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

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.