梯度弹性细长压杆的稳定性分析

he problems of stability of slender columns are solved analytically on the basis of modified couple stress theory. The governing equations of equilibrium and the corresponding boundary conditions are obtained by a combination of the basic equations of modified couple stress theory and variational statement. The governing equations of equilibrium are solved and the buckling load of the slender column is assessed. It is found that the buckling load predicted by the newly established model is size-dependent. The difference between the buckling loads calculated from the newly developed model and classical model is significant when the characteristic sizes such as thickness and diameter are small, but is diminishing with the increase of the characteristic sizes. Comparison of buckling loads and buckling modal shapes for various boundary conditions are presented.