ON THE FINITE-ELEMENT ANALYSIS OF NONLINEAR VIBRATION FOR CYLINDRICAL-SHELLS WITH HIGH-ORDER SHEAR DEFORMATION-THEORY

The development of an existing 36 degrees-of-freedom (dof), curved, quadrilateral, thin shell element, for large displacement/rotation static analysis of shell structures, is extended for the study of non-linear vibration of a cylindrical shell. Parabolic transverse shear strains are assumed to vary through the shell thickness and vanish at the top and bottom surface. The equations of motion are based on a total Lagrangian frame of reference, and the applied dynamic loads are assumed conservative. A beta-m method, which is a generalization of Newmark's time marching integration scheme, and the Newton-Raphson iterative method, are both applied in order to numerically solve the set of non-linear equations of motion. An algorithm based on the above numerical procedures is developed. The isotropic or composite structures comprising laminates of orthotropic or multi-layered anisotropic materials are considered to be elastic. Comparisons with several existing solutions demonstrate the validity and accuracy of the present development.