Comparação das formulações lagrangena com a corrotacional para a obtenção dos deslocamentos nodais via MEF

Abstract

The present work deals with the Finite Element Method (FEM) regarding non-linear analysis for large displacement cases. The interest of modelling FEM non-linearities is first of all shown and exemplified. The incremental-iteractive solution procedure for non-linearities is then introduced. The two following kinematic descriptions are studied: the Total Lagrangian formulation, which is already well consolidated in FEM and becomes an more detailed approach in this work. The corrotational formulation, which is recent and much promising, however not so widespreaded than the Total Lagrangian formulation. The application of the Total Lagrangian formulation is done at the end, through the implementation of the FEM software ABAQUS to three already solved problem examples from the literature. The results of these three examples are deliberately comparable with those obtained from the same problems, but solved through the Corrotational method. In this work, all assessments make use of triangular shell elements. Finally, stress data from the deformed state of the examples are provided for the future development of the Corrotational Formulation in the tensional area. Also correlations between the non-linear FEM theory and the interface how the software ABAQUS allows to deal with the non-linear solution process is shown at the end of this work.