Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various shear deformation theories

Equations of motion with required boundary conditions for doubly curved deep thick composite shells are shown using two formulations. The first is based upon the formulation that was presented initially by Rath and Das [1] and followed by Reddy [2]. In this formulation, plate stiffness parameters are used for thick shells, which reduced the equations to hose applicable for shallow shells. The second formulation is based upon that of Qatu [3,4]. In this formulation, the stiffness parameters are calculated using exact integration (and/or terms truncated to a specific order) of stress resultant equations. In addition, Qatu considered the radius of twist in his formulation. In both formulations, first order polynomials for in-plane displacements in the z-direction are utilized allowing for the inclusion of shear deformation and rotary inertia effects (first order shear deformation theory or FSDT). Exact static and free vibration solutions for isotropic and symmetric and anti-symmetric cross-ply cylindrical shells for different length-to-thickness and length-to-radius ratios are obtained using the above theories. Results of both theories are compared with those obtained using a three-dimensional (3D) analysis to test the accuracy of the shell theories presented here.