PSI - Issue 23

Michal Jedlička et al. / Procedia Structural Integrity 23 (2019) 445– 450 M ichal Jedlička, Václav Rek, Ji ří Vala / Structural Integrity Procedia 00 (2019) 000 – 000

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It is necessary to deal with cases where the crack surface partially interferes with some elements because the least affected end element should not be considered in the same way as in the fully cracked body. Two criteria have been introduced for these cases, depending on the ratio  , as evident from Fig. 4: the approach a) works with the real crack area, which is supported by the library Genex from NE-XX, whereas the approach b) switches to  = 0 or  = 1 artificially, depending on some its prescribed value. Consequently, Fig. 5 demonstrates the basic classification of the extended finite elements created in this way. Here (namely in our illustrative example) we shall consider just one type of an enriched function, representing a fully cracked body, i.e. passing through the entire relevant finite element everywhere.

Fig. 5. Numerical treatment of cracks in the XFEM analysis.

Fig. 5. Basic classification of extended finite elements, crucial for the number of Gaussian integration nodes.

Fig. 6. Computational results of an illustrative example of behavior of a structure under tension (using the RFEM post-processing).

The practical implementation of XFEM into an existing FEM solver inside the NE-XX environment works with the call of the special alternative XFEM solver. The relevant library is responsible for assembling the stiffness ma trix, for evaluation of internal forces, for generation of integration nodes for finite elements, for evaluation of energy functionals and for output of results in the desired form. This software is still under development: now all function ality is guaranteed for the selected 3-dimensional finite elements: for the hexahedra (8 nodes) and the tetrahedral (4 nodes). Enriched elements, due to Fig. 5, containing discontinuous base functions, need 64 Gaussian nodes for a hexahedron and 15 nodes for a tetrahedron. In the case of a standard of blending element, 8 Gaussian nodes for a hexahedron and 1 node for a tetrahedron are sufficient.