层合板在固支边界条件下的不稳定后屈曲分析

Analysis on Unstable Postbuckling of Laminated Plates under Clamped Boundary Condition

为了深入地研究复合材料层板所独具的后屈曲特性,利用能量变分原理和非线性几何方程建立了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,并运用广义傅立叶级数法对其进行求解。重点分析了非对称层板在固支边界条件下的稳定性问题,发现层板在此条件下有可能存在非对称的失稳临界点和不稳定的后屈曲路径,进而构造了简化的物理模型进行解释。指出后屈曲的非对称性是由于结构关于Z轴不对称,而不稳定性是由于固支边界条件阻碍了前屈曲的发生。

In order to study the postbuckling of composite laminated plates deeply, the nonlinear governing equations of composite laminated plates with elastic restraint are established by use of the energy variational principle and nonlinear geometric equations, and they are solved by means of the generalized Fourier series method. The stability problems of unsymmetrical laminated plates under clamped boundary condition are primarily analyzed. In this condition, it is found that the unsymmetric critical point and unstable postbuckling path may exist. In the end of this paper, the simplified physical model is constructed to explain this phenomena. It is pointed out that the unsymmetry of the postbuckling is caused by the unsymmetry of the structure about the axis Z, and the causation of the instability is that the prebuckling is prevented by the clamped boundary condition.