Buckling and post-buckling behavior of nano-laminates considering surface effects

Abstract

Based on the surface elasticity theory combined with the theories of Kirchhoff plate and Mindlin plate, the influences of surface effects on the buckling and post-buckling behaviors of nano-laminates are studied. Analytical solutions for critical buckling loads under uniaxial and biaxial compressions are obtained. Furthermore, approximate solutions for critical post-buckling loads under moveable and immoveable edge conditions are provided by using the Galerkin’s method. Numerical examples are given to study the influences of thickness, number of layers, surface parameters and the length of the nano-laminates on buckling and post-buckling critical loads. Results obtained indicate that the surface/interface energy is connected with the number of layers. In addition, the effects of the surface/interface energy on the critical loads enhance through increasing the length of the laminates but reduce by increasing the thickness. Mechanical model, analytical method and conclusions of this work are helpful for designing and examining the stability of the nano-laminates and nanoscale devices.