Influence of Third-Order Elastic Modulus on Postbuckling Behavior of Functionally Graded Porous Nanobeams: A Nonlocal Strain Gradient Approach

This study pioneeringly investigates the effect of material nonlinearity, characterized by the third-order elastic modulus, on the post-buckling characteristics of functionally graded porous nanobeams. To capture the small-scale effects, the nonlocal strain gradient theory is employed. The material properties are graded along the thickness based on a modified power-law formulation accounting for porosities. The governing equations are derived using Hamilton's principle within the framework of the EulerBernoulli beam theory and the von Krmn geometric nonlinearity. The resulting nonlinear equations for a simply-supported beam are solved numerically using the Generalized Differential Quadrature Method (GDQM) coupled with the pseudo-arc length continuation technique. A comprehensive parametric analysis is conducted to elucidate the influences of the third-order elastic modulus, nonlocal parameter, strain gradient length-scale parameter, porosity volume index, and power-law index. Results demonstrate that the third-order elastic modulus significantly alters the structural stiffness, thereby critically influencing the post-buckling load-deflection path. A positive nonlinear modulus increases the buckling load and reduces deflection, while a negative value has the opposite effect. This work provides novel insights into the intricate coupling of material and geometric nonlinearities at the nano-scale, with substantial implications for the design of advanced nano-electro-mechanical systems (NEMS).