Bending and hygro-thermo-mechanical vibration analysis of a functionally graded porous sandwich nanoshell resting on elastic foundation

This article presents the finite element method (FEM) used four-unknown shear deformation theory for the static bending and hygro-thermo-mechanical vibration analysis of sandwich functionally graded porous (SFGP) doubly curved nanoshells resting on the elastic foundation (EF). The configurations of SFGP nanoshells include a homogenous core made of full ceramic while the top and bottom layers vary through the thickness with the law of uneven porosity distribution. The governing equations are obtained by using Hamilton’s principle and the nonlocal elasticity theory of Eringen (nonlocal theory). For the first time, a four-node quadrilateral element with ten degrees of freedom (DOFs) for each node using Lagrangian and Hermitian interpolation functions to approximate the membrane and bending displacement fields are proposed to analyze the SFGP nanoshells. The numerical results are compared with other exact solutions to evaluate the performance of the proposed method. Furthermore, influences of geometrical parameters and material properties such as the power-law index n, the porosity coefficient (Formula presented.) the nonlocal coefficient (Formula presented.) and EF-stiffness (Formula presented.)) on the static bending, free vibration of SFGP nanoshells are comprehensive studied.