Geometrical Non-Linear Dynamic Analysis of Plates and Shells by a Fem Based on Positions

Abstract

In this work it is presented a Finite Element (FEM) formulation based on positions to analyze plates and shells exhibiting large deformations under dynamic loads. The objective is to apply a geometrically exact total Lagrangian description associated with Reissner kinematics capable of accurately solving non linear dynamics using a simple time integration procedure, i.e., the Newmark β. In order to make it possible co-rotational formulations must be avoided and the positional formulation, based on unconstrained vectors, is applied. This formulation does not apply the Euler-Rodrigues formula for finite rotations, resulting into a constant mass matrix. A simple proof of the momentum conserving property for rigid bodies is provided and high order curved elements are used to avoid locking. For flexible structures the conserving property is checked by selected examples.