双轴受压反对称角铺设复合材料层合板在固支边界下的后屈曲和模态跃迁

Post-buckling and mode jumping analysis of clamped supported composite laminates with antisymmetric angle-ply under bi-axial compressive load

为有效分析双轴受压反对称角铺设复合材料层压板在固支边界下的后屈曲性能,由渐近修正几何非线性理论推导其双耦合四阶偏微分方程(即应变协调方程和稳定性控制方程),通过双Fourier级数将耦合非线性控制偏微分方程转换为系列非线性常微分方程,从而获得相对简单的求解方法。使用广义Galerkin方法求解与角交铺设复合层合板相关的边界值问题,研究了模态跃迁前后不同复杂程度的后屈曲模式。对四层固支边界复合层合板的数值模拟结果表明:该解析法与有限元方法在主后屈曲区域的线性屈曲荷载计算结果吻合良好;有限元方法在解靠近二次分岔点时失去收敛性,而解析方法可深入后屈曲区域,准确捕捉模态跃迁现象;对于反对称角铺设层合板,可仅用纯对称模态来定性预测主后屈曲分支、二次分岔荷载及远程跃迁路径。

The governing partial differential equations （PDEs） were deduced from the asymptotically correct geometrically nonlinear theory to research the buckling and mode jumping behavior of clamped supported composite laminates with antisymmetric angle- ply under bi - axial compressive load. The two coupled fourth - order partial differential equations （PDEs）, namely, the compatibility equation and the dynamic governing equation were transformed into a system of nonlinear ordinary differential equations （ODEs）. Then a relatively simpler solution method was developed. The generalized Galerkin method was used to solve boundary value problems corresponding to antisymmetric angle-ply composite plates. The post-buckling patterns with different complexity before and after mode jumping were analyzed. An numerical example of 4- layers clamped composite laminates shows that the numerical results in the primary post-buckling region from the present method agree well with the finite element analysis （FEA）. The FEA may lose its convergence when solution comes close the secondary point, while the analytic method can explore deeply into the post-buckling realm and accuratty capture the mode jumping phenomenon. Only the pure symmetric modes may be used to qualitatively predict the primary post- buckling branch, the secondary bifurcation load and the remote jumped branch of the composite laminates with antisymmetric angle-ply.