On the shear buckling of porous nanoplates using a new size-dependent quasi-3D shear deformation theory

This article is motivated by the lack of a study on the size-dependent shear buckling force of functionally graded materials. In this study, the shear buckling force of imperfect FG nanoplates including porosities while resting on an elastic Kerr foundation and exposed to hygrothermal environment is analyzed. Three different templates of porosity distributions (even, uneven, and logarithmic-uneven distribution templates) are taken into account. Hamilton’s principle is employed to derive the governing equations based on a new polynomial quasi-three-dimensional (quasi-3D) shear deformation theory in conjunction with the Eringen nonlocal differential model (ENDM). Coupling effects between bending, shear, and thickness stretching are included by using the quasi-3D theory, and the size effects are considered by using the ENDM. Galerkin method is applied to find the shear buckling forces. A comparative study is given by using various structural models. By considering the size-dependent effects on the shear buckling of FG nanoplates, the influence of power-law index, porosity amount, and template, geometry, temperature, moisture, and elastic foundation components is explored.