Crack propagation modeling in plane structures using two-scale generalized/extended finite element method

Abstract

Finite Element Method (FEM) has been widely used for the numerical modeling of structural/mechanical problems. Use of computer-based FEM programs was greatly facilitated with the development of pre- and post-processors rich interactive graphics capabilities, allowing users with basic knowledge of geometry to easily work with them. However, modeling of discontinuous elds with a standard nite element approximation presents challenges like restrictions on the nite element mesh to align with the discontinuity and the need for remeshing as the discontinuity evolves. The generalized or extended FEM (G/XFEM) was proposed as a numerical method to solve some of these challenges. TheG/XFEM method enriches the standard nite element shape functions locally with enrichment functions which are based on the physics associated with the problem. The goal of this thesis is to fracture modeling in thin-walled structure, specically Plate structures, by extending the available capabilities of the G/XFEM method implementedin INSANE (INteractive Structural ANalysis Environment) in-house code, a computational environment developed by the Department of Structural Engineering (DEEs) at the Federal University of Minas Gerais (UFMG), which has been implemented using Object Oriented Programming (OOP). A stable version of G/XFEM is implemented to have a well-conditioning systems of equations. Then, the crack propagation strategy is applied to plane stress/strain and Reissner-Mindlin problems using classical and two-scale G/XFEM. These whole implementationsand design are explained in detail and their robustnesses and accuracies are examined by solving various structural problems