A size-dependent thermal buckling model for micro-beams based on modified gradient elasticity

Abstract

To investigate the size effect in thermal buckling behaviors of micro-beams, a new size-dependent thermal buckling model based on modified gradient elasticity is presented. The governing equation and boundary conditions of the model are derived by applying the variation principle. Numerical examples of different supported beams are solved. The critical buckling temperature rises and normalized deflection of different modes are presented. The results show that the smaller the beam size is, the bigger the critical buckling temperature rise is. The internal length scales significantly affect the critical buckling temperature rises of each mode, and this effect is mainly controlled by the strain gradient on thickness direction. The difference of critical buckling temperature rises caused by choosing different higher-order boundary conditions cannot be ignored. Compared with other size-dependent models, the presented model is featured by evidently physical meaning and simple form.