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.

为了研究尺寸对微梁热屈曲行为的影响，提出了一种基于修正梯度弹性的尺寸依赖型热屈曲模型。应用变分原理推导了模型的控制方程和边界条件。求解了不同支撑梁的数值示例。给出了临界屈曲温度升高和不同模态的归一化挠度。结果表明，光束尺寸越小，临界屈曲温度上升幅度越大。内部长度尺度显着影响每种模式的临界屈曲温度升高，并且这种影响主要受厚度方向上的应变梯度控制。选择不同的高阶边界条件引起的临界屈曲温度升高的差异不容忽视。与其他尺寸依赖模型相比，该模型具有明显的物理意义和简单形式。