Nonlinear Analysis of Axially Moving Plates Using Fem

In the present study, a nonlinear finite element formulation is developed for analysis of axially moving two-dimensional materials, based on the classical thin plate theory. Using Green's strain definition, the membrane stresses variation due to transverse displacements is considered. Hamilton's principle is employed to obtain the secant stiffness matrix, the in-plane and out-of-plane gyroscopic matrices and the dynamic stability matrix due to centripetal acceleration for a traveling thin plate. In order to extract the numerical results, a p-version finite element is adopted by selecting only an quadrilateral super element with Lagrangian interpolation functions. With a few test cases, the reliability of the formulation and the solution procedure is shown.