Shell dynamics with three-dimensional degenerate finite elements

Abstract

An explicitly through the thickness integrated two-dimensional version of the three-dimensional degenerated shell element is formulated here to study the dynamics of elastic shells. A nine-noded quadrilateral Lagrangian element is used with five degrees of freedom per node. A specialized mass diagonalization scheme, developed by Hinton, Rock and Zienkiewicz, is used which conserves the total mass of the element and also includes the effects of the rotary inertia terms. Hamilton's principle is used to derive the equations of motion. Mode superposition coupled with Duhamel's integral is first employed to obtain a solution of the equations of motion in time. Mode shapes and frequencies are computed by subspace iteration technique. Direct time integration using the implicit Newmark-β method is also carried out. Several examples are presented and the results obtained by mode superposition and direct time integration methods are compared.