Análise de técnicas de refino H-adaptativo em MEF utilizando estimativas de erro a posteriori em problemas de elasticidade unidimensional

Abstract

Finding the exact solution for boundary value problems, in physical systems modeling for engineering purposes, can be complex or even imposible. Then, the Finite Element Method (FEM) is an available alternative to obtain aproximating solutions. Primarily, this work aims to study discretization error in FEM analysis using a posteriori error estimates based on stress recovery methods: the Simple Nodal Stress Averaging, the Zienkiewicz-Zhu (ZZ), and the Superconvergent Patch Recovery (SPR) techniques. For this, the one-dimensional problem of linear elasticity is considered. Other aspect of concern is to study the behavior of two adaptive h-refinement strategies, the classical Chp and the novel Isotropic Error Density Recovery (IEDR) technique, considering these three errors estimators. By verifying the error estimators performance it is possible to note how each recovery technique behaves in case of regular nested h-refinement, for some degrees of shape functions, being this step carried out aiming for code verification. These first results show that the estimates are directly influenced by the element degree and the number of elements in the mesh. Further, for the adaptive h-refinement processes, it was found an especific situation in which the novel IEDR methodology intensify the mesh refinement, leading to more degrees of freedom. For other particular case, the Chp provides meshes with more elements if compared to the IEDR methodology. Such situations depend on the features of the recovered stress field and the original stress approximation in a given element. Moreover, imposing some additional restrictions on the new element size seems to influence positively the both approaches, reducing some prohibitive mesh refinements.