复合材料层合板的二次屈曲和二次分枝点分析

为了研究复合材料层合板的二次分叉特性 ,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合板在面内载荷作用下的非线性稳定性控制方程组。控制方程组用广义傅立叶级数法进行求解 ,并得到载荷 -挠度曲线。基于分叉理论中的 Lerray-Schaulder定理 ,采用小挠动法 ,直接导出了复合材料层合板的二次失稳方程。研究结果表明 ,非对称层板也可能存在分叉 ,弹性转动支持系数和铺层等因素对二次分叉有很重要的影响。随着弹性系数的增大 ,二次失稳载荷值与初次失稳载荷值之比下降

Analysis of secondary buckling and secondary bifurcation point for composite laminated plates

In order to study the secondary bifurcation of composite laminated plates, the nonlinear governing equations of composite laminated plates with edges elastically supported against rotation are established by using energy variational principle and nonlinear geometric equations. The governing equations are solved by means of a generalized Fourier series method, and subsequently the corresponding load deflection curves are obtained. The secondary critical equations of composite laminated plates are deduced directly through small perturbation method, which is based on Lerray Schaulder principle of the bifurcation theoretics. The investigation results show that bifurcation may also exist in unsymmetrical laminated plates, and the elastic coefficients and stacking sequence have a great influence on the secondary bifurcation. The ratio of the secondary buckling load to the first buckling load drops with increasing the elastic coefficients.