基于偶应力理论的压杆屈曲载荷的尺寸效应

SIZE EFFECT ON THE BUCKLING LOADS OF SLENDER COLUMNS BASED ON A MODIFIED COUPLE STRESS THEORY

许多微尺度实验证实,一些材料在微尺度下的力学性能存在尺寸效应。基于修正偶应力理论研究细长压杆屈曲载荷的尺寸效应,利用变分原理得到细长压杆屈曲的控制方程和边界条件,求解相应的屈曲边界值问题。结果表明,当细长压杆的特征尺寸与其材料本征尺度参数相当时,其屈曲载荷显著增大,表现出明显的尺寸效应;而当细长压杆的特征尺寸远大于其材料本征尺度参数时,其屈曲载荷与传统理论值基本相等,即其尺寸效应消失。

Many micro experiments had shown that the mechanical properties of some materials at micro scales are size depen- dence. Based on modified couple stress theory, size effect on buckling loads of slender colunms has been analyzed theoretically. The governing equation and boundary conditions of slender coltunns are derived with the aid of variational principle and the solutions of corre- sponding boundary values problems for buckling are presented. The results show that the buckling load of slender columns increase re- markably as the characteristic sizes of slender columns become comparable to the material length scale parameter. However, the buckling load of slender columns conforms to that calculated from classical theory model when the characteristic sizes of slender columns are far greater than the material length scale parameter.