A mode-independent energy-based buckling analysis method and its application on substrate-supported graphene

Stability is an important problem in applications of plate and shell structures as well as newly arisen nano-structures, such as nanotubes and graphene sheets. Most classical methods for stability analysis require buckling modes, which are difficult to be accurately predicted, especially for the structures with complex boundary boundaries and load conditions. In this paper, we propose a half-analytical method to predict the critical buckling of structures, named mode-independent energy-based buckling analysis method (MIEM), in which the buckling mode is not needed to be presupposed. The proposed MIEM shows great superiority in dealing with structure buckling under complicated loads and constraints. Besides, it is more suitable for large-scale nanostructures due to its extremely small amount of calculations, and the calculation amount can be further reduced for periodic structures. With the MIEM, the critical buckling of substrate-supported graphene sheets under complex strain states is investigated comprehensively. Furthermore, a unified criterion to predict the critical buckling of substrate-supported graphene is given by a simple expression, which could be of great help in design and manufacture of graphene-based electronics and devices. The MIEM developed in this paper can be used in buckling analysis of structures such as beams and plates as well.