  We investigate the in-plane oscillations of the relaxed shape graphene due to
externally applied tensile edge stress along both the armchair and zigzag
directions. We show that the total elastic energy density is enhanced with
temperature for the case of applied tensile edge stress along the zigzag
direction. Thermo-electromechanical effects are treated via pseudomorphic
vector potentials to analyze the influence of these coupled effects on the
bandstructures of bilayer graphene quantum dots (QDs). We report that the level
crossing between ground and first excited states in the localized edge states
can be achieved with the accessible values of temperature. In particular, the
level crossing point extends to higher temperatures with decreasing values of
externally applied tensile edge stress along the armchair direction. This kind
of level crossings is absent in the states formed at the center of the graphene
sheet due to the presence of three fold symmetry.
