Métodos de elementos finitos mistos e malhas adaptativas na análise de cascas axissimétricas

Abstract

Thin axissimetric shell studied through the use of Reissner-Mindlin theory presents some difficulties in constructing stable finite elements aproximations due to its dependence on the thickness of the shell. Classical single field as well as two fields finite element formulations are discussed. A consistent mixed Petrov-Galerkin formulation is considered in order to achieve both stability and accuracy. It consists in adding to the classical Galerkin formulation a residual form of the equilibrium equation in the interior of each element. Numerical experiments, using elements with equal order interpolation, are conducted for a variety of structures and loading, which confirms the improvement in stability obtained by this new formulation. Adaptive mesh refinements, in theirs r, h e p versions, are used in order to improve the rate of convergence in presence of boundary layers, caused by the operator singularity.