recent contributions on the buckling and free vibration response of perfect and porous FG plates applied first-order shear deformation theory (FSDT) combined with the Chebyshev Polynomials-Ritz method [12; 13; 14; 15], even for graphene-reinforced nanocomposites. [PERSON] et al. [16], instead, proposed a Galerkin-based solution for the nonlinear buckling and post-buckling study of imperfect porous plates subjected to different mechanical loads while applying classical shell theory-Von Karman nonlinearity. In addition, [PERSON] et al. [17] focused on a novel quasi-3D HSDT to assess the buckling and vibration response of FG plates, whose solution was determined analytically. [PERSON] et al.