Local Buckling, Stationary and Non-Stationary Vibrations of Thin Composite Laminated Shells having the Weakest Spots
The problems of buckling, stationary and non-stationary vibrations of thin composite laminated cylindrical shells having the “weakest” spots are studied. The shell can be non-circular and open in the circumferential direction. The shell edges are not necessary plane curves, with the conditions of a joint support or rigid clamp edges being considered as the boundary conditions. The shell is supposed to experience external pressure or axial loads which may be non-uniform in the circumferential direction. The load is stationary in the problems of buckling or free vibrations, and it may be dynamical one when the non-stationary wave processes are analyzed. The peculiarity of the problems under consideration lies in the possible localization of the egeinforms in a neighborhood of the weakest generator. Based on the generalized kinematics hypothesis of Timoshenko, the semi-membrane differential equations of the laminated shell theory are utilized here as the governing ones. The problems of the localized forms of buckling and free vibrations are studied by using the asymptotic Tovstik’s method. Alternatively the finite element approximation method is used to solve some of these problems numerically. Finally, a new asymptotic approach is presented to examine non-stationary localized bending vibrations of the laminated cylindrical shells under time-dependent, arbitrarily distributed over the shell surface or edges loading.