Nonlinear static/dynamic instability and vibration characteristics of composite shells

Abstract

The finite element method based on the total Lagrangian description of the motion and the Heillinger-Reissner principle with independent strain is applied to investigate the nonlinear static and dynamic response including vibration characteristics for laminated composite shells. The nonlinear static problems are solved using arc-length method to trace the load-equilibrium path of snapping behaviors for thin shells. The nonlinear dynamic response is obtained by employing the implicit time integration method. Even with a small number of elements, the present finite element gives not only reliable solutions, but also good convergence independently of configurations and boundary conditions. In this study, three cases of numerical studies are carried out: (1) the vibration characteristics of twisted cantilevered conical shell, (2) the thermal post-buckling response of reinforced patched shell and (3) the dynamic instability (or buckling) of spherical shell. For a twisted cantilevered conical shell, the twisting angle affects greatly the twisting mode rather than the first bending mode. For a patched laminated cylindrical shell under thermal load, the patch on the panel can alleviate the snapping phenomena and give an improved performance of load-carrying capability, when the patch has the same order of the panel thickness. In addition, the lamination and location of the patch affect significantly the nonlinear thermal response. The dynamic (or transient) analysis with damping included can represent the true dynamic nature of the response of a structure for all equilibrium point and follows the evolution of the response as a function of time as seen in a large deformation (or collapse) of the spherical shell. For thin shells subjected to suddenly dynamic load, the critical load is lower than the expected static one. That is, the snapping can occur at the load below the static critical load. Also, the damping can give two possible load-equilibrium solutions with pr...