EXTENDED ISOGEOMETRIC FINITE ELEMENT FOR THE SIMULATION OF FRACTURE MECHANICS PROBLEMS

Abstract

The isogeometric analysis approach bridges the gap between the modelling methods and analysis methods. The gap arises because traditional Finite Element Analysis doesn't use any basis which are used to generate the Computer Aided Design (CAD) model instead it uses Lagrangian basis for the analysis due to which there exist a considerable difference between results obtained from solution and actual results. In order to reduce this accuracy gap between the actual and calculated results isogeometric approach is being used. Since Non-Uniform Rational B-Splines (NURBS) are very widely used tool in modelling field to generate exact and accurate profiles and shapes. Therefore, in isogeometric analysis NURBS are used as basis for solving the problems. This not only reduces the error due approximation of geometry but also creates interface between modelling and analysis tools. This report gives an introduction to B-Splines and NURBS, a detailed review of past developments in the field of isogeometric analysis and basic isogeometric theory and FEM formulation. In this dissertation, isogeometric analysis has been applied to solve solid mechanics and fracture mechanics problems. There are mainly two approaches which have been used to solve the problems i.e. Single patch approach and multiple patch approach. Single patch approach has been used for simple geometries and Multiple patch approach has been used for relatively complex geometries i.e. geometries having irregularities or discontinuities. In the case of Fracture mechanics problems the XFEM approach is used for the solving. The problems are first solved numerically with the help of MATLAB and the results obtained are compared with the results given by FEM software ABAQUS and a good agreement between the two results have been observed.