استفاده از دستگاه مختصات متعامد محلی در مدل کردن ترک دو بعدی به روش المان محدود توسعه یافته

The extended finite element method (X-FEM) is a numerical method for modeling discontinuties, such as cracks, within the standard finite element framework. In X-FEM, special functions are added to the finite element approximation. For crack modeling in linear elasticity, appropriate functions are used for modeling discontinuties along the crack length and simulating the singularity in the crack tip element. As a result, the degrees of freedom (D.O.F.) for the nodes arround the crack tip and the crack length are increased, the so-called node-enrichment scheme. This virtual crack modeling, which is mesh independent, avoids the usage of refined mesh and singular elements arround the crack tip, and does not require remeshing during crack growth simulation. In this paper the principles of the X-FEM are described. A new method, based on the local orthogonal coordinate system, is proposed for the node-enrichment scheme. The development of a special-purpose computer code for modeling 2D cracks using the X-FEM and the new method is presented. The code and the new method are verified through the analyses of different standard cracked geometries.