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

Abstract

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 $\xi ,$ the nonlocal coefficient $\mu ,$ and EF-stiffness $(K_w, K_s$) on the static bending, free vibration of SFGP nanoshells are comprehensive studied.

Keywords:

• Nonlocal elasticity theory
• FGP material
• nanoshell
• elastic foundation
• four-unknown shear deformation theory

Disclosure statement

The authors declared that they have no conflict of interest.

Ethical statement

This research was done according to ethical standards.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.