Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation

This article aims to study bending, buckling, and free vibration behaviors of the functionally graded porous (FGP) nanoshell resting on an elastic foundation (EF) including static bending, free vibration, hydrothermal-mechanical buckling. We use the four-unknown high-order shear deformation theory based on Eringen's nonlocal theory and Hamilton's principle to obtain the system of the governing differential equations. By using Navier's solution, the static, buckling, and free vibration responses of the FGP nanoshells are solved. The FGP material with uneven porosity and logarithmic-uneven porosity distribution is employed. The EF is a Winkler-Pasternak foundation with the stiffness coefficient k(w) and sliding stiffness coefficient k(s). The numerical results in the present work are compared with those of the published works to evaluate the accuracy and reliability of the proposed formulas. Afterward, the influences of the geometric dimensions, material properties, and the elastic foundation stiffness on the response of the FGP nanoshell is studied in detail.