Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment

Abstract

Abstract This work proposes a novel quasi three-dimensional (3D) approach for the bending analysis of moderately thick plates with a functionally graded material (FGM), in presence of porosities due to some incorrect manufacturing processes. Such porosities can appear within the plate in two forms, namely, even and uneven distributions. The modeled system has a polymer matrix where both shear and transverse factors coexist. The bending equations of the problem are obtained from the Hamiltonian principle. In order to apply the quantum effects for the nanosystem, the well-known nonlocal theory of Eringen is here assumed, while checking for its numerical accuracy. A physically-consistent analysis of the nanostructures would investigate possible surrounding effects. Thus, the thermal and humidity influence is accounted for the 3D problem, whose governing equations are solved through a semi-analytical polynomial method (SAPM), as recently proposed in literature for different applications. The proposed method is based on a simple procedure with very accurate numerical outcomes, whose performance is checked against the available literature. After computing the deflection relations, a systematic study is performed for the bending response of nanoporous FGMs in a hygro-thermal surrounding environment, with promising results for practical applications.