The analyzing of the discontinuity problem by enriched interpolation covers

In this paper, we focus on an enriched finite element procedure for discontinuity problems based on the use of interpolation cover functions. The numerical cover method is based on method of partition of unity that increases precision by using different levels of enrichment functions. We consider the 3-node triangular displacement-based elements for discontinuity analyses. The standard finite element shape functions are used with interpolation cover functions over patches of elements to increase the convergence of the finite element scheme. This method has been used very successfully to model cracks because the finite element mesh can be created independent from the crack geometry, and in particular the domain does not have to be remeshed as the crack propagation. This method enriched the usual finite element spaces with additional degrees of freedom, which incorporate the near tip asymptotic solutions and allow the displacements to be discontinuous across the crack face. It consists on the enrichment by a step function along the crack line to take into consideration the discontinuity field and on some functions to represent the asymptotic displacement in a vicinity of the crack tip The computational tests are performed on 3 example and the results are validated by some numerical computations and comparisons with the XFEM and exact solution. Reasonably coarse meshes might be used, and if the results obtained with the traditional finite elements are not acceptable, covers are applied to obtain improved solution results; hence, the approach has considerable potential for discontinuity problems independent of the crack geometry.