Static stability of functionally graded porous nanoplates under uniform and non-uniform in-plane loads and various boundary conditions based on the nonlocal strain gradient theory

Abstract

This work examines the buckling behavior of functionally graded porous nanoplates embedded in elastic media. Size effects are added to the nanoplate constitutive equations using nonlocal strain gradient theory. The four-variable refined plate theory is employed for nanoplate modeling. This theory assures stress-free conditions on both sides of the nanoplate and has less uncertainty than high-order shear deformation theories. It is postulated that the nanoplate experiences in-plane compressive loads, which may have both linear and nonlinear distributions. Additionally, uniform and non-uniform porosity distributions are considered. The governing partial differential equations are extracted using the notion of the minimal total potential energy. Following this, the Galerkin method is employed to solve these equations utilizing trigonometric shape functions. Simple, clamped, and combined boundary conditions for nanoplate edges are studied. Once the governing algebraic equations were extracted, the critical buckling load of the nanoplate is determined. To conduct a validation study, the obtained data are juxtaposed with the findings of previous studies, revealing a notable level of concurrence. After the critical buckling load has been ascertained, an inquiry is undertaken to assess the influence of various parameters including nonlocal and length scale parameters, boundary conditions, porosity distribution type, in-plane loading type, geometric dimensions of the nanoplate, and stiffness of the elastic environment, on the static stability of nanoplates.