![]() To date, the SFEM has only been investigated for bilinear and Wachspress approximations and limited to linear reproducing conditions. Although the SFEM is not yet well-understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. for meshless methods in the context of the finite element method (FEM), Liu et al. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code.īy using the strain smoothing technique proposed by Chen et al. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem show that the proposed method yields accurate results. DOI: 10.1002/nme.2589) to suppress the need for element sub-division. In this paper, we use a simple integration technique, proposed for polygonal domains (Int. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing, as the discontinuity evolves. ![]() Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. The findings demonstrate the accuracy and efficiency of the proposed method. The proposed method has been used to analyze numerical examples, and the SIFs results were compared with reference results. In addition, crack propagation is modeled by successive linear extensions, that are determined by the stress intensity factors (SIFs) under linear elastic fracture mechanics. ![]() The method is based on the XIGA method, in which discontinuous enrichment functions are added to the IGA approximation and this method does not require remeshing as the cracks grow. To drive the adaptive mesh refinement, we present a recovery-based error estimator for the proposed method. ![]() ![]() The PHT-splines overcome certain limitations of non-uniform rational B-splines (NURBS)-based formulations in particular, they make local refinements feasible. In this paper, an adaptive extended IGA (XIGA) approach based on polynomial splines over hierarchical T-meshes (PHT-splines) for modeling crack propagation is presented. SUMMARY Adaptive local refinement is one of the main issues for isogeometric analysis (IGA). ![]()
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