Unraveling the buckling phenomena in butterfly-shaped auxetic nanostructures: A nonlocal strain gradient approach

This article is focused on the examination of the buckling properties of butterfly-shaped honeycomb (BSH) auxetic doubly curved nanoshells. First, higher-order shear deformation theory (HSDT) is applied, followed by nonlocal strain gradient theory (NSGT) and Hamilton’s method to derive the motion equations. Finally, Navier’s method is employed to analyze the buckling behavior of BSH nanoshells by solving these equations. The numerical results of this research are compared with previous works, and thus, the accuracy of the results is confirmed. Furthermore, a comprehensive analysis is conducted on how the nonlocal parameter, strain gradient length scale, curvature radius, and geometric dimensions of the butterfly-shaped auxetic structure influence the behavior of the BSH nanoshell.