The influence of geometric imperfections on post-buckling behavior and free vibrations of a fiber-reinforced composite laminated plate under thermal loading

The post-buckling equilibrium paths (including the whole unstable region) and natural characteristics of fiber-reinforced composite laminated plates with different imperfections under thermal load are studied. Based on the Incremental Von Karman nonlinear relationship, Third-order shear deformation plate theory and Hamilton's principle, the theoretical governing equations are formulated. Firstly, the Cylindrical Arc-length method is developed with a direction judgement to capture the unstable post-buckling path including a number of snap-back and limit points. Then the natural characteristics are derived at the stable buckling position. The results show that in post-buckling state, the number of limit points along the unstable paths is directly related to the number of negative eigenvalues at the initial position. As long as the perturbation load is small enough, the buckling deformation of the flat plate keeps the same under different perturbation load. For the plate with imperfection, if the imperfection is really small, the buckling deformation is the same as that of the flat plate. If the imperfection is relatively larger, the buckling deformation is of high correlation with the imperfection shape. The effects of thermal stress and buckling deformation on the natural frequencies and mode shapes are further analyzed. Some new interesting phenomena are presented.