Buckling and postbuckling response of nonlocal strain gradient porous functionally graded micro/nano-plates via NURBS-based isogeometric analysis

The prime objective of the present investigation is to analyze the nonlinear buckling and postbuckling characteristics of micro/nano-plates made of a porous functionally graded material (PFGM) in the presence of nonlocality and strain gradient size dependencies. In accordance with this purpose, a modified porosity-dependent power-law function is put to use to estimate the effective mechanical properties of PFGM micro/nano-plates with various porosity distribution patterns. To solve the constructed nonlinear nonlocal strain gradient problem, the non-uniform rational B-spline (NURBS)-based isogeometric analysis is utilized as an efficient discretization technique. It is concluded that by taking the geometrical nonlinearity into account and moving to deeper part of the postbuckling regime, the significance of the both nonlocality and strain gradient size dependencies decreases. Also, by increasing the material property gradient index, an enhancement in the nonlocal and strain gradient size effects is found which is more considerable at deeper part of the postbuckling domain. In addition, it is demonstrated that for a PFGM micro/nano-plate, the value of the porosity index has a negligible influence on the significance of size dependencies, and this observation is the same for the both types of simply supported and clamped boundary conditions.

Automated summary

The study shows that considering geometric nonlinearity and moving to deeper part of the postbuckling regime reduces the significance of both nonlocality and strain gradient size dependencies. Additionally, increasing the material property gradient index results in an enhancement of nonlocal and strain gradient size effects, especially in the deeper part of the postbuckling domain. Moreover, the study demonstrates that the porosity index has a negligible influence on the significance of size dependencies for a PFGM micro/nano-plate, regardless of the boundary conditions.