层合板分叉方程的Lyapunov-Schmidt约化分析

THE LYAPUNOV-SCHMIDT REDUCTION ANALYSES OF LAMINATED PLATES BIFURCATION EQUATIONS

在建立具有弹性约束的复合材料层板在面内载荷作用下的非线性稳定性控制方程组的基础上 ,利用分叉理论和泛函知识 ,对有限维的分叉方程进行了Lyapunov Schmidt约化 ,获得了三种典型的分叉图形式 。

Based on the establishment of the nonlinear governing equations of composite laminated plates with edges elastically supported against rotation, the finite dimension bifurcation equations are Lyapunov Schmidt reduced by utilizing the bifurcation theoretics and the functional knowledge. Three typical bifurcation figure forms are achieved, and it is proved that the bifurcation occurs consequentially as the nonuniform order term equals to zero.