Abstract

This presentation is about a positional FEM formulation to deal with shells undergoing large displacements due to dynamic actions. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions. Velocity, acceleration and strain are achieved directly from positions, not displacements, characterizing the novelty of the proposed technique. A non-dimensional space is created and the change of configuration function is written following two independent mappings, from which the strain energy function is written. The classical Newmark equations are used to integrate time resulting in a stable and energy conserving procedure. Dumping and non-conservative forces are introduced into the mechanical system by a rheonomic energy functional. The final formulation has the advantage of being simple and easy to teach, when compared to classical counterparts. The propose shell element is locking free due to the presence of the seventh parameter. The curved, high order element, together with the implicit procedure guarantees precision in calculations. Selected examples are provided to prove the formulation regarding accuracy and applicability, including static and dynamic situations.