弹性基础上方形板的二次分叉

Secondary Bifurcation of a Square Plate on an Elastic Foundation

本文研究了弹性基础上,一对边受到面内均匀压力的四边简支方板,当其最低两屈曲荷载很近时的后屈曲行为.应用Liapunov-Schmidt约化揭示了板的二次分叉现象并给出原始后屈曲分支及二次分支的渐近展开.从稳定性分析出发,指明从最小屈曲荷载产生的原始后屈曲分支是稳定的;从第二屈曲荷载产生的原始后屈曲分支经二次分叉由不稳定变得稳定;由应用二次分叉计算方法对板所做的数值计算,给出了有关二次分叉数值结果的图表.

The present paper deals with the post-buckling behavior of a simply supported elastic square plate on an elastic foundation. The attention is focused on those values of foundation stiffness at which, under uniaxial load, the plate becomes critical with respect to two nearly simultaneous buckling load. At first, we revealed the secondary bifurcation of the plate and gave the asymptotical expansion of the primary post-buckling branch and the secondary branch by means of Liapunov-Schmidt reduction; on the basis of the analysis of stability, we also found that the primary post-buckling branch from the lowest buckling load is stable, and unstable one from the second buckling load becomes stable after secondary bifurcation. Secondly, numerical computations of the secondary buckling of the plate was done by the method which has been developed by the author. The numerical results are given in figures and tables.