角铺设复合材料层合板的后屈曲和模态跃迁

为研究双轴受压反对称角铺设复合材料层压板的后屈曲和模态跳迁性能,由渐近修正几何非线性理论推导其双耦合四阶控制偏微分方程(即协调方程和动态控制方程)；通过采用广义Galerkin方法将层合板的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组；然后,采用解的延拓方法软件对层合板的后屈曲行为进行分析,确定面内直边边界下层合板出现屈曲模态跃迁的路径和临界载荷.通过对四层简支复合层合板算例计算表明:该方法数值结果与有限元分析(FEA)相比,在主后屈曲区域有很好的吻合性；而当解接近第2分岔点时,有限元分析失去收敛性,而所提分析方法仍具有深入探索二次分岔后屈曲区域和准确捕捉模态跃迁现象的能力.

Post-buckling and mode jumping analysis of angle-ply composite laminates

The governing partial differential equations (PDEs) are deduced from the asymptotically correct, geometrically nonlinear theory to research the bucking and mode jumping behavior of biaxially antisymmetric angle-ply composite laminates. The PDEs are transformed into a system of nonlinear ordinary differential equations (ODEs) by using the generalized Galerkin method. Then, the post-buckling behavior is analyzed by using the solution extension software. At last, the paths of buckling mode jumping and critical loads for the composite laminates under the in-plane boundary condition of straight edge are determined. An example of 4-layer composite laminates shows that the numerical results in the primary post-buckling region from the present method agree with the finite element analysis (FEA); while the FEA may lose its convergence when solution comes close to the secondary bifurcation point, the analytic method has the capability to explore deeply into the post-secondary bucking realm and capture the mode jumping phenomenon.