A comparison study of singularities in cracks and re-entrant corners : A study of how the singularities behave under stress using the Finite Element Method and the Cut Finite Element Method

This thesis aims to compare two distinct methods, the Finite Element Method (FEM) andthe Cut Finite Element Method (CutFEM), in investigating the behavior of singularitiesat the tip of cracks and re-entrant corners. The Finite Element Method, widely employed in structural mechanics, serves as the mathematical framework underlying computer-aided design (CAD) engineering software. The thesis will be divided into two main sections. The first section will focus on the theoretical foundations of both the FEM and CutFEM approaches. Subsequently, the second section will focus on the implementation of numerical examples that exemplify the theoretical concepts described earlier. Finally, the thesis will conclude with a comprehensive comparative analysis of the FEM and CutFEM methods.