Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous-cellular core reinforced with graphene nanoplatelets

Abstract This paper presents a robust and accurate analytical solution based on the refined higher-order shear deformation theory for establishing the buckling capacity of a series of simply-supported sandwich plates. Each sandwich plate consists of an open-cell metal foam core with various pore distributions and two metal face sheets. Cores with and without GNP-reinforcements are considered. Three different distributions of porosity are considered for the core (i.e., uniform and two different non-uniform distributions along the thickness of the core). The effective properties of the porous cores are estimated by employing the modified Halpin-Tsai micromechanical model and the rule of mixture. The governing differential equations are solved analytically using the Navier method. The integrity of the proposed solution is evaluated through comparisons of the calculated buckling capacities for an isotropic and a set of porous plates against those obtained using the numerical and analytical solutions available in the literature. Subsequently, the Box-Behnken design (BBD) statistical method, which is a subset of the response surface methodology (RSM), is employed to investigate the simultaneous effect of the input variables (i.e., porosity coefficient, the core to total thickness ratio and the weight fraction of graphene nanoplatelets (GNPs)) on the buckling capacity of the sandwich plates. This is followed by the development of a set of simple and practical equations for evaluating the critical buckling capacity of the sandwich plates as a function of the input variables.