Análise geometricamente não linear por métodos baseados na partição daunidade

Abstract

This masters thesis presents a computational implementation project for the solution of geometrically nonlinear problems by the Generalized Finite Element Method (GFEM), a method that can be considered as an instance of the Partition of Unity Method (PUM). The partition of unity is provided by using the Finite Element Method (FEM) approximation functions, which are enriched by others functions specially chosen according to the analyzed problem. In the analysis with geometric nonlinearity, you can have a significant distortion of the element mesh due to the effects of large displacements and deformations, which can penalize the quality of the FEM solution. However, it is noted that the GFEM is less prone to be influenced by this mesh distortion, which make it more advantageous for this type of analysis. Thus, an existing computational environment developed in the Department of Structural Engineering of Federal University of Minas Gerais (UFMG), that allows linear and nonlinear analysis, has been expanded in order to execute the analysis with geometric nonlinearity by GFEM. As a way to validate the implementation of this expansion, the results of numerical simulations, for this type of analysis, are compared with results found in the literature.