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采用广义傅立叶级数法建立了具有弹性约束的复合材料矩形层板在面内载荷作用下的非线性稳定性控制方程组 ,并简化为矩阵形式。利用分叉理论和泛函知识 ,对有限维的该分叉方程进行了Lyapunov Schmidt约化 ,获得了三种典型的分叉图形式 ,同时指出当非齐次项等于零时必然发生分叉。数值计算结果指明了三种分叉图分别所对应的典型的力学模型 ,主要因素在于边界条件、铺层方式及初始缺陷三方面。
The generalized Fourier series method is used to establish the governing equations of nonlinear stability of rectangular plates with elastic confinement under in-plane loads. The equations are simplified to matrix form. By using bifurcation theory and functional knowledge, Lyapunov Schmidt reductions of this bifurcation equation of finite dimension are obtained, and three typical bifurcation diagrams are obtained. At the same time, it is pointed out that bifurcation inevitably occurs when the nonhomogeneous term is equal to zero. The numerical results indicate the typical mechanical models respectively corresponding to the three bifurcations. The main factors are the boundary conditions, the way of laying and the initial defects.