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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。
In order to effectively analyze the post-buckling performance of anti-symmetrical biaxial compression composite laminate under fixed-support boundary, the double-coupled fourth-order partial differential equations (ie, strain coordination equation and stability Control equations), the coupled nonlinear governing partial differential equations are transformed into a series of nonlinear ordinary differential equations by using double Fourier series, and a relatively simple solution method is obtained. The generalized Galerkin method is used to solve the boundary value problems associated with corner interlacing composite laminates. The post-modal post-buckling modes with different complexity before and after modal transition are studied. The numerical simulation of the four-layer clamped boundary composite laminates shows that the analytical results are in good agreement with the finite element method in the calculation of the linear buckling loads in the post-buckling region. The finite element method loses convergence when the solution approaches the second bifurcation point However, the analytic method can penetrate deep into the area of post-buckling to capture the phenomenon of modal transition accurately. For the anti-symmetry angle laying laminate, the purely symmetrical modalities can be used to qualitatively predict the post-posterior buckling branches, secondary bifurcation loads and long-range transition paths .