考虑尺度影响的平面正交各向异性功能梯度微梁的屈曲分析

基于新修正偶应力理论，建立了能描述尺度效应的各向异性功能梯度微梁的屈曲分析模型。基于最小势能原理推导了控制方程及边界条件，并以简支梁为例分析了屈曲载荷及尺度效应受材料尺度参数和几何尺寸的影响。算例结果表明，在材料几何尺寸较小时，本文模型预测到的屈曲载荷明显大于传统理论的结果，有效地反映了尺度效应。几何尺寸较大时，尺度效应消失，本文模型将自动退化为传统宏观模型。模型反映出不同方向上的尺度参数对各向异性材料影响的效果不同。

Size-dependent buckling analysis of plane orthotropic functionally graded micro-beams

A model for the buckling analysis of functionally graded (FG) micro-beams is developed.In consideration of the plane ortho-anisotropy and the size effect of FG beams,the formulation is developed on the new modified couple stress theory.The model contains two material length scale parameters which are capable to separately represent the different scale effects in two orthogonal directions.A variational formulation based on the principle of minimum total potential energy is employed.A simply supported micro-beam is taken as an illustrative example and solved.When the beam thickness is small the results manifest that the buckling loads predicted by the new model are much higher than those predicted by the classical model.When the geometrical size of the beam is much larger than the material length scale parameters the present model degenerates to the classical macroscopic model.The scale effects influenced by the material length scale parameters in two directions are different.