Positional Finite Elements for Geometrical Non-Linear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical non-linear dynamics of shells. The main objective is to develop a FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. An algebraic proof for the linear and angular momentum conservation property of the Newmark beta algorithm for rigid bodies is provided for total Lagrangian description. The curved, high order element, together with an implicit procedure to solve non-linear equations guarantees precision in calculations. The momentum conserving, the locking free behavior and the frame invariance of the adopted mapping are numerically confirmed in examples.